Equivalent Fractions, Help With Fractions, equivalent fractions answers.#Equivalent #fractions #answers


Equivalent Fractions

Equivalent fractions represent the same part of a whole

Equivalent fractions answers

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

Equivalent fractions answers

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.

That sounds like a mouthful, so let s try it with numbers

Equivalent fractions answers

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

Equivalent fractions answers

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


Equivalent Fractions, Help With Fractions, equivalent fractions answers.#Equivalent #fractions #answers


Equivalent Fractions

Equivalent fractions represent the same part of a whole

Equivalent fractions answers

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

Equivalent fractions answers

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.

That sounds like a mouthful, so let s try it with numbers

Equivalent fractions answers

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

Equivalent fractions answers

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


Grade 5 – Number – Fractions, Common Core State Standards Initiative, 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.


Fraction Game – Match Equivalent Fractions, equivalent fractions answers.#Equivalent #fractions #answers


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

Games

Worksheets

  • Equivalent fractions answersComparing Fractions (1 of 4) – two fractions – includes with fraction bar
  • Equivalent fractions answersComparing Fractions (2 of 4) – using common denominators
  • Equivalent fractions answersEquivalent Fractions (1 of 3) e.g. 1/3 = 3/9
  • Equivalent fractions answersEquivalent Fractions (2 of 3) e.g. 9/3 = 1/3
  • Equivalent fractions answersEquivalent Fractions (3 of 3)
  • Equivalent fractions answersReducing 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

  • Equivalent fractions answersComparing Fractions (From Page)
  • Equivalent fractions answersComparing Fractions (3 of 4) – ordering sets of three and four fractions (From Worksheets)
  • Equivalent fractions answersCommon Denominators (From Lessons)
  • Equivalent fractions answersImproper Fractions and Mixed Numbers (From Lessons)
  • Equivalent fractions answersSimplifying Fractions (From Lessons)

Adding Fractions with the Same Denominator, Help With Fractions, equivalent fractions answers.#Equivalent


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!

Equivalent fractions answers

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

Equivalent fractions answers

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.

How to Simplify Your Answers

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

Equivalent fractions answers

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.

Equivalent fractions answers

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

Equivalent fractions answers

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.

Equivalent fractions answers

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.


Fraction Game – Match Equivalent Fractions, equivalent fractions answers.#Equivalent #fractions #answers


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

Games

Worksheets

  • Equivalent fractions answersComparing Fractions (1 of 4) – two fractions – includes with fraction bar
  • Equivalent fractions answersComparing Fractions (2 of 4) – using common denominators
  • Equivalent fractions answersEquivalent Fractions (1 of 3) e.g. 1/3 = 3/9
  • Equivalent fractions answersEquivalent Fractions (2 of 3) e.g. 9/3 = 1/3
  • Equivalent fractions answersEquivalent Fractions (3 of 3)
  • Equivalent fractions answersReducing 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

  • Equivalent fractions answersComparing Fractions (From Page)
  • Equivalent fractions answersComparing Fractions (3 of 4) – ordering sets of three and four fractions (From Worksheets)
  • Equivalent fractions answersCommon Denominators (From Lessons)
  • Equivalent fractions answersImproper Fractions and Mixed Numbers (From Lessons)
  • Equivalent fractions answersSimplifying Fractions (From Lessons)

Equivalent Fraction Pairs, equivalent fractions answers.#Equivalent #fractions #answers


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 ‘clicks’ 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

Algebra Pairs

Equivalent fractions answers

Circle Pairs

Equivalent fractions answers

Circle Theorem Pairs

Equivalent fractions answers

Clock Times Pairs

Equivalent fractions answers

Fill Graph Pairs

Equivalent fractions answers

Formulae Pairs

Equivalent fractions answers

Formulae to Remember

Equivalent fractions answers

Fraction Decimal Pairs

Equivalent fractions answers

Fraction Percentage Pairs

Equivalent fractions answers

Hard Times

Equivalent fractions answers

Imperial Units Pairs

Equivalent fractions answers

Indices Pairs

Equivalent fractions answers

Math vs Maths Pairs

Equivalent fractions answers

Mathematician Pairs

Equivalent fractions answers

Metric Units Pairs

Equivalent fractions answers

Pairs 240

Equivalent fractions answers

Pairs Eleven

Equivalent fractions answers

Pairs Twenty One

Equivalent fractions answers

Rotational Symmetry Pairs

Equivalent fractions answers

Venn Diagram Pairs

Equivalent fractions answers

Sharon Fajou, Twitter

Wednesday, November 4, 2015

Friday, November 3, 2017

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Equivalent fractions answers

Equivalent fractions answers


Simplifying Fractions, equivalent fractions answers.#Equivalent #fractions #answers


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.

Equivalent fractions answers

Equivalent fractions answers

Equivalent fractions answers

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 24 108 :

Equivalent fractions answers Equivalent fractions answersEquivalent fractions answers

Equivalent fractions answers Equivalent fractions answersEquivalent fractions answers

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

Example: Simplify the fraction 10 35 :

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!

Equivalent fractions answers

Equivalent fractions answers

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 – Fractions, Common Core State Standards Initiative, 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.


Fractions Worksheets #online #math #answers


#math answers free

#

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 .

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