Comparing Fractions Worksheet

Welcome to our Comparing Fractions Worksheets page.

Here you will find our selection of worksheets to help you to learn and practice comparing two or more fractions.

Comparing Fractions Worksheets

How do we compare fractions?

We can compare fractions using different ways.

  • using diagrams - this is a supported, easier way;
  • using knowledge of converting fractions to the same denominators which is harder.

One thing to remember is that if we are comparing two fractions without using diagrams, then it is much easier to do if they have the same denominator (or the same numerator).

Before you start comparing fractions, you should know about equivalent fractions.

Comparing fractions using diagrams

Using diagrams can be a great way to help children understand about comparing fractions.

Also, if we are used to seeing fractions visually, this can really help us get an understanding of how much of a whole they represent.

You can see and compare how much of each diagram is shaded and see which fraction is bigger, or whether they are the same size.

Example 1) Compare \[ {3 \over 4} \; and \; {5 \over 6} \]

We can use diagrams to look at two fraction circles with the relevant fractions shaded.

comparing fractions example 1

These diagrams clearly show that: \[ {3 \over 4} \] is the smaller of the two fractions as less of the diagram is shaded.

So we now know \[ {3 \over 4} \; < \; {5 \over 6} \]


Example 2) Let us compare \[ {2 \over 8} \; and \; {1 \over 4} \].

We can use diagrams to look at two fraction circles with the relevant fractions shaded.

comparing fractions example 2

These diagrams show the same amount shaded for each fraction, so the two fractions are equal.

We have found out that \[ {2 \over 8} \; = \; {1 \over 4} \].

Comparing fractions without diagrams

If there are no diagrams to help us, then we can use our knowledge of fractions to help us.

There are several examples given here which use different ways to compare the size of the fractions.

Example 1) Compare \[ {1 \over 2} \; and \; {3 \over 7} \]

If we are comparing a fraction with a half, it is usually quite quick and easy to tell whether it is bigger or not.

If a fraction is equivalent to a half, then the numerator is equal to half the denominator.

In this case, half of 7 = 3.5, so if the numerator was 3.5 the two fractions would be equal, or equivalent.

However, this numerator is equal to 3, which is smaller than 3.5, so the fraction is less than a half.

So this tells us \[ {1 \over 2} \; > \; {3 \over 7} \]


Example 2) Compare \[ {2 \over 5} \; and \; {3 \over 10} \]

We cannot directly compare these two fractions until their denominators are the same!

You will notice that in this case, one of the denominators is a multiple of the other: 10 is double 5.

So all we need to do is double the numerator and denominator of the first fraction to give us an equivalent fraction with the same denominator as the second fraction.

\[ {2 \over 5} = {2 \times 2 \over 5 \times 2} = {4 \over 10} \]

We can now compare the two fractions directly by looking at the numerators as the denominators are now the same.

4 is bigger than 3 so \[ {4 \over 10} \; > \; {3 \over 10}\]

So we have found out that \[ {2 \over 5} \; > \; {3 \over 10} \]


Example 3) Compare \[ {4 \over 9} \; and \; {3 \over 5} \]

These fractions are not multiples of each other but we can see that by comparing them each to a half, one is clearly bigger and the other is smaller.

If we look at \[ {4 \over 9} \] we can see that it is less than a half because the numerator is less than half of the denominator.

If we look at \[ {3 \over 5} \] we can see that it is more than a half because the numerator is greater than half of the denominator.

This tells us that \[ {4 \over 9} \; < \; {3 \over 5} \]


Example 4) Compare \[ {3 \over 7} \; and \; {3 \over 10} \]

You will notice that these fractions do not have the same denominator but they do have the same numerator.

This really helps us to compare them, because it means that if we think of fraction diagrams the circles have been split into different numbers of parts, but both fractions have the same number shaded in.

If we consider unit fractions, where the numerator is 1.

We know that: \[ {1 \over 7} \; > \; {1 \over 10} \] because the whole has been split into fewer pieces.

This tells us that \[ {3 \over 7} \; > \; {3 \over 10} \] because we are just shading in three pieces of each circle, and each of the sevenths is bigger than each of the tenths as the diagram below shows.

comparing fractions example 3


Example 5) Compare \[ {3 \over 7} \; and \; {2 \over 5} \]

If we look at both of these fractions, we can see (using the method above) that they are both smaller than a half.

We cannot directly compare these two fractions until their denominators are the same!

We now need to convert them both to fractions with the same denominator (or a common denominator) so we can compare them.

The best way to do this is to multiply the denominators together to tell us the denominator we need.

In this case 7 x 5 = 35, so we need a common denominator of 35.

To get a denominator of 35, we need to multiply the numerator and denominator of the first fraction by 5, and multiply the numerator and denominator of the 2nd fraction by 7.

This gives us: \[ {3 \over 7} \; = \; {3 \times 5 \over 7 \times 5} \; = \; {15 \over 35} \]

and \[ {2 \over 5} \; = \; {2 \times 7 \over 5 \times 7} \; = \; {14 \over 35} \]

Now that the fractions have the same denominator, we can compare the two numerators.

We can clearly see that \[ {15 \over 35} \; > \; {14 \over 35} \]

This tells us that: \[ {3 \over 7} \; > \; {2 \over 5} \]

Comparing Fractions Worksheets

Here you will find a selection of Fraction worksheets designed to help your child learn to compare and order fractions.

The sheets are carefully graded so that the easiest supported sheets come first, and the most difficult sheets come later on.

We have split the sheets into 5 sections with the first two section looking at comparing and ordering visual fractions using diagrams.

For the sheets in the third and fourth sections, children need to understand how to convert fractions to fractions with like denominators.

The 5th section is applying your knowledge and skills of comparing fractions to solving some comparing fraction riddles.

Using these sheets will help your child to:

  • understand how to compare fractions using diagrams;
  • practice comparing and ordering a range of fractions;
  • use equivalence to compare two fractions.

These sheets are suitable for 4th and 5th graders.

Section 1 - Comparing Fractions Worksheet with diagrams

These sheets are all about using fraction diagrams to compare two fractions.

Section 2 - Ordering Fractions Worksheet with diagrams

These sheets are similar to those in the section above, but you have to put 4 fractions in order from smallest to largest using diagrams for support.

Section 3 - Comparing Fractions Worksheet

These sheets are all about using fraction knowledge and converting fractions to the same denominator to compare two fractions.

Section 4 - Ordering Fractions Worksheets

These sheets are similar to those in the section above, but you have to put 5 fractions in order from smallest to largest.

Section 5 - Comparing Fractions Riddles

A great opportunity to test your fraction comparing skills and fraction knowledge to solve a range of fraction riddles!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Equivalent Fractions

Equivalent fractions are fractions which have the same value as each other.

Before you can compare fractions, you should have a good understanding of what equivalent fractions are.

The printable fraction page below contains more support, examples and practice using equivalent fractions.

Simplifying Fractions

Take a look at our Simplifying Fractions Practice Zone or try our worksheets for finding the simplest form for a range of fractions.

You can choose from proper fractions, improper fractions or both.

You can print out your results or benchmark your scores against future achievements.

Good for practising equivalent fractions as well as converting to simplest form.

Great for using with a group of children as well as individually.

Learning Fractions

Are you looking for free fraction help or fraction support?

Here you will find a range of fraction help on a variety of fraction topics, from simplest form to converting fractions.

There are fraction videos, worked examples and practice fraction worksheets.

Improper Fractions

We have a support page to help students understand how what improper fractions are and how to conver them.

We also have a wide range of Improper Fraction Worksheets, some of which use visual fractions to aid understanding and some sheets which are more abstract.

 

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