# Grade 5 Number & Operations Fractions

#### Use equivalent fractions as a strategy to add and subtract fractions.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 1/2.

#### Apply and extend previous understandings of multiplication and division.

Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Interpret multiplication as scaling (resizing), by:

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3.

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 (1/5) = 4.

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

# Simplifying Fractions

To simplify a fraction, divide the top and bottom by the highest number that

can divide into both numbers exactly.

## Simplifying Fractions

Simplifying (or reducing) fractions means to make the fraction as simple as possible.

## How do I Simplify a Fraction ?

There are two ways to simplify a fraction:

## Method 1

Try to evenly divide (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 . etc, until we can’t go any further.

### Example: Simplify the fraction 24108 :

That is as far as we can go. The fraction simplifies to 2 9

### Example: Simplify the fraction 1035 :

Dividing by 2 doesn’t work because 35 can’t be evenly divided by 2 (35/2 = 17 )

No need to check 4 (we checked 2 already, and 4 is just 2 2).

But 5 does work!

That is as far as we can go. The fraction simplifies to 2 7

Notice that after checking 2 we didn’t need to check 4 (4 is 2 2)?

We also don’t need to check 6 when we have checked 2 and 3 (6 is 2×3).

In fact, when checking from smallest to largest we use prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, .

## Method 2

Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).

### Example: Simplify the fraction 812 :

The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4.

# Grade 5 Number & Operations Fractions

#### Use equivalent fractions as a strategy to add and subtract fractions.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 1/2.

#### Apply and extend previous understandings of multiplication and division.

Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Interpret multiplication as scaling (resizing), by:

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3.

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 (1/5) = 4.

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

# Matching Fraction Game – Equivalent Fractions

Drag and Drop the answers on the right to match them with their equivalent fractions.

In other words: Click and hold the button down while moving the answer. Release the button when the answer is over the equivalent fraction.

### Related Resources

The resources listed below are aligned to the same standard, (4NF01) re: Common Core Standards For Mathematics as the Fractions game shown above.

Explain why a fraction a/b is equivalent to a fraction (n .

#### Activities

##### Domino Cards
• Equivalent Fraction Cards #1 (matching equivalent fractions. e.g. 4/10 = 2/5)
• Equivalent Fraction Cards #2 (matching equivalent fractions. e.g. 6/15 = 2/5 – slightly harder)

#### Worksheets

• Comparing Fractions (1 of 4) – two fractions – includes with fraction bar
• Comparing Fractions (2 of 4) – using common denominators
• Equivalent Fractions (1 of 3) e.g. 1/3 = 3/9
• Equivalent Fractions (2 of 3) e.g. 9/3 = 1/3
• Equivalent Fractions (3 of 3)
• Reducing Fractions – Simplest Form e.g. 6/12 = 1/2

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Extend understanding of fraction equivalence and ordering

• Comparing Fractions (From Page)
• Comparing Fractions (3 of 4) – ordering sets of three and four fractions (From Worksheets)
• Common Denominators (From Lessons)
• Improper Fractions and Mixed Numbers (From Lessons)
• Simplifying Fractions (From Lessons)

# Matching Fraction Game – Equivalent Fractions

Drag and Drop the answers on the right to match them with their equivalent fractions.

In other words: Click and hold the button down while moving the answer. Release the button when the answer is over the equivalent fraction.

### Related Resources

The resources listed below are aligned to the same standard, (4NF01) re: Common Core Standards For Mathematics as the Fractions game shown above.

Explain why a fraction a/b is equivalent to a fraction (n .

#### Activities

##### Domino Cards
• Equivalent Fraction Cards #1 (matching equivalent fractions. e.g. 4/10 = 2/5)
• Equivalent Fraction Cards #2 (matching equivalent fractions. e.g. 6/15 = 2/5 – slightly harder)

#### Worksheets

• Comparing Fractions (1 of 4) – two fractions – includes with fraction bar
• Comparing Fractions (2 of 4) – using common denominators
• Equivalent Fractions (1 of 3) e.g. 1/3 = 3/9
• Equivalent Fractions (2 of 3) e.g. 9/3 = 1/3
• Equivalent Fractions (3 of 3)
• Reducing Fractions – Simplest Form e.g. 6/12 = 1/2

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Extend understanding of fraction equivalence and ordering

• Comparing Fractions (From Page)
• Comparing Fractions (3 of 4) – ordering sets of three and four fractions (From Worksheets)
• Common Denominators (From Lessons)
• Improper Fractions and Mixed Numbers (From Lessons)
• Simplifying Fractions (From Lessons)

# Equivalent Fractions

## Equivalent fractions represent the same part of a whole

The best way to think about equivalent fractions is that they are fractions that have the same overall value.

For example, if we cut a pie exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.

And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the same amount of pie that 1/2 did.

So we can say that 1/2 is equivalent (or equal) to 2/4.

## Don’t let equivalent fractions confuse you!

Take a look at the four circles above.Can you see that the one 1/2 , the two 1/4 and the four 1/8 take up the same amount of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also equal to 4/8. And yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you already know, we are nuts about rules. So, let s look at the Rule to check to see if two fractions are equivalent or equal. The rule for equivalent fractions can be a little tough to explain, but hang in there, we will clear things up in just a bit.

## Here s the Rule

What this Rule says is that two fractions are equivalent (equal) only if the product of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.

A product simply means you multiply.

## Test the Rule

Now let s plug the numbers into the Rule for equivalent fractions to be sure you have it down cold . 3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3) of the first fraction and the denominator (12) of the other fraction is equal to the product of the denominator (4) of the first fraction and the numerator (9) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3 12=36 and 4 9=36. A simple way to look at how to check for equivalent fractions is to do what is called cross-multiply , which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

### The graphic below shows you how to cross multiply

Okay, let s do one with numbers where the fractions are not equivalent

# Equivalent Fractions

## Equivalent fractions represent the same part of a whole

The best way to think about equivalent fractions is that they are fractions that have the same overall value.

For example, if we cut a pie exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.

And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the same amount of pie that 1/2 did.

So we can say that 1/2 is equivalent (or equal) to 2/4.

## Don’t let equivalent fractions confuse you!

Take a look at the four circles above.Can you see that the one 1/2 , the two 1/4 and the four 1/8 take up the same amount of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also equal to 4/8. And yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you already know, we are nuts about rules. So, let s look at the Rule to check to see if two fractions are equivalent or equal. The rule for equivalent fractions can be a little tough to explain, but hang in there, we will clear things up in just a bit.

## Here s the Rule

What this Rule says is that two fractions are equivalent (equal) only if the product of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.

A product simply means you multiply.

## Test the Rule

Now let s plug the numbers into the Rule for equivalent fractions to be sure you have it down cold . 3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3) of the first fraction and the denominator (12) of the other fraction is equal to the product of the denominator (4) of the first fraction and the numerator (9) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3 12=36 and 4 9=36. A simple way to look at how to check for equivalent fractions is to do what is called cross-multiply , which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

### The graphic below shows you how to cross multiply

Okay, let s do one with numbers where the fractions are not equivalent

# Equivalent Fraction Pairs

The traditional pairs or Pelmanism game adapted to test knowledge of equivalent fractions.

Click on the cards to find matching pairs.

Score: Number of Clicks:

## Instructions

This is a game for one or many players. Click on a card to see what it contains. Click on a second card and if the two cards make a pair you win them.

In the two (or more) player version a free turn is awarded to the player who finds a pair. The winner is the player who finds the most pairs.

The option to claim a trophy is available when all of the pairs have been found. The objective is to have the fewest number of вЂclicksвЂ™ recorded on your trophy.

## Congratulations!

All of the pairs have been found. . Can you do it using fewer clicks?

## Here are some other Pairs games for you to enjoy

### Venn Diagram Pairs

Wednesday, November 4, 2015

Friday, November 3, 2017

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# Adding Fractions with the Same Denominator

Adding fractions with the same denominators is pretty straightforward when you follow the rules. This lesson covers adding fractions with same denominator. We will include all of the information you will need to make working with common denominator problems a breeze!

The equation above shows the Rule for addition. So, if your are dealing with the same (common) denominator (b), the answer is the sum of the numerators (a and c) over their common denominator. Remember that a fraction refers to the number of parts in a whole , and the WHOLE that we are talking about is always the number in the denominator (on the bottom). So, all we have to do is add up the parts and keep our same point of reference.

## Instructions for adding fractions with the same denominator

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

1. Build each fraction (if needed) so that both denominators are equal.
2. Add the numerators of the fractions.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

That s all there is to it!

Here s an example of adding fractions with the same denominator

## Want to practice adding fractions with the same denominator?

Now that you have this part of adding fractions down, let s dig a little deeper

You do want to be a whiz at fractions? Right?

It would be great if the rule as stated above was all you needed to know about adding fractions. But there are still a few more things we need to talk about to complete this lesson. So, let s get right to it.

Click here to learn how to re-write your answer as a simplified or reduced fraction.

Sometimes when you add fractions of any type, you will need to simplify your answer. What that really means is that you must show your results in the best fractional form possible. As a result, here are a few more things to think about

First, your answer may be a higher equivalent fraction, which is better represented in its reduced form. Many teachers will insist that you reduce a fraction whenever possible.

Also, adding two fractions could result in what s called an improper fraction. This is where the numerator is larger than the denominator. To write these answers in their simplest form you will have to convert them to a mixed number. This will show a representation of the Whole Parts and the Fractional Parts.

So let s continue with some detailed information about adding fractions in these special cases.

### Reducing Fractions To Their Lowest Equivalent

Here s the situation. You have added the fractions okay, but your answer may not be showing the lowest equivalent fraction. So how do you make sure when you are adding fractions that your answer is shown in its lowest equivalent?

Let s use an easy example of adding fractions so you will get the idea

Notice that the original answer to adding the fractions our sample problem is 2/4. To determine if our answer is in its simplest form, we must factor the numerator and the denominator into its prime numbers.

The factors of a number are numbers that when multiplied together will equal that number. The easiest way to be sure that you have accounted for ALL of the factors of a number contained in a fraction is to break them down into prime numbers.

What we are looking for are the prime numbers that are common factors in both the numerator and the denominator of a fraction. If we find these common factors, we can then cancel them out. The results will be the lowest fractional equivalent fraction.

Since 2 is a common factor in both the numerator and denominator of our example, it indicates that our answer is not a fraction in its simplest form. Therefore, we will cancel out (/) one of the 2 s in both the numerator and denominator by dividing by 2 . The results is a reduced fraction in its simplest form.

Always keep in mind

Whatever you do to the numerator of a fraction you must also do to the fraction s denominator. So if you have to divide the numerator by a number, you must also divide the denominator by the same number. That way you will not change the overall value of the fraction.

Let s add a little tougher fraction to be sure you ve got it

In this problem, a 2 and a 3 can be found as factors in both the numerator and the denominator of a fraction. Notice how we only cancel-out one-for-one! First we divide the numerator and denominator by 2 , then divide both the numerator and denominator by 3. So what is left in the numerator is 1 x 1 x 3 = 3 and the denominator is 1 x 2 x 2 x 1 = 4. That leaves use with a reduced fraction equal to 3/4.

Simplify Improper Fractions

You may remember that an improper fractions is where the numerator has a greater value than that of the denominator. So each time you add two fractions and your answer ends up as an improper fraction, you must simplify your answer. The results will be in the form of a mixed number.

To convert an improper fraction into a mixed number, just divide the numerator by the denominator. The results will be a whole number part and a fractional part.

As you can see, this is a pretty straightforward operation. But keep in mind that if there is no remainder, the answer is the WHOLE NUMBER only.

Now you have an uncomplicated way to add fractions with the same denominators.

# Equivalent Fractions

## Equivalent fractions represent the same part of a whole

The best way to think about equivalent fractions is that they are fractions that have the same overall value.

For example, if we cut a pie exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.

And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the same amount of pie that 1/2 did.

So we can say that 1/2 is equivalent (or equal) to 2/4.

## Don’t let equivalent fractions confuse you!

Take a look at the four circles above.Can you see that the one 1/2 , the two 1/4 and the four 1/8 take up the same amount of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also equal to 4/8. And yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you already know, we are nuts about rules. So, let s look at the Rule to check to see if two fractions are equivalent or equal. The rule for equivalent fractions can be a little tough to explain, but hang in there, we will clear things up in just a bit.

## Here s the Rule

What this Rule says is that two fractions are equivalent (equal) only if the product of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.

A product simply means you multiply.

## Test the Rule

Now let s plug the numbers into the Rule for equivalent fractions to be sure you have it down cold . 3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3) of the first fraction and the denominator (12) of the other fraction is equal to the product of the denominator (4) of the first fraction and the numerator (9) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3 12=36 and 4 9=36. A simple way to look at how to check for equivalent fractions is to do what is called cross-multiply , which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

### The graphic below shows you how to cross multiply

Okay, let s do one with numbers where the fractions are not equivalent

# Equivalent Fractions

## Equivalent fractions represent the same part of a whole

The best way to think about equivalent fractions is that they are fractions that have the same overall value.

For example, if we cut a pie exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.

And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the same amount of pie that 1/2 did.

So we can say that 1/2 is equivalent (or equal) to 2/4.

## Don’t let equivalent fractions confuse you!

Take a look at the four circles above.Can you see that the one 1/2 , the two 1/4 and the four 1/8 take up the same amount of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also equal to 4/8. And yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you already know, we are nuts about rules. So, let s look at the Rule to check to see if two fractions are equivalent or equal. The rule for equivalent fractions can be a little tough to explain, but hang in there, we will clear things up in just a bit.

## Here s the Rule

What this Rule says is that two fractions are equivalent (equal) only if the product of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c) of the other fraction.

A product simply means you multiply.

## Test the Rule

Now let s plug the numbers into the Rule for equivalent fractions to be sure you have it down cold . 3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3) of the first fraction and the denominator (12) of the other fraction is equal to the product of the denominator (4) of the first fraction and the numerator (9) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3 12=36 and 4 9=36. A simple way to look at how to check for equivalent fractions is to do what is called cross-multiply , which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

### The graphic below shows you how to cross multiply

Okay, let s do one with numbers where the fractions are not equivalent

# Grade 5 Number & Operations Fractions

#### Use equivalent fractions as a strategy to add and subtract fractions.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 1/2.

#### Apply and extend previous understandings of multiplication and division.

Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Interpret multiplication as scaling (resizing), by:

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3.

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 (1/5) = 4.

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

# Matching Fraction Game – Equivalent Fractions

Drag and Drop the answers on the right to match them with their equivalent fractions.

In other words: Click and hold the button down while moving the answer. Release the button when the answer is over the equivalent fraction.

### Related Resources

The resources listed below are aligned to the same standard, (4NF01) re: Common Core Standards For Mathematics as the Fractions game shown above.

Explain why a fraction a/b is equivalent to a fraction (n .

#### Activities

##### Domino Cards
• Equivalent Fraction Cards #1 (matching equivalent fractions. e.g. 4/10 = 2/5)
• Equivalent Fraction Cards #2 (matching equivalent fractions. e.g. 6/15 = 2/5 – slightly harder)

#### Worksheets

• Comparing Fractions (1 of 4) – two fractions – includes with fraction bar
• Comparing Fractions (2 of 4) – using common denominators
• Equivalent Fractions (1 of 3) e.g. 1/3 = 3/9
• Equivalent Fractions (2 of 3) e.g. 9/3 = 1/3
• Equivalent Fractions (3 of 3)
• Reducing Fractions – Simplest Form e.g. 6/12 = 1/2

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Extend understanding of fraction equivalence and ordering

• Comparing Fractions (From Page)
• Comparing Fractions (3 of 4) – ordering sets of three and four fractions (From Worksheets)
• Common Denominators (From Lessons)
• Improper Fractions and Mixed Numbers (From Lessons)
• Simplifying Fractions (From Lessons)

# Adding Fractions with the Same Denominator

Adding fractions with the same denominators is pretty straightforward when you follow the rules. This lesson covers adding fractions with same denominator. We will include all of the information you will need to make working with common denominator problems a breeze!

The equation above shows the Rule for addition. So, if your are dealing with the same (common) denominator (b), the answer is the sum of the numerators (a and c) over their common denominator. Remember that a fraction refers to the number of parts in a whole , and the WHOLE that we are talking about is always the number in the denominator (on the bottom). So, all we have to do is add up the parts and keep our same point of reference.

## Instructions for adding fractions with the same denominator

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

1. Build each fraction (if needed) so that both denominators are equal.
2. Add the numerators of the fractions.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

That s all there is to it!

Here s an example of adding fractions with the same denominator

## Want to practice adding fractions with the same denominator?

Now that you have this part of adding fractions down, let s dig a little deeper

You do want to be a whiz at fractions? Right?

It would be great if the rule as stated above was all you needed to know about adding fractions. But there are still a few more things we need to talk about to complete this lesson. So, let s get right to it.

Click here to learn how to re-write your answer as a simplified or reduced fraction.

Sometimes when you add fractions of any type, you will need to simplify your answer. What that really means is that you must show your results in the best fractional form possible. As a result, here are a few more things to think about

First, your answer may be a higher equivalent fraction, which is better represented in its reduced form. Many teachers will insist that you reduce a fraction whenever possible.

Also, adding two fractions could result in what s called an improper fraction. This is where the numerator is larger than the denominator. To write these answers in their simplest form you will have to convert them to a mixed number. This will show a representation of the Whole Parts and the Fractional Parts.

So let s continue with some detailed information about adding fractions in these special cases.

### Reducing Fractions To Their Lowest Equivalent

Here s the situation. You have added the fractions okay, but your answer may not be showing the lowest equivalent fraction. So how do you make sure when you are adding fractions that your answer is shown in its lowest equivalent?

Let s use an easy example of adding fractions so you will get the idea

Notice that the original answer to adding the fractions our sample problem is 2/4. To determine if our answer is in its simplest form, we must factor the numerator and the denominator into its prime numbers.

The factors of a number are numbers that when multiplied together will equal that number. The easiest way to be sure that you have accounted for ALL of the factors of a number contained in a fraction is to break them down into prime numbers.

What we are looking for are the prime numbers that are common factors in both the numerator and the denominator of a fraction. If we find these common factors, we can then cancel them out. The results will be the lowest fractional equivalent fraction.

Since 2 is a common factor in both the numerator and denominator of our example, it indicates that our answer is not a fraction in its simplest form. Therefore, we will cancel out (/) one of the 2 s in both the numerator and denominator by dividing by 2 . The results is a reduced fraction in its simplest form.

Always keep in mind

Whatever you do to the numerator of a fraction you must also do to the fraction s denominator. So if you have to divide the numerator by a number, you must also divide the denominator by the same number. That way you will not change the overall value of the fraction.

Let s add a little tougher fraction to be sure you ve got it

In this problem, a 2 and a 3 can be found as factors in both the numerator and the denominator of a fraction. Notice how we only cancel-out one-for-one! First we divide the numerator and denominator by 2 , then divide both the numerator and denominator by 3. So what is left in the numerator is 1 x 1 x 3 = 3 and the denominator is 1 x 2 x 2 x 1 = 4. That leaves use with a reduced fraction equal to 3/4.

Simplify Improper Fractions

You may remember that an improper fractions is where the numerator has a greater value than that of the denominator. So each time you add two fractions and your answer ends up as an improper fraction, you must simplify your answer. The results will be in the form of a mixed number.

To convert an improper fraction into a mixed number, just divide the numerator by the denominator. The results will be a whole number part and a fractional part.

As you can see, this is a pretty straightforward operation. But keep in mind that if there is no remainder, the answer is the WHOLE NUMBER only.

Now you have an uncomplicated way to add fractions with the same denominators.

# Matching Fraction Game – Equivalent Fractions

Drag and Drop the answers on the right to match them with their equivalent fractions.

In other words: Click and hold the button down while moving the answer. Release the button when the answer is over the equivalent fraction.

### Related Resources

The resources listed below are aligned to the same standard, (4NF01) re: Common Core Standards For Mathematics as the Fractions game shown above.

Explain why a fraction a/b is equivalent to a fraction (n .

#### Activities

##### Domino Cards
• Equivalent Fraction Cards #1 (matching equivalent fractions. e.g. 4/10 = 2/5)
• Equivalent Fraction Cards #2 (matching equivalent fractions. e.g. 6/15 = 2/5 – slightly harder)

#### Worksheets

• Comparing Fractions (1 of 4) – two fractions – includes with fraction bar
• Comparing Fractions (2 of 4) – using common denominators
• Equivalent Fractions (1 of 3) e.g. 1/3 = 3/9
• Equivalent Fractions (2 of 3) e.g. 9/3 = 1/3
• Equivalent Fractions (3 of 3)
• Reducing Fractions – Simplest Form e.g. 6/12 = 1/2

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Extend understanding of fraction equivalence and ordering

• Comparing Fractions (From Page)
• Comparing Fractions (3 of 4) – ordering sets of three and four fractions (From Worksheets)
• Common Denominators (From Lessons)
• Improper Fractions and Mixed Numbers (From Lessons)
• Simplifying Fractions (From Lessons)

# Equivalent Fraction Pairs

The traditional pairs or Pelmanism game adapted to test knowledge of equivalent fractions.

Click on the cards to find matching pairs.

Score: Number of Clicks:

## Instructions

This is a game for one or many players. Click on a card to see what it contains. Click on a second card and if the two cards make a pair you win them.

In the two (or more) player version a free turn is awarded to the player who finds a pair. The winner is the player who finds the most pairs.

The option to claim a trophy is available when all of the pairs have been found. The objective is to have the fewest number of вЂclicksвЂ™ recorded on your trophy.

## Congratulations!

All of the pairs have been found. . Can you do it using fewer clicks?

## Here are some other Pairs games for you to enjoy

### Venn Diagram Pairs

Wednesday, November 4, 2015

Friday, November 3, 2017

Good learning resource.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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A Transum subscription also gives you access to the ‘Class Admin’ student management system, downloadable worksheets many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.

# Simplifying Fractions

To simplify a fraction, divide the top and bottom by the highest number that

can divide into both numbers exactly.

## Simplifying Fractions

Simplifying (or reducing) fractions means to make the fraction as simple as possible.

## How do I Simplify a Fraction ?

There are two ways to simplify a fraction:

## Method 1

Try to evenly divide (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 . etc, until we can’t go any further.

### Example: Simplify the fraction 24108 :

That is as far as we can go. The fraction simplifies to 2 9

### Example: Simplify the fraction 1035 :

Dividing by 2 doesn’t work because 35 can’t be evenly divided by 2 (35/2 = 17 )

No need to check 4 (we checked 2 already, and 4 is just 2 2).

But 5 does work!

That is as far as we can go. The fraction simplifies to 2 7

Notice that after checking 2 we didn’t need to check 4 (4 is 2 2)?

We also don’t need to check 6 when we have checked 2 and 3 (6 is 2×3).

In fact, when checking from smallest to largest we use prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, .

## Method 2

Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).

### Example: Simplify the fraction 812 :

The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4.

# Grade 5 Number & Operations Fractions

#### Use equivalent fractions as a strategy to add and subtract fractions.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 1/2.

#### Apply and extend previous understandings of multiplication and division.

Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Interpret multiplication as scaling (resizing), by:

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3.

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 (1/5) = 20 because 20 (1/5) = 4.

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

#

# Fractions Worksheets

Fractions Worksheets Sub-Topics

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person’s life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren’t that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they’ll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting. by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Multiplying and Dividing Fractions (A)

Adding and Subtracting Mixed Fractions (A)

Adding Fractions with Unlike Denominators (A)

Converting Mixed Fractions to Improper Fractions (A)

Adding and Subtracting Fractions — No Mixed Fractions (A)

Simplify Proper Fractions to Lowest Terms (Harder Version) (A)

Converting Fractions to Terminating and Repeating Decimals (A)

Missing Numbers in Equivalent Fractions (A)

Multiplying and Dividing Mixed Fractions (A)

Subtracting Fractions with Unlike Denominators (A)

## General Use Fractions Printables

General use fractions printables that are used in a variety of contexts when understanding and calculating fractions.

The black and white fraction circles can be used as a manipulative to compare fractions. Photocopy the worksheet onto an overhead projection slide. Use a pencil to lightly color the appropriate circle to represent the first fraction on the paper copy. Use a non-permanent overhead pen to color the appropriate circle to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Fraction strips can be laminated for durability and cut out to compare, order, add and subtract fractions. They are very useful for comparing fractions. You can also copy the fractions strips onto overhead projection slides and cut them out. Not only will they be durable, they will also be transparent which is useful when used in conjunction with paper versions (e.g. for comparing fractions).

## Comparing Ordering Fractions Worksheets

Comparing and ordering fractions worksheets for learning about the relative sizes of fractions.

There are many different strategies other than staring at the page that will help in comparing fractions. Try starting with something visual that will depict the fractions in question. We highly recommend our fraction strips (scroll up a bit). Using a straight edge like a ruler or book or folding will help students to easily see which fraction is greater or if they are equal. We should also mention that the things that are compared should be the same. Each fraction strip for example is the same size whereas if you took a third of a watermelon and half of a grape, the watermelon would probably win out.

Another strategy to use when comparing fractions is to use a number line and to use benchmarks like 0, 1, 1/2 to figure out where each fraction goes then see which one is bigger. Students actually do this one all the time since they can often compare fractions by recognizing that one is less than half and the other is greater than half. They might also see that one fraction is much closer to a whole than another fraction even though they might both be greater than a half.

We’ll mention one other strategy, but there are more. This one requires a little bit more knowledge, but it works out well in the long run because it is a certain way of comparing fractions. Convert each fraction to a decimal and compare the decimals. Decimal conversions can be memorized (especially for the common fractions) calculated with long division or using a calculator or look-up table. We suggest the latter since using a look-up table often leads to mental recall.

Comparing simple fractions.

Comparing Simple and Improper Fractions

Comparing Simple, Improper and Mixed Fractions

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We’ve probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won’t cut it. Try using some visuals to reinforce this important concept. Even though we’ve included number lines below, feel free to use your own strategies.

Ordering fractions with easy denominators on a Number Line.

Ordering fractions with all denominators on a Number Line.

## Simplifying Converting Fractions Worksheets

Simplifying fractions and converting fractions to other number formats worksheets to give students some necessary skills for more complex fractions topics.

Learning how to simplify fractions makes a student’s life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

Converting fractions to other fractions .

Order of Operations with Fractions .

As with other order of operation worksheets, the fractions order of operations worksheets require some pre-requisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what pre-requisite knowledge is missing then spend some time going over those concepts/skills before proceeding. Otherwise, the worksheets below should have fairly straight-forward answers and shouldn’t result in too much hair loss.

Order of Operations with Fractions Decimals .

You may use the math worksheets on this website according to our Terms of Use to help students learn math.

#

# Math Homework Help for Fractions

This introduction will be great math homework help for fractions. You’ll get a quick refresher on fraction fundamentals and the other concepts needed to do your lessons.

The information on this page may seem like a lot of details to remember, but I promise we ll get you through the actual math lessons like a breeze! This page is simply a tool that takes the place of a boring Glossary of Terms.

Math is a building process. To work with fractions, the student needs, at a minimum, strong skills in mathematical fundamentals including adding, subtracting, multiplying and dividing. Without these basic skills, attempting to do higher level work such as fractions will be very frustrating to the student. If the student is weak in these areas, time is better spent reviewing the basics for additional help.

## General Homework Help

### The Basic Concept of a Fraction

Before you can make heads or tails out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.

### Definition of a Fraction

You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by a/b. where a and b are whole numbers and b is not equal to 0 .

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes

There are three distinct meanings of fractions —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

The Part-Whole The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole

As a homework helper, this table shows you how the same whole can be divided into a different number of equal parts.

The Division Symbol ( / or __ ) used in a fraction tells you that everything above the division symbol is the numerator and must be treated as if it were one number, and everything below the division symbol is the denominator and also must be treated as if it were one number.

Basically, the numerator tells you how many part we are talking about, and the denominator tells you how many parts the whole is divided into. So a fraction like 6/7 tells you that we are looking at six (6 ) parts of a whole that is divided into seven (7 ) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

A Quotient The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

But what if you only have two cookies?

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

Here s a brief explanation of

A Ratio A comparison of things as a ratio can be expressed in one of two ways: first, the old fashioned method, a:b. pronounced a is to b ; and second, as found in newer books, a/b. If the ratio of a to b is 1 to 4 , or 1/4. then a is one-quarter of b . Alternately, b is four times as great as a .

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or

7ft/19ft = 7/19
Since we are comparing feet to feet, we don t need to write the units.

The ratio of its length to its width is 19 to 7

That was already a lot of homework help and you haven t worked a problem yet. So let s put some this stuff to WORK! But remember this is NOT the actual lesson. just a quick overview of some to the RULES and PRINCIPLES we ll need to use when working with fractions. Don t worry about memorizing everything, you ll see all of this stuff again as they apply to a particular operation during the homework lessons. So

We ll finish up with the

## Rules for Fraction Operations

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

1. Build each fraction (if needed) so that both denominators are equal.
2. Add the numerators of the fractions.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Subtracting Fractions

To subtract fractions, the denominators must be equal. You basically following the same steps as in addition.

1. Build each fraction (if required) so that both denominators are equal.
2. Combine the numerators according to the operation of subtraction.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Multiplying Fractions

To multiply two simple fractions, complete the following steps.

1. Multiply the numerators.
2. Multiply the denominators.
3. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To multiply a whole number and a fraction. complete the following steps.

1. Convert the whole number to a fraction.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Dividing Fractions

To divide one fraction by a second fraction. convert the problem to multiplication and multiply the two fractions.

1. Change the ÷ sign to x and invert the fraction to the right of the sign.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To divide a fraction by a whole number. convert the division process to a multiplication process, by using the following steps.

1. Convert the whole number to a fraction.
2. Change the ÷ sign to x and invert the fraction to the right of the sign.
3. Multiply the numerators.
4. Multiply the denominators.
5. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

## Multiplying Fractions Math Practice #questions #answered

#fraction problems with answers

#

Press here to CLOSE X Instructions for Fraction Multiplication

## Multiply the fractions

on the left and simplify the answer to its lowest terms. Type in the numerator and denominator in the

## fraction

on right side of the equal sign. When both the numerator and denominator are correct, the

## fraction multiplication problem

will change color. Use the arrow keys or mouse to move between the numerator and denominator.

## Multiplying fractions

can be pretty difficult – if you need help you can move the mouse pointer over the question mark to see the solution. Click on the

## fraction

problem, press the ENTER or RETURN key, or click on the reset problem button to set a new fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of fraction problems by clicking up and down by the 25 default. After you think you’ve correctly multiplied the fractions, reset it. Please note the problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen.

#

# Fractions Worksheets

Fractions Worksheets Sub-Topics

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person’s life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren’t that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they’ll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting. by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Multiplying and Dividing Fractions (A)

Adding and Subtracting Mixed Fractions (A)

Adding Fractions with Unlike Denominators (A)

Converting Mixed Fractions to Improper Fractions (A)

Adding and Subtracting Fractions — No Mixed Fractions (A)

Simplify Proper Fractions to Lowest Terms (Harder Version) (A)

Converting Fractions to Terminating and Repeating Decimals (A)

Missing Numbers in Equivalent Fractions (A)

Multiplying and Dividing Mixed Fractions (A)

Subtracting Fractions with Unlike Denominators (A)

## General Use Fractions Printables

General use fractions printables that are used in a variety of contexts when understanding and calculating fractions.

The black and white fraction circles can be used as a manipulative to compare fractions. Photocopy the worksheet onto an overhead projection slide. Use a pencil to lightly color the appropriate circle to represent the first fraction on the paper copy. Use a non-permanent overhead pen to color the appropriate circle to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Fraction strips can be laminated for durability and cut out to compare, order, add and subtract fractions. They are very useful for comparing fractions. You can also copy the fractions strips onto overhead projection slides and cut them out. Not only will they be durable, they will also be transparent which is useful when used in conjunction with paper versions (e.g. for comparing fractions).

## Comparing Ordering Fractions Worksheets

Comparing and ordering fractions worksheets for learning about the relative sizes of fractions.

There are many different strategies other than staring at the page that will help in comparing fractions. Try starting with something visual that will depict the fractions in question. We highly recommend our fraction strips (scroll up a bit). Using a straight edge like a ruler or book or folding will help students to easily see which fraction is greater or if they are equal. We should also mention that the things that are compared should be the same. Each fraction strip for example is the same size whereas if you took a third of a watermelon and half of a grape, the watermelon would probably win out.

Another strategy to use when comparing fractions is to use a number line and to use benchmarks like 0, 1, 1/2 to figure out where each fraction goes then see which one is bigger. Students actually do this one all the time since they can often compare fractions by recognizing that one is less than half and the other is greater than half. They might also see that one fraction is much closer to a whole than another fraction even though they might both be greater than a half.

We’ll mention one other strategy, but there are more. This one requires a little bit more knowledge, but it works out well in the long run because it is a certain way of comparing fractions. Convert each fraction to a decimal and compare the decimals. Decimal conversions can be memorized (especially for the common fractions) calculated with long division or using a calculator or look-up table. We suggest the latter since using a look-up table often leads to mental recall.

Comparing simple fractions.

Comparing Simple and Improper Fractions

Comparing Simple, Improper and Mixed Fractions

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We’ve probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won’t cut it. Try using some visuals to reinforce this important concept. Even though we’ve included number lines below, feel free to use your own strategies.

Ordering fractions with easy denominators on a Number Line.

Ordering fractions with all denominators on a Number Line.

## Simplifying Converting Fractions Worksheets

Simplifying fractions and converting fractions to other number formats worksheets to give students some necessary skills for more complex fractions topics.

Learning how to simplify fractions makes a student’s life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

Converting fractions to other fractions .

Order of Operations with Fractions .

As with other order of operation worksheets, the fractions order of operations worksheets require some pre-requisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what pre-requisite knowledge is missing then spend some time going over those concepts/skills before proceeding. Otherwise, the worksheets below should have fairly straight-forward answers and shouldn’t result in too much hair loss.

Order of Operations with Fractions Decimals .

You may use the math worksheets on this website according to our Terms of Use to help students learn math.

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# Math Homework Help for Fractions

This introduction will be great math homework help for fractions. You’ll get a quick refresher on fraction fundamentals and the other concepts needed to do your lessons.

The information on this page may seem like a lot of details to remember, but I promise we ll get you through the actual math lessons like a breeze! This page is simply a tool that takes the place of a boring Glossary of Terms.

Math is a building process. To work with fractions, the student needs, at a minimum, strong skills in mathematical fundamentals including adding, subtracting, multiplying and dividing. Without these basic skills, attempting to do higher level work such as fractions will be very frustrating to the student. If the student is weak in these areas, time is better spent reviewing the basics for additional help.

## General Homework Help

### The Basic Concept of a Fraction

Before you can make heads or tails out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.

### Definition of a Fraction

You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by a/b. where a and b are whole numbers and b is not equal to 0 .

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes

There are three distinct meanings of fractions —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

The Part-Whole The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole

As a homework helper, this table shows you how the same whole can be divided into a different number of equal parts.

The Division Symbol ( / or __ ) used in a fraction tells you that everything above the division symbol is the numerator and must be treated as if it were one number, and everything below the division symbol is the denominator and also must be treated as if it were one number.

Basically, the numerator tells you how many part we are talking about, and the denominator tells you how many parts the whole is divided into. So a fraction like 6/7 tells you that we are looking at six (6 ) parts of a whole that is divided into seven (7 ) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

A Quotient The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

But what if you only have two cookies?

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

Here s a brief explanation of

A Ratio A comparison of things as a ratio can be expressed in one of two ways: first, the old fashioned method, a:b. pronounced a is to b ; and second, as found in newer books, a/b. If the ratio of a to b is 1 to 4 , or 1/4. then a is one-quarter of b . Alternately, b is four times as great as a .

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or

7ft/19ft = 7/19
Since we are comparing feet to feet, we don t need to write the units.

The ratio of its length to its width is 19 to 7

That was already a lot of homework help and you haven t worked a problem yet. So let s put some this stuff to WORK! But remember this is NOT the actual lesson. just a quick overview of some to the RULES and PRINCIPLES we ll need to use when working with fractions. Don t worry about memorizing everything, you ll see all of this stuff again as they apply to a particular operation during the homework lessons. So

We ll finish up with the

## Rules for Fraction Operations

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

1. Build each fraction (if needed) so that both denominators are equal.
2. Add the numerators of the fractions.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Subtracting Fractions

To subtract fractions, the denominators must be equal. You basically following the same steps as in addition.

1. Build each fraction (if required) so that both denominators are equal.
2. Combine the numerators according to the operation of subtraction.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Multiplying Fractions

To multiply two simple fractions, complete the following steps.

1. Multiply the numerators.
2. Multiply the denominators.
3. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To multiply a whole number and a fraction. complete the following steps.

1. Convert the whole number to a fraction.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Dividing Fractions

To divide one fraction by a second fraction. convert the problem to multiplication and multiply the two fractions.

1. Change the ÷ sign to x and invert the fraction to the right of the sign.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To divide a fraction by a whole number. convert the division process to a multiplication process, by using the following steps.

1. Convert the whole number to a fraction.
2. Change the ÷ sign to x and invert the fraction to the right of the sign.
3. Multiply the numerators.
4. Multiply the denominators.
5. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

## Multiplying Fractions Math Practice #cryptic #clue #answers

#fraction problems with answers

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Press here to CLOSE X Instructions for Fraction Multiplication

## Multiply the fractions

on the left and simplify the answer to its lowest terms. Type in the numerator and denominator in the

## fraction

on right side of the equal sign. When both the numerator and denominator are correct, the

## fraction multiplication problem

will change color. Use the arrow keys or mouse to move between the numerator and denominator.

## Multiplying fractions

can be pretty difficult – if you need help you can move the mouse pointer over the question mark to see the solution. Click on the

## fraction

problem, press the ENTER or RETURN key, or click on the reset problem button to set a new fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of fraction problems by clicking up and down by the 25 default. After you think you’ve correctly multiplied the fractions, reset it. Please note the problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen.

## Fraction Math Problems – Fractions Practice #home #work #answers

#

Press here to CLOSE X

Now practice fractions anywhere! We have fractions math teaching resources optimized for cell phones. Access Mr. Martini’s Classroom Fractions page using your smartphone and you will automatically go to a special fractions for cell phones page. We have addition, subtraction, division, and multiplication flash cards optimized for Android and other smartphones.

Press here to CLOSE X Instructions for Fractions

Practice solving fractions with math student and teacher resources. Click on a box in the middle column to select the type of online fraction practice you would like to do. You can practice solving fractional equivalents, solving fraction greater than or less than problems, simplifying fractions to their lowest terms, adding fractions, dividing fractions, or multiplying fractions. Each fraction math problem will have its own set of instructions, but they all will change color when they are correct. When doing fraction addition, fraction division, or fraction multiplication, the answer must be simplified to be correct. Click on the fraction problem, press the ENTER or RETURN key, or click on the reset problem button to reset the online fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of problems by clicking up and down by the 25 default. After you think you’ve correctly solved the fraction problem, reset it. Please note the fraction math problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen. When you’re done practicing, challenge yourself with an online fraction quiz.

# Fractions

## Free equivalent fractions worksheets with visual models #peter #answers #trick

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You are here: Home Worksheets Equivalent fractions

# Free Equivalent Fractions Worksheets

Create an unlimited supply of worksheets for equivalent fractions (grades 4-5)! The worksheets can be made in html or PDF format both are easy to print. You can also customize them using the generator below .

Students usually encounter the concept of equivalent fractions in 4th grade (such as 1/2 = 5/10). Visual models are essential in helping children to grasp this idea, and the worksheets below provide just that!

Then, in 5th grade, students learn how to add unlike fractions. This procedure involves converting the fractions to equivalent fractions with a common denominator. So, the concept of equivalent fractions is an important prerequisite to fraction addition and subtraction.

## Basic instructions for the worksheets

Each worksheet is randomly generated and thus unique. The answer key is automatically generated and is placed on the second page of the file.

You can generate the worksheets either in html or PDF format both are easy to print. To get the PDF worksheet, simply push the button titled “Create PDF ” or “Make PDF worksheet “. To get the worksheet in html format, push the button “View in browser ” or “Make html worksheet “. This has the advantage that you can save the worksheet directly from your browser (choose File Save) and then edit it in Word or other word processing program.

Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:

• PDF format: come back to this page and push the button again.
• Html format: simply refresh the worksheet page in your browser window.

## Equivalent fractions with visual models

The two equivalent fractions are shown; student colors the pie models

Two pie models are already colored; student writes the fractions

Two pie images; one is colored, the other is not, the student writes both fractions

Two pie images to color, one fraction is given, one not

Allow improper fractions, the student writes both fractions

Allow mixed numbers, the student writes both mixed numbers

Allow mixed numbers and improper fractions, the student writes both fractions/mixed numbers

Allow mixed numbers and improper fractions, one fraction is given, the other not

## Equivalent fractions without visual models

Write the missing part, small denominators
(e.g. 2/3 = ?/12)

Improper fractions allowed, small denominators (e.g. 7/4 = ?/16)

Equivalent mixed numbers, small denominators
(e.g. 2 3/4 = 2 ?/12)

Both mixed numbers and improper fractions allowed, small denominators

The following worksheets are similar to the ones above, but using larger numbers in the denominators and numerators.

Equivalent fractions, proper fractions only

Improper fractions allowed
(e.g. 17/14 = ?/56)

Includes mixed numbers

Includes both improper fractions and mixed numbers

## Generator

With this worksheet generator, you can make worksheets for equivalent fractions. The worksheet can include problems with visual models (pie images) or not. There are five problem types to choose from:

1. Two fractions are given with 2 empty pie images to color in (e.g. 3/5 = 6/10).
2. There are 2 pie images that are already colored; the student writes both fractions.
3. Two pie images are given, one colored in, one not; the student writes both fractions.
4. There are 2 pie images to color, one fraction is given, one not (e.g. 4/5 = / )
5. Problems without any visual model; the student writes the missing numerator or denominator in one of the fractions (e.g. 2/3 = /12).

You can choose to include or not include mixed numbers and improper fractions. You can control the minimum and maximum values for the numerator and the denominator. However, for the problems with visual models, the maximum denominator is limited to 16.

## Equivalent Fractions Worksheet Generator

#### Math Made Easy, Grade 4 Math Workbook

This workbook has been compiled and tested by a team of math experts to increase your child’s confidence, enjoyment, and success at school. Fourth Grade: Provides practice at all the major topics for Grade 4 with emphasis on multiplication and division of larger numbers. Includes a review of Grade 3 topics and a preview of topics in Grade 5. Includes Times Tables practice.

## Primary Resources: Maths: Numbers and the Number System: Fractions, Decimals – Percentages #ask #questions #get #answers

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• Fractions 1: Mixed Numbers (Reuben McIntyre)
• Fractions 2: Improper Fractions (Reuben McIntyre)
• Fractions 3: Equivalet Fractions (Reuben McIntyre)
• Fractions 4: Simplifying Fractions (Reuben McIntyre)
• Fractional Parts of Shapes (R. Lovelock)
• Fractions Marking Ladder (Y1-4) Spring 1 (Victoria Scott) DOC
• Fractions 5: Fractions of Whole Numbers (Reuben McIntyre)
• Fractions 6: Adding Fractions (Reuben McIntyre)
• Fractions (Quarters) (Tracey Short) DOC
• Fractions to Order (Lisa Dunn) DOC
• Fractions Display Cards (Jane Campbell) DOC
• Colour One Half (Margaret-Anne McGinley) DOC
• Colour Half and Quarters (Sarah Dibley) DOC
• Halves and Quarters Shading (Jackie Simbler) DOC
• Basic Fractions (Adam Jewkes)
• Fractions (Halves) (Lisa Mary McNamee)
• Fun Fractions (3 dif. sheets) (Cara Hayman) PDF
• Quarter It! (Jackie Chidwick) PDF
• Half of numbers (Sheena Florey) PDF
• Fractions of Shapes (Block E Unit 2) (David-Guy Parkin) DOC
• Half or Not Half (Dhipa Begum) DOC
• Shade One Half and One Quarter (Dhipa Begum) DOC
• Shade Quarters (Dhipa Begum) DOC
• Simple Fractions (Peter Dunbar) PDF
• Fractions of Quantities (Mark Wilson) DOC
• Shade Two Thirds (Elaine Smith)
• Finding a Half (Kat Hester)
• Fractions of Shapes (Emma Foster) DOC
• Fractions of Numbers (Emma Foster) DOC
• Fractions Problems (Cara Lynch) DOC
• Halves and Quarters Shading (Gaynor Davis) DOC
• Halving (Karen Mercer)
• Introduction to Fractions (Emily Corble)
• Fractions (Liz Hazelden) DOC
• Fractions for Beginners (Carol Wright) DOC
• Hatching Fractions (Arthur Daley) PDF
• Pizza Fractions (Vicky Frampton) DOC
• Colour Halves and Quarters (Gwyneth Pocock) DOC
• Fraction Walls (blank) (Gareth Pitchford)
• Interactive Fraction Wall (Lorraine Oldale)
• Fraction Target Board (Liz Greenwood) PDF
• Fraction Wall (Carol Bloomfield) PDF
• Colour Fraction Wall (Carole-Ann Balaam) DOC
• Equivalent Fraction Strips (Jennifer Orgill) DOC
• Fraction Wall (Jackie Launders) PDF
• Fraction Wall (Mandy Smith) PDF
• Fractions Cards (Joanne Nalton) DOC
• Large Fraction Wall (Jeremy Harris) DOC
• Would You Rather Have. (Clare Martin)
• Fractions Test (Leanne Wilson) DOC
• Fractions – thirds fifths (Rachael Wilkie)
• What fraction is shaded? (Kate Warner)
• Introducing Fractions (Steve Kersys)
• Fractions 1 (Gareth Rossiter)
• Fractions 2 (Gareth Rossiter)
• Equivalent Fractions (Sarah Sergeant)
• Smartie Fractions (Sheila Black) PDF
• Smartie Fractions (Mandy Smith) PDF
• Fractions Worksheets (Gareth Rossiter) PDF
• Ordering Fractions (Nadine Turner) PDF
• Fraction Mats (Stuart Arlow) DOC
• Whole, Halves and Quarters (Rachael Wilkie) DOC
• Equivalent Fractions (Christina Holmes)
• Fraction Numberlines (Eve Croft) DOC
• Fraction Number Lines (Rhodri Thomas) DOC
• Pizza Maths – Fractions of amounts (5 sheets) PDF
• Equivalent Fractions Match Up (Louise Macdonald) DOC
• Fractions Word Problems (Louise Macdonald) DOC
• Shade One Half / Quarter (Cindy Hoy) DOC
• Fractions of Shapes (Jay Birmingham) DOC
• Fractions of Quantities Problems (Helen Langford) DOC
• Fraction Posters (Paula Alty DOC
• Fractions (Paul Rigby)
• Fractions of Shapes Amounts (Yvonne Anderson)
• Equivalent Fractions (Margaret Carr)
• Fractions (T1 U11 Day 1) (Louise Hutchinson)
• Fractions (T1 U11 Day 2) (Louise Hutchinson)
• Fractions (T1 U11 Day 4) (Louise Hutchinson)
• Numerators and Denominators (Natasha Duffy)
• Pizza Problems (Georgina Burtenshaw)
• The Fraction Hunter’s Story (Hilary Minor) PDF
• Simple Fraction Problems (Stephen Norwood) PDF
• Equivalent Fractions (Kevin Kerr) PDF
• Fraction Circles (Mandy Smith) DOC
• Coloured Fraction Wall (Karen Holt) DOC
• Fractions of Sets (LA) (Bindiya Bhudia) DOC
• Fractions of Money (Rosie Iribas) DOC
• Mixed Number Pizzas 1 (Carole-Ann Balaam)
• Mixed Number Pizzas 2 (Carole-Ann Balaam)
• Fraction Wall and Questions (Jay Birmingham) DOC
• Adding Fractions to Make One Whole (Meryl York) DOC
• Putting Fractions on a Number Line (Anne Hayton)
• One and Two Step Fraction Problems (Carrie Magee) DOC
• Fractions Cards (to order) HA (Nick Hutson) DOC
• Fractions Cards (to order) LA (Nick Hutson) DOC
• Fractions (Aimi Kinsey-Jones) DOC
• Adding Subtracting Fractions with Same Denominators (Victoria Scott) DOC
• Compare Order Fractions with Same Denominators (Victoria Scott) DOC
• Which is Bigger? (Emma Allonby)
• Equivalent Fractions Lesson (Zip) (Shaun Kelliher)
• Fractions of Recipes (J. Adams) DOC
• Types of Fractions Poster (Cath Walls) DOC
• Finding Fractions of Numbers using Rectangles (Paul Wren) DOC
• Colour the Fractions (Matt Lovegrove)
• Build the Fraction Wall (Dot Hullah)
• Fractions Equivalent to a Half (Joanne Pooley)
• Fractions (WWtbaM) (Dot Hullah)
• Comparing and Ordering Fractions (Katherin Weeks)
• T1 U11 Fractions and Decimals (David Arthur)
• Fraction Problems (Anna Mongan) PDF
• Finding Fractions of Whole Numbers (Hilary Minor) PDF
• Real Life Fractions (2 sheets) (Cara Hayman) PDF
• A Fraction of the Problem (2 sheets) (Cara Hayman) PDF
• Fractions of Numbers (Rosie Iribas) DOC
• Toy Sale Fractions (Kath Huggett) DOC
• Fractions Sale (Louise Pickering) PDF
• Improper Fractions to Mixed Numbers (Becky Cheshire) DOC
• Shade the Fractions (Melanie Osborne)
• Fraction Wall Questions (Pete Smith) DOC
• Shade Equivalent Fractions (Joanna Martin)
• Equivalent Fractions (Jay Birmingham) DOC
• Equivalent Fractions Display (Diane Hartley) DOC
• Fraction Matching (Helen Graham) DOC
• Equivalent Fractions to One Half/Quarter (Meryl York) DOC
• Fraction Cards That Total 1 (Linda Kielty/Ceri Hill) DOC
• Fraction Cards to Total 1 (Claire Richmond) DOC
• Fractions of Quartiles (Rebecca Joyce)
• Chocolate Fractions (Shaun Kelliher) DOC
• What Fraction is Shaded? (Gwyneth Pocock) DOC
• Fraction Flags (Claire Richmond) DOC
• Finding Equivalent Fractions (Morag Watson)
• Finding Fractions of Numbers (Jennifer Craft)
• Finding Fractions of Whole Numbers (Dhipa Begum) DOC
• Fraction Cake Activity Recipe (Alison Richmond) DOC
• Reducing Fractions (Louise Whitby)
• Comparing Fractions (Susan Williams)
• Multiplying Dividing Fractions (Joe Pinnock) DOC
• Multiplying Fractions (Triangle) Jigsaw (Peter Barnett) PDF
• Multiplying Fractions (Rhombus) Jigsaw (Peter Barnett) PDF
• Multiplying Dividing Fractions (Peter Barnett)
• Equivalent Fraction Cards (Lisa Dunn) DOC
• Adding Subtracting Fractions Jigsaw (Peter Barnett) PDF
• Simplifying Fractions (Jessica Ganley)
• Dividing Fractions (Triangle) Jigsaw (Peter Barnett) PDF
• Dividing Fractions (Rhombus) Jigsaw (Peter Barnett) PDF

## Equivalent Fractions #answer #to #riddles

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You can multiply the numerator and the denominator of a fraction by any nonzero whole number, as long as you multiply both by the same whole number! For example, you can multiply the numerator and the denominator by 3. as shown in part A above. But you cannot multiply the numerator by 3 and the denominator by 5. You can multiply the numerator and the denominator by 4. as shown in part B above. But you cannot multiply the numerator by 4 and the denominator by 2.

The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions. You may be wondering why this is so. In the last lesson, we learned that a fraction that has the same numerator and denominator is equal to one. This is shown below.

In example 6, the fraction given in part a is a proper fraction; whereas the fractions given in parts b and c are improper fractions. Note that the procedure for finding equivalent fractions is the same for both types of fractions. Looking at each part of example 6, the answers vary, depending on the nonzero whole number chosen. However, the equivalent fractions found in each part all have the same value.

Write the fraction five-sixths as an equivalent fraction with a denominator of 24.

In example 7, we multiplied the numerator AND the denominator by 4.

Write the fraction two-sevenths as an equivalent fraction with a denominator of 21.

In example 8, we multiplied the numerator AND the denominator by 3.

Write the fraction three-eighths as an equivalent fraction with a numerator of 15.

In example 9, we multiplied the numerator AND the denominator by 5.

We can now redefine the terms fraction and equivalent fraction as follows:

Equivalent fractions are different fractions that name the same number. The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions.

### Exercises

In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Note: To write the fraction two-thirds, enter 2/3 into the form.

Are the fractions three-fourths and fourteen-sixteenths equivalent (Yes or No)?

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# Understanding Equivalent Fractions

The best way to think about equivalent fractions is that they are fractions that have the same overall value .

For example, if we cut a pie exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.

And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the same amount of pie that 1/2 did.

So we can say that 1/2 is equivalent (or equal) to 2/4.

## Don’t let equivalent fractions confuse you!

Take a look at the four circles above.Can you see that the one 1/2 , the two 1/4 and the four 1/8 take up the same amount of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also equal to 4/8. And yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you already know, we are nuts about rules. So, let s look at the Rule to check to see if two fractions are equivalent or equal. The rule for equivalent fractions can be a little tough to explain, but hang in there, we will clear things up in just a bit.

## Here s the Rule

What this Rule says is that two fractions are equivalent (equal) only if the product of the numerator (a ) of the first fraction and the denominator (d ) of the other fraction is equal to the product of the denominator (b ) of the first fraction and the numerator (c ) of the other fraction.

A product simply means you multiply.

## Test the Rule

Now let s plug the numbers into the Rule for equivalent fractions to be sure you have it down cold . 3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3 ) of the first fraction and the denominator (12 ) of the other fraction is equal to the product of the denominator (4 ) of the first fraction and the numerator (9 ) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3 12=36 and 4 9=36. A simple way to look at how to check for equivalent fractions is to do what is called cross-multiply , which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

### The graphic below shows you how to cross multiply

Okay, let s do one with numbers where the fractions are not equivalent

#

# Fractions Worksheets

Fractions Worksheets Sub-Topics

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person’s life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren’t that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they’ll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting. by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Multiplying and Dividing Fractions (A)

Adding and Subtracting Mixed Fractions (A)

Adding Fractions with Unlike Denominators (A)

Converting Mixed Fractions to Improper Fractions (A)

Adding and Subtracting Fractions — No Mixed Fractions (A)

Simplify Proper Fractions to Lowest Terms (Harder Version) (A)

Converting Fractions to Terminating and Repeating Decimals (A)

Missing Numbers in Equivalent Fractions (A)

Multiplying and Dividing Mixed Fractions (A)

Subtracting Fractions with Unlike Denominators (A)

## General Use Fractions Printables

General use fractions printables that are used in a variety of contexts when understanding and calculating fractions.

The black and white fraction circles can be used as a manipulative to compare fractions. Photocopy the worksheet onto an overhead projection slide. Use a pencil to lightly color the appropriate circle to represent the first fraction on the paper copy. Use a non-permanent overhead pen to color the appropriate circle to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Fraction strips can be laminated for durability and cut out to compare, order, add and subtract fractions. They are very useful for comparing fractions. You can also copy the fractions strips onto overhead projection slides and cut them out. Not only will they be durable, they will also be transparent which is useful when used in conjunction with paper versions (e.g. for comparing fractions).

## Comparing Ordering Fractions Worksheets

Comparing and ordering fractions worksheets for learning about the relative sizes of fractions.

There are many different strategies other than staring at the page that will help in comparing fractions. Try starting with something visual that will depict the fractions in question. We highly recommend our fraction strips (scroll up a bit). Using a straight edge like a ruler or book or folding will help students to easily see which fraction is greater or if they are equal. We should also mention that the things that are compared should be the same. Each fraction strip for example is the same size whereas if you took a third of a watermelon and half of a grape, the watermelon would probably win out.

Another strategy to use when comparing fractions is to use a number line and to use benchmarks like 0, 1, 1/2 to figure out where each fraction goes then see which one is bigger. Students actually do this one all the time since they can often compare fractions by recognizing that one is less than half and the other is greater than half. They might also see that one fraction is much closer to a whole than another fraction even though they might both be greater than a half.

We’ll mention one other strategy, but there are more. This one requires a little bit more knowledge, but it works out well in the long run because it is a certain way of comparing fractions. Convert each fraction to a decimal and compare the decimals. Decimal conversions can be memorized (especially for the common fractions) calculated with long division or using a calculator or look-up table. We suggest the latter since using a look-up table often leads to mental recall.

Comparing simple fractions.

Comparing Simple and Improper Fractions

Comparing Simple, Improper and Mixed Fractions

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We’ve probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won’t cut it. Try using some visuals to reinforce this important concept. Even though we’ve included number lines below, feel free to use your own strategies.

Ordering fractions with easy denominators on a Number Line.

Ordering fractions with all denominators on a Number Line.

## Simplifying Converting Fractions Worksheets

Simplifying fractions and converting fractions to other number formats worksheets to give students some necessary skills for more complex fractions topics.

Learning how to simplify fractions makes a student’s life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

Converting fractions to other fractions .

Order of Operations with Fractions .

As with other order of operation worksheets, the fractions order of operations worksheets require some pre-requisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what pre-requisite knowledge is missing then spend some time going over those concepts/skills before proceeding. Otherwise, the worksheets below should have fairly straight-forward answers and shouldn’t result in too much hair loss.

Order of Operations with Fractions Decimals .

You may use the math worksheets on this website according to our Terms of Use to help students learn math.

#

# Math Homework Help for Fractions

This introduction will be great math homework help for fractions. You’ll get a quick refresher on fraction fundamentals and the other concepts needed to do your lessons.

The information on this page may seem like a lot of details to remember, but I promise we ll get you through the actual math lessons like a breeze! This page is simply a tool that takes the place of a boring Glossary of Terms.

Math is a building process. To work with fractions, the student needs, at a minimum, strong skills in mathematical fundamentals including adding, subtracting, multiplying and dividing. Without these basic skills, attempting to do higher level work such as fractions will be very frustrating to the student. If the student is weak in these areas, time is better spent reviewing the basics for additional help.

## General Homework Help

### The Basic Concept of a Fraction

Before you can make heads or tails out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.

### Definition of a Fraction

You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by a/b. where a and b are whole numbers and b is not equal to 0 .

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes

There are three distinct meanings of fractions —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

The Part-Whole The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole

As a homework helper, this table shows you how the same whole can be divided into a different number of equal parts.

The Division Symbol ( / or __ ) used in a fraction tells you that everything above the division symbol is the numerator and must be treated as if it were one number, and everything below the division symbol is the denominator and also must be treated as if it were one number.

Basically, the numerator tells you how many part we are talking about, and the denominator tells you how many parts the whole is divided into. So a fraction like 6/7 tells you that we are looking at six (6 ) parts of a whole that is divided into seven (7 ) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

A Quotient The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

But what if you only have two cookies?

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

Here s a brief explanation of

A Ratio A comparison of things as a ratio can be expressed in one of two ways: first, the old fashioned method, a:b. pronounced a is to b ; and second, as found in newer books, a/b. If the ratio of a to b is 1 to 4 , or 1/4. then a is one-quarter of b . Alternately, b is four times as great as a .

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or

7ft/19ft = 7/19
Since we are comparing feet to feet, we don t need to write the units.

The ratio of its length to its width is 19 to 7

That was already a lot of homework help and you haven t worked a problem yet. So let s put some this stuff to WORK! But remember this is NOT the actual lesson. just a quick overview of some to the RULES and PRINCIPLES we ll need to use when working with fractions. Don t worry about memorizing everything, you ll see all of this stuff again as they apply to a particular operation during the homework lessons. So

We ll finish up with the

## Rules for Fraction Operations

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

1. Build each fraction (if needed) so that both denominators are equal.
2. Add the numerators of the fractions.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Subtracting Fractions

To subtract fractions, the denominators must be equal. You basically following the same steps as in addition.

1. Build each fraction (if required) so that both denominators are equal.
2. Combine the numerators according to the operation of subtraction.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Multiplying Fractions

To multiply two simple fractions, complete the following steps.

1. Multiply the numerators.
2. Multiply the denominators.
3. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To multiply a whole number and a fraction. complete the following steps.

1. Convert the whole number to a fraction.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Dividing Fractions

To divide one fraction by a second fraction. convert the problem to multiplication and multiply the two fractions.

1. Change the ÷ sign to x and invert the fraction to the right of the sign.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To divide a fraction by a whole number. convert the division process to a multiplication process, by using the following steps.

1. Convert the whole number to a fraction.
2. Change the ÷ sign to x and invert the fraction to the right of the sign.
3. Multiply the numerators.
4. Multiply the denominators.
5. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

## Multiplying Fractions Math Practice #economics #answers

#fraction problems with answers

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Press here to CLOSE X Instructions for Fraction Multiplication

## Multiply the fractions

on the left and simplify the answer to its lowest terms. Type in the numerator and denominator in the

## fraction

on right side of the equal sign. When both the numerator and denominator are correct, the

## fraction multiplication problem

will change color. Use the arrow keys or mouse to move between the numerator and denominator.

## Multiplying fractions

can be pretty difficult – if you need help you can move the mouse pointer over the question mark to see the solution. Click on the

## fraction

problem, press the ENTER or RETURN key, or click on the reset problem button to set a new fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of fraction problems by clicking up and down by the 25 default. After you think you’ve correctly multiplied the fractions, reset it. Please note the problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen.

## Fraction Math Problems – Fractions Practice #crossword #puzzle #answers

#

Press here to CLOSE X

Now practice fractions anywhere! We have fractions math teaching resources optimized for cell phones. Access Mr. Martini’s Classroom Fractions page using your smartphone and you will automatically go to a special fractions for cell phones page. We have addition, subtraction, division, and multiplication flash cards optimized for Android and other smartphones.

Press here to CLOSE X Instructions for Fractions

Practice solving fractions with math student and teacher resources. Click on a box in the middle column to select the type of online fraction practice you would like to do. You can practice solving fractional equivalents, solving fraction greater than or less than problems, simplifying fractions to their lowest terms, adding fractions, dividing fractions, or multiplying fractions. Each fraction math problem will have its own set of instructions, but they all will change color when they are correct. When doing fraction addition, fraction division, or fraction multiplication, the answer must be simplified to be correct. Click on the fraction problem, press the ENTER or RETURN key, or click on the reset problem button to reset the online fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of problems by clicking up and down by the 25 default. After you think you’ve correctly solved the fraction problem, reset it. Please note the fraction math problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen. When you’re done practicing, challenge yourself with an online fraction quiz.

# Fractions

## Free equivalent fractions worksheets with visual models #live #answering #service

#

You are here: Home Worksheets Equivalent fractions

# Free Equivalent Fractions Worksheets

Create an unlimited supply of worksheets for equivalent fractions (grades 4-5)! The worksheets can be made in html or PDF format both are easy to print. You can also customize them using the generator below .

Students usually encounter the concept of equivalent fractions in 4th grade (such as 1/2 = 5/10). Visual models are essential in helping children to grasp this idea, and the worksheets below provide just that!

Then, in 5th grade, students learn how to add unlike fractions. This procedure involves converting the fractions to equivalent fractions with a common denominator. So, the concept of equivalent fractions is an important prerequisite to fraction addition and subtraction.

## Basic instructions for the worksheets

Each worksheet is randomly generated and thus unique. The answer key is automatically generated and is placed on the second page of the file.

You can generate the worksheets either in html or PDF format both are easy to print. To get the PDF worksheet, simply push the button titled “Create PDF ” or “Make PDF worksheet “. To get the worksheet in html format, push the button “View in browser ” or “Make html worksheet “. This has the advantage that you can save the worksheet directly from your browser (choose File Save) and then edit it in Word or other word processing program.

Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:

• PDF format: come back to this page and push the button again.
• Html format: simply refresh the worksheet page in your browser window.

## Equivalent fractions with visual models

The two equivalent fractions are shown; student colors the pie models

Two pie models are already colored; student writes the fractions

Two pie images; one is colored, the other is not, the student writes both fractions

Two pie images to color, one fraction is given, one not

Allow improper fractions, the student writes both fractions

Allow mixed numbers, the student writes both mixed numbers

Allow mixed numbers and improper fractions, the student writes both fractions/mixed numbers

Allow mixed numbers and improper fractions, one fraction is given, the other not

## Equivalent fractions without visual models

Write the missing part, small denominators
(e.g. 2/3 = ?/12)

Improper fractions allowed, small denominators (e.g. 7/4 = ?/16)

Equivalent mixed numbers, small denominators
(e.g. 2 3/4 = 2 ?/12)

Both mixed numbers and improper fractions allowed, small denominators

The following worksheets are similar to the ones above, but using larger numbers in the denominators and numerators.

Equivalent fractions, proper fractions only

Improper fractions allowed
(e.g. 17/14 = ?/56)

Includes mixed numbers

Includes both improper fractions and mixed numbers

## Generator

With this worksheet generator, you can make worksheets for equivalent fractions. The worksheet can include problems with visual models (pie images) or not. There are five problem types to choose from:

1. Two fractions are given with 2 empty pie images to color in (e.g. 3/5 = 6/10).
2. There are 2 pie images that are already colored; the student writes both fractions.
3. Two pie images are given, one colored in, one not; the student writes both fractions.
4. There are 2 pie images to color, one fraction is given, one not (e.g. 4/5 = / )
5. Problems without any visual model; the student writes the missing numerator or denominator in one of the fractions (e.g. 2/3 = /12).

You can choose to include or not include mixed numbers and improper fractions. You can control the minimum and maximum values for the numerator and the denominator. However, for the problems with visual models, the maximum denominator is limited to 16.

## Equivalent Fractions Worksheet Generator

#### Math Made Easy, Grade 4 Math Workbook

This workbook has been compiled and tested by a team of math experts to increase your child’s confidence, enjoyment, and success at school. Fourth Grade: Provides practice at all the major topics for Grade 4 with emphasis on multiplication and division of larger numbers. Includes a review of Grade 3 topics and a preview of topics in Grade 5. Includes Times Tables practice.

## Primary Resources: Maths: Numbers and the Number System: Fractions, Decimals – Percentages #math #problems #with #answers

#

• Fractions 1: Mixed Numbers (Reuben McIntyre)
• Fractions 2: Improper Fractions (Reuben McIntyre)
• Fractions 3: Equivalet Fractions (Reuben McIntyre)
• Fractions 4: Simplifying Fractions (Reuben McIntyre)
• Fractional Parts of Shapes (R. Lovelock)
• Fractions Marking Ladder (Y1-4) Spring 1 (Victoria Scott) DOC
• Fractions 5: Fractions of Whole Numbers (Reuben McIntyre)
• Fractions 6: Adding Fractions (Reuben McIntyre)
• Fractions (Quarters) (Tracey Short) DOC
• Fractions to Order (Lisa Dunn) DOC
• Fractions Display Cards (Jane Campbell) DOC
• Colour One Half (Margaret-Anne McGinley) DOC
• Colour Half and Quarters (Sarah Dibley) DOC
• Halves and Quarters Shading (Jackie Simbler) DOC
• Basic Fractions (Adam Jewkes)
• Fractions (Halves) (Lisa Mary McNamee)
• Fun Fractions (3 dif. sheets) (Cara Hayman) PDF
• Quarter It! (Jackie Chidwick) PDF
• Half of numbers (Sheena Florey) PDF
• Fractions of Shapes (Block E Unit 2) (David-Guy Parkin) DOC
• Half or Not Half (Dhipa Begum) DOC
• Shade One Half and One Quarter (Dhipa Begum) DOC
• Shade Quarters (Dhipa Begum) DOC
• Simple Fractions (Peter Dunbar) PDF
• Fractions of Quantities (Mark Wilson) DOC
• Shade Two Thirds (Elaine Smith)
• Finding a Half (Kat Hester)
• Fractions of Shapes (Emma Foster) DOC
• Fractions of Numbers (Emma Foster) DOC
• Fractions Problems (Cara Lynch) DOC
• Halves and Quarters Shading (Gaynor Davis) DOC
• Halving (Karen Mercer)
• Introduction to Fractions (Emily Corble)
• Fractions (Liz Hazelden) DOC
• Fractions for Beginners (Carol Wright) DOC
• Hatching Fractions (Arthur Daley) PDF
• Pizza Fractions (Vicky Frampton) DOC
• Colour Halves and Quarters (Gwyneth Pocock) DOC
• Fraction Walls (blank) (Gareth Pitchford)
• Interactive Fraction Wall (Lorraine Oldale)
• Fraction Target Board (Liz Greenwood) PDF
• Fraction Wall (Carol Bloomfield) PDF
• Colour Fraction Wall (Carole-Ann Balaam) DOC
• Equivalent Fraction Strips (Jennifer Orgill) DOC
• Fraction Wall (Jackie Launders) PDF
• Fraction Wall (Mandy Smith) PDF
• Fractions Cards (Joanne Nalton) DOC
• Large Fraction Wall (Jeremy Harris) DOC
• Would You Rather Have. (Clare Martin)
• Fractions Test (Leanne Wilson) DOC
• Fractions – thirds fifths (Rachael Wilkie)
• What fraction is shaded? (Kate Warner)
• Introducing Fractions (Steve Kersys)
• Fractions 1 (Gareth Rossiter)
• Fractions 2 (Gareth Rossiter)
• Equivalent Fractions (Sarah Sergeant)
• Smartie Fractions (Sheila Black) PDF
• Smartie Fractions (Mandy Smith) PDF
• Fractions Worksheets (Gareth Rossiter) PDF
• Ordering Fractions (Nadine Turner) PDF
• Fraction Mats (Stuart Arlow) DOC
• Whole, Halves and Quarters (Rachael Wilkie) DOC
• Equivalent Fractions (Christina Holmes)
• Fraction Numberlines (Eve Croft) DOC
• Fraction Number Lines (Rhodri Thomas) DOC
• Pizza Maths – Fractions of amounts (5 sheets) PDF
• Equivalent Fractions Match Up (Louise Macdonald) DOC
• Fractions Word Problems (Louise Macdonald) DOC
• Shade One Half / Quarter (Cindy Hoy) DOC
• Fractions of Shapes (Jay Birmingham) DOC
• Fractions of Quantities Problems (Helen Langford) DOC
• Fraction Posters (Paula Alty DOC
• Fractions (Paul Rigby)
• Fractions of Shapes Amounts (Yvonne Anderson)
• Equivalent Fractions (Margaret Carr)
• Fractions (T1 U11 Day 1) (Louise Hutchinson)
• Fractions (T1 U11 Day 2) (Louise Hutchinson)
• Fractions (T1 U11 Day 4) (Louise Hutchinson)
• Numerators and Denominators (Natasha Duffy)
• Pizza Problems (Georgina Burtenshaw)
• The Fraction Hunter’s Story (Hilary Minor) PDF
• Simple Fraction Problems (Stephen Norwood) PDF
• Equivalent Fractions (Kevin Kerr) PDF
• Fraction Circles (Mandy Smith) DOC
• Coloured Fraction Wall (Karen Holt) DOC
• Fractions of Sets (LA) (Bindiya Bhudia) DOC
• Fractions of Money (Rosie Iribas) DOC
• Mixed Number Pizzas 1 (Carole-Ann Balaam)
• Mixed Number Pizzas 2 (Carole-Ann Balaam)
• Fraction Wall and Questions (Jay Birmingham) DOC
• Adding Fractions to Make One Whole (Meryl York) DOC
• Putting Fractions on a Number Line (Anne Hayton)
• One and Two Step Fraction Problems (Carrie Magee) DOC
• Fractions Cards (to order) HA (Nick Hutson) DOC
• Fractions Cards (to order) LA (Nick Hutson) DOC
• Fractions (Aimi Kinsey-Jones) DOC
• Adding Subtracting Fractions with Same Denominators (Victoria Scott) DOC
• Compare Order Fractions with Same Denominators (Victoria Scott) DOC
• Which is Bigger? (Emma Allonby)
• Equivalent Fractions Lesson (Zip) (Shaun Kelliher)
• Fractions of Recipes (J. Adams) DOC
• Types of Fractions Poster (Cath Walls) DOC
• Finding Fractions of Numbers using Rectangles (Paul Wren) DOC
• Colour the Fractions (Matt Lovegrove)
• Build the Fraction Wall (Dot Hullah)
• Fractions Equivalent to a Half (Joanne Pooley)
• Fractions (WWtbaM) (Dot Hullah)
• Comparing and Ordering Fractions (Katherin Weeks)
• T1 U11 Fractions and Decimals (David Arthur)
• Fraction Problems (Anna Mongan) PDF
• Finding Fractions of Whole Numbers (Hilary Minor) PDF
• Real Life Fractions (2 sheets) (Cara Hayman) PDF
• A Fraction of the Problem (2 sheets) (Cara Hayman) PDF
• Fractions of Numbers (Rosie Iribas) DOC
• Toy Sale Fractions (Kath Huggett) DOC
• Fractions Sale (Louise Pickering) PDF
• Improper Fractions to Mixed Numbers (Becky Cheshire) DOC
• Shade the Fractions (Melanie Osborne)
• Fraction Wall Questions (Pete Smith) DOC
• Shade Equivalent Fractions (Joanna Martin)
• Equivalent Fractions (Jay Birmingham) DOC
• Equivalent Fractions Display (Diane Hartley) DOC
• Fraction Matching (Helen Graham) DOC
• Equivalent Fractions to One Half/Quarter (Meryl York) DOC
• Fraction Cards That Total 1 (Linda Kielty/Ceri Hill) DOC
• Fraction Cards to Total 1 (Claire Richmond) DOC
• Fractions of Quartiles (Rebecca Joyce)
• Chocolate Fractions (Shaun Kelliher) DOC
• What Fraction is Shaded? (Gwyneth Pocock) DOC
• Fraction Flags (Claire Richmond) DOC
• Finding Equivalent Fractions (Morag Watson)
• Finding Fractions of Numbers (Jennifer Craft)
• Finding Fractions of Whole Numbers (Dhipa Begum) DOC
• Fraction Cake Activity Recipe (Alison Richmond) DOC
• Reducing Fractions (Louise Whitby)
• Comparing Fractions (Susan Williams)
• Multiplying Dividing Fractions (Joe Pinnock) DOC
• Multiplying Fractions (Triangle) Jigsaw (Peter Barnett) PDF
• Multiplying Fractions (Rhombus) Jigsaw (Peter Barnett) PDF
• Multiplying Dividing Fractions (Peter Barnett)
• Equivalent Fraction Cards (Lisa Dunn) DOC
• Adding Subtracting Fractions Jigsaw (Peter Barnett) PDF
• Simplifying Fractions (Jessica Ganley)
• Dividing Fractions (Triangle) Jigsaw (Peter Barnett) PDF
• Dividing Fractions (Rhombus) Jigsaw (Peter Barnett) PDF

## Equivalent Fractions #answers #to #impossible #quiz

#

You can multiply the numerator and the denominator of a fraction by any nonzero whole number, as long as you multiply both by the same whole number! For example, you can multiply the numerator and the denominator by 3. as shown in part A above. But you cannot multiply the numerator by 3 and the denominator by 5. You can multiply the numerator and the denominator by 4. as shown in part B above. But you cannot multiply the numerator by 4 and the denominator by 2.

The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions. You may be wondering why this is so. In the last lesson, we learned that a fraction that has the same numerator and denominator is equal to one. This is shown below.

In example 6, the fraction given in part a is a proper fraction; whereas the fractions given in parts b and c are improper fractions. Note that the procedure for finding equivalent fractions is the same for both types of fractions. Looking at each part of example 6, the answers vary, depending on the nonzero whole number chosen. However, the equivalent fractions found in each part all have the same value.

Write the fraction five-sixths as an equivalent fraction with a denominator of 24.

In example 7, we multiplied the numerator AND the denominator by 4.

Write the fraction two-sevenths as an equivalent fraction with a denominator of 21.

In example 8, we multiplied the numerator AND the denominator by 3.

Write the fraction three-eighths as an equivalent fraction with a numerator of 15.

In example 9, we multiplied the numerator AND the denominator by 5.

We can now redefine the terms fraction and equivalent fraction as follows:

Equivalent fractions are different fractions that name the same number. The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions.

### Exercises

In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Note: To write the fraction two-thirds, enter 2/3 into the form.

Are the fractions three-fourths and fourteen-sixteenths equivalent (Yes or No)?

#

# Understanding Equivalent Fractions

The best way to think about equivalent fractions is that they are fractions that have the same overall value .

For example, if we cut a pie exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.

And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the same amount of pie that 1/2 did.

So we can say that 1/2 is equivalent (or equal) to 2/4.

## Don’t let equivalent fractions confuse you!

Take a look at the four circles above.Can you see that the one 1/2 , the two 1/4 and the four 1/8 take up the same amount of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also equal to 4/8. And yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you already know, we are nuts about rules. So, let s look at the Rule to check to see if two fractions are equivalent or equal. The rule for equivalent fractions can be a little tough to explain, but hang in there, we will clear things up in just a bit.

## Here s the Rule

What this Rule says is that two fractions are equivalent (equal) only if the product of the numerator (a ) of the first fraction and the denominator (d ) of the other fraction is equal to the product of the denominator (b ) of the first fraction and the numerator (c ) of the other fraction.

A product simply means you multiply.

## Test the Rule

Now let s plug the numbers into the Rule for equivalent fractions to be sure you have it down cold . 3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3 ) of the first fraction and the denominator (12 ) of the other fraction is equal to the product of the denominator (4 ) of the first fraction and the numerator (9 ) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3 12=36 and 4 9=36. A simple way to look at how to check for equivalent fractions is to do what is called cross-multiply , which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

### The graphic below shows you how to cross multiply

Okay, let s do one with numbers where the fractions are not equivalent

#

# Fractions Worksheets

Fractions Worksheets Sub-Topics

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person’s life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren’t that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they’ll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting. by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Multiplying and Dividing Fractions (A)

Adding and Subtracting Mixed Fractions (A)

Adding Fractions with Unlike Denominators (A)

Converting Mixed Fractions to Improper Fractions (A)

Adding and Subtracting Fractions — No Mixed Fractions (A)

Simplify Proper Fractions to Lowest Terms (Harder Version) (A)

Converting Fractions to Terminating and Repeating Decimals (A)

Missing Numbers in Equivalent Fractions (A)

Multiplying and Dividing Mixed Fractions (A)

Subtracting Fractions with Unlike Denominators (A)

## General Use Fractions Printables

General use fractions printables that are used in a variety of contexts when understanding and calculating fractions.

The black and white fraction circles can be used as a manipulative to compare fractions. Photocopy the worksheet onto an overhead projection slide. Use a pencil to lightly color the appropriate circle to represent the first fraction on the paper copy. Use a non-permanent overhead pen to color the appropriate circle to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Fraction strips can be laminated for durability and cut out to compare, order, add and subtract fractions. They are very useful for comparing fractions. You can also copy the fractions strips onto overhead projection slides and cut them out. Not only will they be durable, they will also be transparent which is useful when used in conjunction with paper versions (e.g. for comparing fractions).

## Comparing Ordering Fractions Worksheets

Comparing and ordering fractions worksheets for learning about the relative sizes of fractions.

There are many different strategies other than staring at the page that will help in comparing fractions. Try starting with something visual that will depict the fractions in question. We highly recommend our fraction strips (scroll up a bit). Using a straight edge like a ruler or book or folding will help students to easily see which fraction is greater or if they are equal. We should also mention that the things that are compared should be the same. Each fraction strip for example is the same size whereas if you took a third of a watermelon and half of a grape, the watermelon would probably win out.

Another strategy to use when comparing fractions is to use a number line and to use benchmarks like 0, 1, 1/2 to figure out where each fraction goes then see which one is bigger. Students actually do this one all the time since they can often compare fractions by recognizing that one is less than half and the other is greater than half. They might also see that one fraction is much closer to a whole than another fraction even though they might both be greater than a half.

We’ll mention one other strategy, but there are more. This one requires a little bit more knowledge, but it works out well in the long run because it is a certain way of comparing fractions. Convert each fraction to a decimal and compare the decimals. Decimal conversions can be memorized (especially for the common fractions) calculated with long division or using a calculator or look-up table. We suggest the latter since using a look-up table often leads to mental recall.

Comparing simple fractions.

Comparing Simple and Improper Fractions

Comparing Simple, Improper and Mixed Fractions

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We’ve probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won’t cut it. Try using some visuals to reinforce this important concept. Even though we’ve included number lines below, feel free to use your own strategies.

Ordering fractions with easy denominators on a Number Line.

Ordering fractions with all denominators on a Number Line.

## Simplifying Converting Fractions Worksheets

Simplifying fractions and converting fractions to other number formats worksheets to give students some necessary skills for more complex fractions topics.

Learning how to simplify fractions makes a student’s life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

Converting fractions to other fractions .

Order of Operations with Fractions .

As with other order of operation worksheets, the fractions order of operations worksheets require some pre-requisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what pre-requisite knowledge is missing then spend some time going over those concepts/skills before proceeding. Otherwise, the worksheets below should have fairly straight-forward answers and shouldn’t result in too much hair loss.

Order of Operations with Fractions Decimals .

You may use the math worksheets on this website according to our Terms of Use to help students learn math.

#

# Math Homework Help for Fractions

This introduction will be great math homework help for fractions. You’ll get a quick refresher on fraction fundamentals and the other concepts needed to do your lessons.

The information on this page may seem like a lot of details to remember, but I promise we ll get you through the actual math lessons like a breeze! This page is simply a tool that takes the place of a boring Glossary of Terms.

Math is a building process. To work with fractions, the student needs, at a minimum, strong skills in mathematical fundamentals including adding, subtracting, multiplying and dividing. Without these basic skills, attempting to do higher level work such as fractions will be very frustrating to the student. If the student is weak in these areas, time is better spent reviewing the basics for additional help.

## General Homework Help

### The Basic Concept of a Fraction

Before you can make heads or tails out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.

### Definition of a Fraction

You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by a/b. where a and b are whole numbers and b is not equal to 0 .

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes

There are three distinct meanings of fractions —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

The Part-Whole The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole

As a homework helper, this table shows you how the same whole can be divided into a different number of equal parts.

The Division Symbol ( / or __ ) used in a fraction tells you that everything above the division symbol is the numerator and must be treated as if it were one number, and everything below the division symbol is the denominator and also must be treated as if it were one number.

Basically, the numerator tells you how many part we are talking about, and the denominator tells you how many parts the whole is divided into. So a fraction like 6/7 tells you that we are looking at six (6 ) parts of a whole that is divided into seven (7 ) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

A Quotient The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

But what if you only have two cookies?

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

Here s a brief explanation of

A Ratio A comparison of things as a ratio can be expressed in one of two ways: first, the old fashioned method, a:b. pronounced a is to b ; and second, as found in newer books, a/b. If the ratio of a to b is 1 to 4 , or 1/4. then a is one-quarter of b . Alternately, b is four times as great as a .

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or

7ft/19ft = 7/19
Since we are comparing feet to feet, we don t need to write the units.

The ratio of its length to its width is 19 to 7

That was already a lot of homework help and you haven t worked a problem yet. So let s put some this stuff to WORK! But remember this is NOT the actual lesson. just a quick overview of some to the RULES and PRINCIPLES we ll need to use when working with fractions. Don t worry about memorizing everything, you ll see all of this stuff again as they apply to a particular operation during the homework lessons. So

We ll finish up with the

## Rules for Fraction Operations

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

1. Build each fraction (if needed) so that both denominators are equal.
2. Add the numerators of the fractions.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Subtracting Fractions

To subtract fractions, the denominators must be equal. You basically following the same steps as in addition.

1. Build each fraction (if required) so that both denominators are equal.
2. Combine the numerators according to the operation of subtraction.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Multiplying Fractions

To multiply two simple fractions, complete the following steps.

1. Multiply the numerators.
2. Multiply the denominators.
3. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To multiply a whole number and a fraction. complete the following steps.

1. Convert the whole number to a fraction.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Dividing Fractions

To divide one fraction by a second fraction. convert the problem to multiplication and multiply the two fractions.

1. Change the ÷ sign to x and invert the fraction to the right of the sign.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To divide a fraction by a whole number. convert the division process to a multiplication process, by using the following steps.

1. Convert the whole number to a fraction.
2. Change the ÷ sign to x and invert the fraction to the right of the sign.
3. Multiply the numerators.
4. Multiply the denominators.
5. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

## Multiplying Fractions Math Practice #mad #gab #phrases #and #answers

#fraction problems with answers

#

Press here to CLOSE X Instructions for Fraction Multiplication

## Multiply the fractions

on the left and simplify the answer to its lowest terms. Type in the numerator and denominator in the

## fraction

on right side of the equal sign. When both the numerator and denominator are correct, the

## fraction multiplication problem

will change color. Use the arrow keys or mouse to move between the numerator and denominator.

## Multiplying fractions

can be pretty difficult – if you need help you can move the mouse pointer over the question mark to see the solution. Click on the

## fraction

problem, press the ENTER or RETURN key, or click on the reset problem button to set a new fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of fraction problems by clicking up and down by the 25 default. After you think you’ve correctly multiplied the fractions, reset it. Please note the problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen.

#

# Understanding Equivalent Fractions

The best way to think about equivalent fractions is that they are fractions that have the same overall value .

For example, if we cut a pie exactly down the middle, into two equally sized pieces, one piece is the same as one half of the pie.

And if another pie (the same size) is cut into 4 equal pieces, then two pieces of that pie represent the same amount of pie that 1/2 did.

So we can say that 1/2 is equivalent (or equal) to 2/4.

## Don’t let equivalent fractions confuse you!

Take a look at the four circles above.Can you see that the one 1/2 , the two 1/4 and the four 1/8 take up the same amount of area colored in orange for their circle?Well that means that each area colored in orange is an equivalent fraction or equal amount. Therefore, we can say that 1/2 is equal to 2/4, and 1/2 is also equal to 4/8. And yes grasshopper, 2/4 is an equivalent fraction for 4/8 too.As you already know, we are nuts about rules. So, let s look at the Rule to check to see if two fractions are equivalent or equal. The rule for equivalent fractions can be a little tough to explain, but hang in there, we will clear things up in just a bit.

## Here s the Rule

What this Rule says is that two fractions are equivalent (equal) only if the product of the numerator (a ) of the first fraction and the denominator (d ) of the other fraction is equal to the product of the denominator (b ) of the first fraction and the numerator (c ) of the other fraction.

A product simply means you multiply.

## Test the Rule

Now let s plug the numbers into the Rule for equivalent fractions to be sure you have it down cold . 3/4 is equivalent (equal) to 9/12 only if the product of the numerator (3 ) of the first fraction and the denominator (12 ) of the other fraction is equal to the product of the denominator (4 ) of the first fraction and the numerator (9 ) of the other fraction. So we know that 3/4 is equivalent to 9/12, because 3 12=36 and 4 9=36. A simple way to look at how to check for equivalent fractions is to do what is called cross-multiply , which means multiple the numerator of one fraction by the denominator of the other fraction. Then do the same thing in reverse. Now compare the two answers to see if they are equal. If they are equal, then the two fractions are equivalent fractions.

### The graphic below shows you how to cross multiply

Okay, let s do one with numbers where the fractions are not equivalent

## Primary Resources: Maths: Numbers and the Number System: Fractions, Decimals – Percentages #answers #to #bible #questions

#

• Fractions 1: Mixed Numbers (Reuben McIntyre)
• Fractions 2: Improper Fractions (Reuben McIntyre)
• Fractions 3: Equivalet Fractions (Reuben McIntyre)
• Fractions 4: Simplifying Fractions (Reuben McIntyre)
• Fractional Parts of Shapes (R. Lovelock)
• Fractions Marking Ladder (Y1-4) Spring 1 (Victoria Scott) DOC
• Fractions 5: Fractions of Whole Numbers (Reuben McIntyre)
• Fractions 6: Adding Fractions (Reuben McIntyre)
• Fractions (Quarters) (Tracey Short) DOC
• Fractions to Order (Lisa Dunn) DOC
• Fractions Display Cards (Jane Campbell) DOC
• Colour One Half (Margaret-Anne McGinley) DOC
• Colour Half and Quarters (Sarah Dibley) DOC
• Halves and Quarters Shading (Jackie Simbler) DOC
• Basic Fractions (Adam Jewkes)
• Fractions (Halves) (Lisa Mary McNamee)
• Fun Fractions (3 dif. sheets) (Cara Hayman) PDF
• Quarter It! (Jackie Chidwick) PDF
• Half of numbers (Sheena Florey) PDF
• Fractions of Shapes (Block E Unit 2) (David-Guy Parkin) DOC
• Half or Not Half (Dhipa Begum) DOC
• Shade One Half and One Quarter (Dhipa Begum) DOC
• Shade Quarters (Dhipa Begum) DOC
• Simple Fractions (Peter Dunbar) PDF
• Fractions of Quantities (Mark Wilson) DOC
• Shade Two Thirds (Elaine Smith)
• Finding a Half (Kat Hester)
• Fractions of Shapes (Emma Foster) DOC
• Fractions of Numbers (Emma Foster) DOC
• Fractions Problems (Cara Lynch) DOC
• Halves and Quarters Shading (Gaynor Davis) DOC
• Halving (Karen Mercer)
• Introduction to Fractions (Emily Corble)
• Fractions (Liz Hazelden) DOC
• Fractions for Beginners (Carol Wright) DOC
• Hatching Fractions (Arthur Daley) PDF
• Pizza Fractions (Vicky Frampton) DOC
• Colour Halves and Quarters (Gwyneth Pocock) DOC
• Fraction Walls (blank) (Gareth Pitchford)
• Interactive Fraction Wall (Lorraine Oldale)
• Fraction Target Board (Liz Greenwood) PDF
• Fraction Wall (Carol Bloomfield) PDF
• Colour Fraction Wall (Carole-Ann Balaam) DOC
• Equivalent Fraction Strips (Jennifer Orgill) DOC
• Fraction Wall (Jackie Launders) PDF
• Fraction Wall (Mandy Smith) PDF
• Fractions Cards (Joanne Nalton) DOC
• Large Fraction Wall (Jeremy Harris) DOC
• Would You Rather Have. (Clare Martin)
• Fractions Test (Leanne Wilson) DOC
• Fractions – thirds fifths (Rachael Wilkie)
• What fraction is shaded? (Kate Warner)
• Introducing Fractions (Steve Kersys)
• Fractions 1 (Gareth Rossiter)
• Fractions 2 (Gareth Rossiter)
• Equivalent Fractions (Sarah Sergeant)
• Smartie Fractions (Sheila Black) PDF
• Smartie Fractions (Mandy Smith) PDF
• Fractions Worksheets (Gareth Rossiter) PDF
• Ordering Fractions (Nadine Turner) PDF
• Fraction Mats (Stuart Arlow) DOC
• Whole, Halves and Quarters (Rachael Wilkie) DOC
• Equivalent Fractions (Christina Holmes)
• Fraction Numberlines (Eve Croft) DOC
• Fraction Number Lines (Rhodri Thomas) DOC
• Pizza Maths – Fractions of amounts (5 sheets) PDF
• Equivalent Fractions Match Up (Louise Macdonald) DOC
• Fractions Word Problems (Louise Macdonald) DOC
• Shade One Half / Quarter (Cindy Hoy) DOC
• Fractions of Shapes (Jay Birmingham) DOC
• Fractions of Quantities Problems (Helen Langford) DOC
• Fraction Posters (Paula Alty DOC
• Fractions (Paul Rigby)
• Fractions of Shapes Amounts (Yvonne Anderson)
• Equivalent Fractions (Margaret Carr)
• Fractions (T1 U11 Day 1) (Louise Hutchinson)
• Fractions (T1 U11 Day 2) (Louise Hutchinson)
• Fractions (T1 U11 Day 4) (Louise Hutchinson)
• Numerators and Denominators (Natasha Duffy)
• Pizza Problems (Georgina Burtenshaw)
• The Fraction Hunter’s Story (Hilary Minor) PDF
• Simple Fraction Problems (Stephen Norwood) PDF
• Equivalent Fractions (Kevin Kerr) PDF
• Fraction Circles (Mandy Smith) DOC
• Coloured Fraction Wall (Karen Holt) DOC
• Fractions of Sets (LA) (Bindiya Bhudia) DOC
• Fractions of Money (Rosie Iribas) DOC
• Mixed Number Pizzas 1 (Carole-Ann Balaam)
• Mixed Number Pizzas 2 (Carole-Ann Balaam)
• Fraction Wall and Questions (Jay Birmingham) DOC
• Adding Fractions to Make One Whole (Meryl York) DOC
• Putting Fractions on a Number Line (Anne Hayton)
• One and Two Step Fraction Problems (Carrie Magee) DOC
• Fractions Cards (to order) HA (Nick Hutson) DOC
• Fractions Cards (to order) LA (Nick Hutson) DOC
• Fractions (Aimi Kinsey-Jones) DOC
• Adding Subtracting Fractions with Same Denominators (Victoria Scott) DOC
• Compare Order Fractions with Same Denominators (Victoria Scott) DOC
• Which is Bigger? (Emma Allonby)
• Equivalent Fractions Lesson (Zip) (Shaun Kelliher)
• Fractions of Recipes (J. Adams) DOC
• Types of Fractions Poster (Cath Walls) DOC
• Finding Fractions of Numbers using Rectangles (Paul Wren) DOC
• Colour the Fractions (Matt Lovegrove)
• Build the Fraction Wall (Dot Hullah)
• Fractions Equivalent to a Half (Joanne Pooley)
• Fractions (WWtbaM) (Dot Hullah)
• Comparing and Ordering Fractions (Katherin Weeks)
• T1 U11 Fractions and Decimals (David Arthur)
• Fraction Problems (Anna Mongan) PDF
• Finding Fractions of Whole Numbers (Hilary Minor) PDF
• Real Life Fractions (2 sheets) (Cara Hayman) PDF
• A Fraction of the Problem (2 sheets) (Cara Hayman) PDF
• Fractions of Numbers (Rosie Iribas) DOC
• Toy Sale Fractions (Kath Huggett) DOC
• Fractions Sale (Louise Pickering) PDF
• Improper Fractions to Mixed Numbers (Becky Cheshire) DOC
• Shade the Fractions (Melanie Osborne)
• Fraction Wall Questions (Pete Smith) DOC
• Shade Equivalent Fractions (Joanna Martin)
• Equivalent Fractions (Jay Birmingham) DOC
• Equivalent Fractions Display (Diane Hartley) DOC
• Fraction Matching (Helen Graham) DOC
• Equivalent Fractions to One Half/Quarter (Meryl York) DOC
• Fraction Cards That Total 1 (Linda Kielty/Ceri Hill) DOC
• Fraction Cards to Total 1 (Claire Richmond) DOC
• Fractions of Quartiles (Rebecca Joyce)
• Chocolate Fractions (Shaun Kelliher) DOC
• What Fraction is Shaded? (Gwyneth Pocock) DOC
• Fraction Flags (Claire Richmond) DOC
• Finding Equivalent Fractions (Morag Watson)
• Finding Fractions of Numbers (Jennifer Craft)
• Finding Fractions of Whole Numbers (Dhipa Begum) DOC
• Fraction Cake Activity Recipe (Alison Richmond) DOC
• Reducing Fractions (Louise Whitby)
• Comparing Fractions (Susan Williams)
• Multiplying Dividing Fractions (Joe Pinnock) DOC
• Multiplying Fractions (Triangle) Jigsaw (Peter Barnett) PDF
• Multiplying Fractions (Rhombus) Jigsaw (Peter Barnett) PDF
• Multiplying Dividing Fractions (Peter Barnett)
• Equivalent Fraction Cards (Lisa Dunn) DOC
• Adding Subtracting Fractions Jigsaw (Peter Barnett) PDF
• Simplifying Fractions (Jessica Ganley)
• Dividing Fractions (Triangle) Jigsaw (Peter Barnett) PDF
• Dividing Fractions (Rhombus) Jigsaw (Peter Barnett) PDF

## Fraction Math Problems – Fractions Practice #bible #questions #answers

#

Press here to CLOSE X

Now practice fractions anywhere! We have fractions math teaching resources optimized for cell phones. Access Mr. Martini’s Classroom Fractions page using your smartphone and you will automatically go to a special fractions for cell phones page. We have addition, subtraction, division, and multiplication flash cards optimized for Android and other smartphones.

Press here to CLOSE X Instructions for Fractions

Practice solving fractions with math student and teacher resources. Click on a box in the middle column to select the type of online fraction practice you would like to do. You can practice solving fractional equivalents, solving fraction greater than or less than problems, simplifying fractions to their lowest terms, adding fractions, dividing fractions, or multiplying fractions. Each fraction math problem will have its own set of instructions, but they all will change color when they are correct. When doing fraction addition, fraction division, or fraction multiplication, the answer must be simplified to be correct. Click on the fraction problem, press the ENTER or RETURN key, or click on the reset problem button to reset the online fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of problems by clicking up and down by the 25 default. After you think you’ve correctly solved the fraction problem, reset it. Please note the fraction math problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen. When you’re done practicing, challenge yourself with an online fraction quiz.

# Fractions

## Free equivalent fractions worksheets with visual models #free #homework #answers

#

You are here: Home Worksheets Equivalent fractions

# Free Equivalent Fractions Worksheets

Create an unlimited supply of worksheets for equivalent fractions (grades 4-5)! The worksheets can be made in html or PDF format both are easy to print. You can also customize them using the generator below .

Students usually encounter the concept of equivalent fractions in 4th grade (such as 1/2 = 5/10). Visual models are essential in helping children to grasp this idea, and the worksheets below provide just that!

Then, in 5th grade, students learn how to add unlike fractions. This procedure involves converting the fractions to equivalent fractions with a common denominator. So, the concept of equivalent fractions is an important prerequisite to fraction addition and subtraction.

## Basic instructions for the worksheets

Each worksheet is randomly generated and thus unique. The answer key is automatically generated and is placed on the second page of the file.

You can generate the worksheets either in html or PDF format both are easy to print. To get the PDF worksheet, simply push the button titled “Create PDF ” or “Make PDF worksheet “. To get the worksheet in html format, push the button “View in browser ” or “Make html worksheet “. This has the advantage that you can save the worksheet directly from your browser (choose File Save) and then edit it in Word or other word processing program.

Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:

• PDF format: come back to this page and push the button again.
• Html format: simply refresh the worksheet page in your browser window.

## Equivalent fractions with visual models

The two equivalent fractions are shown; student colors the pie models

Two pie models are already colored; student writes the fractions

Two pie images; one is colored, the other is not, the student writes both fractions

Two pie images to color, one fraction is given, one not

Allow improper fractions, the student writes both fractions

Allow mixed numbers, the student writes both mixed numbers

Allow mixed numbers and improper fractions, the student writes both fractions/mixed numbers

Allow mixed numbers and improper fractions, one fraction is given, the other not

## Equivalent fractions without visual models

Write the missing part, small denominators
(e.g. 2/3 = ?/12)

Improper fractions allowed, small denominators (e.g. 7/4 = ?/16)

Equivalent mixed numbers, small denominators
(e.g. 2 3/4 = 2 ?/12)

Both mixed numbers and improper fractions allowed, small denominators

The following worksheets are similar to the ones above, but using larger numbers in the denominators and numerators.

Equivalent fractions, proper fractions only

Improper fractions allowed
(e.g. 17/14 = ?/56)

Includes mixed numbers

Includes both improper fractions and mixed numbers

## Generator

With this worksheet generator, you can make worksheets for equivalent fractions. The worksheet can include problems with visual models (pie images) or not. There are five problem types to choose from:

1. Two fractions are given with 2 empty pie images to color in (e.g. 3/5 = 6/10).
2. There are 2 pie images that are already colored; the student writes both fractions.
3. Two pie images are given, one colored in, one not; the student writes both fractions.
4. There are 2 pie images to color, one fraction is given, one not (e.g. 4/5 = / )
5. Problems without any visual model; the student writes the missing numerator or denominator in one of the fractions (e.g. 2/3 = /12).

You can choose to include or not include mixed numbers and improper fractions. You can control the minimum and maximum values for the numerator and the denominator. However, for the problems with visual models, the maximum denominator is limited to 16.

## Equivalent Fractions Worksheet Generator

#### Math Made Easy, Grade 4 Math Workbook

This workbook has been compiled and tested by a team of math experts to increase your child’s confidence, enjoyment, and success at school. Fourth Grade: Provides practice at all the major topics for Grade 4 with emphasis on multiplication and division of larger numbers. Includes a review of Grade 3 topics and a preview of topics in Grade 5. Includes Times Tables practice.

## Equivalent Fractions #answer #math #problems

#

You can multiply the numerator and the denominator of a fraction by any nonzero whole number, as long as you multiply both by the same whole number! For example, you can multiply the numerator and the denominator by 3. as shown in part A above. But you cannot multiply the numerator by 3 and the denominator by 5. You can multiply the numerator and the denominator by 4. as shown in part B above. But you cannot multiply the numerator by 4 and the denominator by 2.

The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions. You may be wondering why this is so. In the last lesson, we learned that a fraction that has the same numerator and denominator is equal to one. This is shown below.

In example 6, the fraction given in part a is a proper fraction; whereas the fractions given in parts b and c are improper fractions. Note that the procedure for finding equivalent fractions is the same for both types of fractions. Looking at each part of example 6, the answers vary, depending on the nonzero whole number chosen. However, the equivalent fractions found in each part all have the same value.

Write the fraction five-sixths as an equivalent fraction with a denominator of 24.

In example 7, we multiplied the numerator AND the denominator by 4.

Write the fraction two-sevenths as an equivalent fraction with a denominator of 21.

In example 8, we multiplied the numerator AND the denominator by 3.

Write the fraction three-eighths as an equivalent fraction with a numerator of 15.

In example 9, we multiplied the numerator AND the denominator by 5.

We can now redefine the terms fraction and equivalent fraction as follows:

Equivalent fractions are different fractions that name the same number. The numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions.

### Exercises

In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Note: To write the fraction two-thirds, enter 2/3 into the form.

Are the fractions three-fourths and fourteen-sixteenths equivalent (Yes or No)?

#

# Fractions Worksheets

Fractions Worksheets Sub-Topics

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person’s life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren’t that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they’ll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting. by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Multiplying and Dividing Fractions (A)

Adding and Subtracting Mixed Fractions (A)

Adding Fractions with Unlike Denominators (A)

Converting Mixed Fractions to Improper Fractions (A)

Adding and Subtracting Fractions — No Mixed Fractions (A)

Simplify Proper Fractions to Lowest Terms (Harder Version) (A)

Converting Fractions to Terminating and Repeating Decimals (A)

Missing Numbers in Equivalent Fractions (A)

Multiplying and Dividing Mixed Fractions (A)

Subtracting Fractions with Unlike Denominators (A)

## General Use Fractions Printables

General use fractions printables that are used in a variety of contexts when understanding and calculating fractions.

The black and white fraction circles can be used as a manipulative to compare fractions. Photocopy the worksheet onto an overhead projection slide. Use a pencil to lightly color the appropriate circle to represent the first fraction on the paper copy. Use a non-permanent overhead pen to color the appropriate circle to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Fraction strips can be laminated for durability and cut out to compare, order, add and subtract fractions. They are very useful for comparing fractions. You can also copy the fractions strips onto overhead projection slides and cut them out. Not only will they be durable, they will also be transparent which is useful when used in conjunction with paper versions (e.g. for comparing fractions).

## Comparing Ordering Fractions Worksheets

Comparing and ordering fractions worksheets for learning about the relative sizes of fractions.

There are many different strategies other than staring at the page that will help in comparing fractions. Try starting with something visual that will depict the fractions in question. We highly recommend our fraction strips (scroll up a bit). Using a straight edge like a ruler or book or folding will help students to easily see which fraction is greater or if they are equal. We should also mention that the things that are compared should be the same. Each fraction strip for example is the same size whereas if you took a third of a watermelon and half of a grape, the watermelon would probably win out.

Another strategy to use when comparing fractions is to use a number line and to use benchmarks like 0, 1, 1/2 to figure out where each fraction goes then see which one is bigger. Students actually do this one all the time since they can often compare fractions by recognizing that one is less than half and the other is greater than half. They might also see that one fraction is much closer to a whole than another fraction even though they might both be greater than a half.

We’ll mention one other strategy, but there are more. This one requires a little bit more knowledge, but it works out well in the long run because it is a certain way of comparing fractions. Convert each fraction to a decimal and compare the decimals. Decimal conversions can be memorized (especially for the common fractions) calculated with long division or using a calculator or look-up table. We suggest the latter since using a look-up table often leads to mental recall.

Comparing simple fractions.

Comparing Simple and Improper Fractions

Comparing Simple, Improper and Mixed Fractions

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We’ve probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won’t cut it. Try using some visuals to reinforce this important concept. Even though we’ve included number lines below, feel free to use your own strategies.

Ordering fractions with easy denominators on a Number Line.

Ordering fractions with all denominators on a Number Line.

## Simplifying Converting Fractions Worksheets

Simplifying fractions and converting fractions to other number formats worksheets to give students some necessary skills for more complex fractions topics.

Learning how to simplify fractions makes a student’s life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

Converting fractions to other fractions .

Order of Operations with Fractions .

As with other order of operation worksheets, the fractions order of operations worksheets require some pre-requisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what pre-requisite knowledge is missing then spend some time going over those concepts/skills before proceeding. Otherwise, the worksheets below should have fairly straight-forward answers and shouldn’t result in too much hair loss.

Order of Operations with Fractions Decimals .

You may use the math worksheets on this website according to our Terms of Use to help students learn math.

#

# Math Homework Help for Fractions

This introduction will be great math homework help for fractions. You’ll get a quick refresher on fraction fundamentals and the other concepts needed to do your lessons.

The information on this page may seem like a lot of details to remember, but I promise we ll get you through the actual math lessons like a breeze! This page is simply a tool that takes the place of a boring Glossary of Terms.

Math is a building process. To work with fractions, the student needs, at a minimum, strong skills in mathematical fundamentals including adding, subtracting, multiplying and dividing. Without these basic skills, attempting to do higher level work such as fractions will be very frustrating to the student. If the student is weak in these areas, time is better spent reviewing the basics for additional help.

## General Homework Help

### The Basic Concept of a Fraction

Before you can make heads or tails out of fractions, it would be helpful if we first agree that the basic idea of a fraction can be ABSTRACT, unless we name the WHOLE to which we are referring. So it is important to keep this in mind while doing your assignments.

### Definition of a Fraction

You might recall that in math a number is a point on the number line. Well, there is a special collection of numbers called fractions, which are usually denoted by a/b. where a and b are whole numbers and b is not equal to 0 .

It may be helpful to get your homework off to a great start by defining what fractions are, that is to say, specifying which of the points on the number line are fractions.

So, here goes

There are three distinct meanings of fractions —part-whole, quotient, and ratio, which are found in most elementary math programs. To reduce confusion while using this homework helper, our lessons will only cover the part-whole relationship.

The Part-Whole The part-whole explanation of a fraction is where a number like 1/5 indicates that a whole has been separated into five equal parts and one of those parts are being considered.

This table is a great help to get a feel of how a fractional part compares to the whole

As a homework helper, this table shows you how the same whole can be divided into a different number of equal parts.

The Division Symbol ( / or __ ) used in a fraction tells you that everything above the division symbol is the numerator and must be treated as if it were one number, and everything below the division symbol is the denominator and also must be treated as if it were one number.

Basically, the numerator tells you how many part we are talking about, and the denominator tells you how many parts the whole is divided into. So a fraction like 6/7 tells you that we are looking at six (6 ) parts of a whole that is divided into seven (7 ) equal parts.

Although we do not cover fractions as a quotient or as a ratio, here is a brief explanation of them.

A Quotient The fraction 2/3 may be considered as a quotient, 2 ÷ 3. This explanation also arises from a dividing up situation.

Suppose you want to give some cookies to three people. Well, you could give each person one cookie, then another, and so on until you had given the same amount to each. So,

If you have six cookies, then you could represent this process with simple math by dividing 6 by 3, and each person would get two cookies.

But what if you only have two cookies?

One way to solve the problem is to break-up each cookie into three equal parts and give each person 1/3 of each cookie so that in the end, each person gets 1/3 + 1/3 or 2/3 cookies. So 2 divided by 3 = 2/3.

Here s a brief explanation of

A Ratio A comparison of things as a ratio can be expressed in one of two ways: first, the old fashioned method, a:b. pronounced a is to b ; and second, as found in newer books, a/b. If the ratio of a to b is 1 to 4 , or 1/4. then a is one-quarter of b . Alternately, b is four times as great as a .

The width of a rectangle is 7ft and its length is 19ft. The ratio of its width to its length is 7ft to 19 ft, or

7ft/19ft = 7/19
Since we are comparing feet to feet, we don t need to write the units.

The ratio of its length to its width is 19 to 7

That was already a lot of homework help and you haven t worked a problem yet. So let s put some this stuff to WORK! But remember this is NOT the actual lesson. just a quick overview of some to the RULES and PRINCIPLES we ll need to use when working with fractions. Don t worry about memorizing everything, you ll see all of this stuff again as they apply to a particular operation during the homework lessons. So

We ll finish up with the

## Rules for Fraction Operations

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

1. Build each fraction (if needed) so that both denominators are equal.
2. Add the numerators of the fractions.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Subtracting Fractions

To subtract fractions, the denominators must be equal. You basically following the same steps as in addition.

1. Build each fraction (if required) so that both denominators are equal.
2. Combine the numerators according to the operation of subtraction.
3. The new denominator will be the denominator of the built-up fractions.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Multiplying Fractions

To multiply two simple fractions, complete the following steps.

1. Multiply the numerators.
2. Multiply the denominators.
3. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To multiply a whole number and a fraction. complete the following steps.

1. Convert the whole number to a fraction.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

### Dividing Fractions

To divide one fraction by a second fraction. convert the problem to multiplication and multiply the two fractions.

1. Change the ÷ sign to x and invert the fraction to the right of the sign.
2. Multiply the numerators.
3. Multiply the denominators.
4. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

To divide a fraction by a whole number. convert the division process to a multiplication process, by using the following steps.

1. Convert the whole number to a fraction.
2. Change the ÷ sign to x and invert the fraction to the right of the sign.
3. Multiply the numerators.
4. Multiply the denominators.
5. Reduce or simplify your answer, if needed.
• Factor the numerator.
• Factor the denominator.
• Cancel-out fraction mixes that have a value of 1.
• Re-write your answer as a simplified or reduced fraction.

## Multiplying Fractions Math Practice #true #or #false #answers

#fraction problems with answers

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Press here to CLOSE X Instructions for Fraction Multiplication

## Multiply the fractions

on the left and simplify the answer to its lowest terms. Type in the numerator and denominator in the

## fraction

on right side of the equal sign. When both the numerator and denominator are correct, the

## fraction multiplication problem

will change color. Use the arrow keys or mouse to move between the numerator and denominator.

## Multiplying fractions

can be pretty difficult – if you need help you can move the mouse pointer over the question mark to see the solution. Click on the

## fraction

problem, press the ENTER or RETURN key, or click on the reset problem button to set a new fraction problem.

Click on the check mark at the bottom to keep score! You can choose the number of fraction problems by clicking up and down by the 25 default. After you think you’ve correctly multiplied the fractions, reset it. Please note the problem will not change color when it is keeping score in the challenge mode. Each time you reset the problem, the left counter increases for each correct answer; the right counter counts the number of problems you’ve done. If the answer isn’t right, the correct answer will display to the right of the counter when you reset the problem. When you’re done, your score will be shown on the screen.