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Interactive Unit Fractions Drag unit fraction pieces (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1,10, 1/12, 1,16, and 1/20) onto a square that represents one whole. You can see that, for example, 6 pieces of 1/6 fit into one whole, or that 3 pieces of 1/9 are equal to 1/3, and many other similar relationships. /interactives/unit_fractions.php

You can also include visual models (fraction pies), which will make comparing easy and works well for making fraction comparison worksheets for grades 3-4.

To create problems where it is necessary to find a common denominator, choose "random fractions".

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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.

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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.

Our worksheets introduce the concept of comparing fractions in a visual way using shapes to aid understanding.

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Quicklinks to...

• How to Compare Fractions?
• All Comparing Fractions Worksheets
• Comparing Fractions Worksheets with diagrams
• Ordering Fractions Worksheets with diagrams
• Comparing Fractions Worksheets without diagrams
• Ordering Fractions Worksheets without diagrams
• Comparing Fractions Riddles
• More related Math resources

Comparing Fractions Online Quiz

Comparing fractions worksheets, how to 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 Examples

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.

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 \[ {2 \over 8} \; and \; {1 \over 4} \].

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 Examples

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.

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 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: \[ {3 \over 7} \; > \; {2 \over 5} \]

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.

Want to test yourself to see how well you have understood this skill?

• Try our NEW quick quiz at the bottom of this page.

Section 1 - Comparing Fractions Worksheet with diagrams

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

• Comparing Fractions Worksheet with diagrams 1
• PDF version
• Comparing Fractions Worksheet with diagrams 2
• Comparing Fractions Worksheet with diagrams 3
• Comparing Fractions Worksheet with diagrams 4

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.

• Ordering Fractions using diagrams sheet 1
• Ordering Fractions using diagrams sheet 2

Section 3 - Comparing Fractions Worksheet without diagrams

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

This first sheet just compares simple fractions with the same denominator or the same numerator, or equivalent to a half.

• Comparing Fractions Worksheet 1
• Comparing Fractions Worksheet 2
• Comparing Fractions Worksheet 3
• Comparing Fractions Worksheet 4

Section 4 - Ordering Fractions Worksheets without diagrams

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

• Ordering Fractions Sheet 1
• Ordering Fractions Sheet 2
• Ordering Fractions Sheet 3
• Ordering Fractions Sheet 4

Section 5 - Comparing Fractions Riddles

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

These sheets are graded, with the easiest one first.

• Comparing Fractions Riddles Sheet 1
• Comparing Fractions Riddles Sheet 2
• Comparing Fractions Riddles Sheet 3

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.

• Finding Equivalent Fractions support page
• Equivalent Fractions Worksheets

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.

• Simplify Fractions Practice Zone
• Simplifying Fractions Worksheet page
• Least Common Multiple Calculator

Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.

It will tell you the smallest multiple to convert the denominators of the fractions you are comaring into.

There are also some worked examples.

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.

• How to Convert Improper Fractions
• Improper Fraction Worksheets

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Comparing Fractions

Comparing fractions means determining the larger and the smaller fraction between any two or more fractions. Since fractions are made up of two parts - a numerator and a denominator, they are compared using a certain set of rules. Let us learn more about comparing fractions in this page.

How to Compare Fractions?

Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction. We need to compare fractions in our everyday lives. For example, when we need to compare the ratio of ingredients while following a recipe or to compare the scores of exams, etc. So, let us go through the different methods of comparing fractions to understand the concept better.

What is a Fraction?

Before exploring the concept of comparing fractions, let us recall fractions. A fraction is a part of a whole and it consists of two parts - the numerator and the denominator . The numerator is the number on the upper part of the fractional bar and the denominator is located below the fractional bar.

Now, let us discuss more about comparing fractions.

Comparing Fractions with Same Denominators

For comparing fractions with the same denominators, it becomes easier to determine the greater or the smaller fraction. After checking if the denominators are the same, we can simply look for the fraction with the bigger numerator. If both the numerators and the denominators are equal, the fractions are also equal. For example, let us compare 6/17 and 16/17

• Step 1: Observe the denominators of the given fractions: 6/17 and 16/17. The denominators are the same.
• Step 2: Now, compare the numerators. We can see that 16 > 6.
• Step 3: The fraction with the larger numerator is the larger fraction. Therefore, 6/17 < 16/17.

Comparing Fractions with Unlike Denominators

For comparing fractions with unlike denominators, we need to convert them to like denominators, for which we should find the Least Common Multiple (LCM) of the denominators. When the denominators are made the same, we can compare the fractions easily. For example, let us compare 1/2 and 2/5.

• Step 1: Observe the denominators of the given fractions: 1/2 and 2/5. They are different. So, let us find the LCM of 2 and 5. LCM(2, 5) = 10.
• Step 2: Now, let us convert them in such a way that the denominators become the same. Let us multiply the first fraction with 5/5, that is, 1/2 × 5/5 = 5/10.
• Step 3: Now, let us multiply the second fraction with 2/2 that is, 2/5 × 2/2 = 4/10.
• Step 4: Compare the fractions: 5/10 and 4/10. Since the denominators are the same, we will compare the numerators, and we can see that, 5 > 4 .
• Step 5: The fraction with the larger numerator is the larger fraction, that is, 5/10 > 4/10. Therefore, 1/2 > 2/5

It should be noted that if the denominators are different and the numerators are the same, then we can easily compare fractions by looking at their denominators. The fraction with a smaller denominator has a greater value and the fraction with a larger denominator has a smaller value. For example, 2/3 > 2/6.

Decimal Method of Comparing Fractions

In this method, we compare the decimal values of fractions. For this, the numerator is divided by the denominator and the fraction is converted into a decimal. Then, the decimal values are compared. For example, let us compare 4/5 and 6/8.

• Step 1: Write 4/5 and 6/8 in decimals. 4/5 = 0.8 and 6/8 = 0.75.
• Step 2: Compare the decimal values. 0.8 > 0.75
• Step 3: The fraction with a larger decimal value would be a larger fraction. Therefore, 4/5 > 6/8

Comparing Fractions Using Visualization

We can use various graphical methods and models to visualize larger fractions. Observe the figure given below which shows Model A and B that represent two fractions. We can easily determine that 4/8 < 4/6 because 4/6 covers a larger shaded area than 4/8. Note that the smaller fraction occupies a lesser area of the same whole. A point to be taken into consideration here is that the size of models A and B should be exactly the same for the comparison to be valid. Each model is then divided into equal parts equivalent to their respective denominators.

Comparing Fractions Using Cross Multiplication

For comparing fractions using cross multiplication , we multiply the numerator of one fraction with the denominator of the other fraction. Let us understand this with the help of an example. Compare 1/2 and 3/4. Observe the figure given below which explains this better.

• Step 1: When we cross multiply the given fractions for comparing them, we need to keep in mind that if we are multiplying the numerator of the first fraction with the denominator of the second fraction, we should write the product next to the first fraction. Here, 1 × 4 = 4, and we will write 4 next to the first fraction. (Write the product on the side of the selected numerator)
• Step 2: Similarly, when we are multiplying the numerator of the second fraction with the denominator of the first fraction, we should write the product next to the second fraction. Here, 3 × 2 = 6, and we will write 6 near the second fraction.
• Step 3: Now, compare the products 4 and 6. Since 4 < 6, the respective fractions can be easily compared, that is, 1/2 < 3/4. Therefore, 1/2 < 3/4

☛ Related Topics

• Types of Fractions
• Comparing Fractions Calculator
• Multiplying Fractions
• Division of Fractions
• Decimals and Fractions

Examples on Comparing Fractions

Example 1: Why is 5/11 > 4/11? Can you explain?

Comparing fractions becomes easier if the denominators are the same. 5/11 and 4/11 have the same denominators; hence, we can simply compare the fractions by observing the numerators. The fraction with a larger numerator will be the larger fraction. 5 > 4. Therefore, 5/11 > 4/11.

Example 2: Ryan was asked to prove that the given fractions: 4/6 and 6/9 are equal. Can you prove this using the LCM method?

We can make the denominators the same by finding the LCM of the denominators of the given fractions. The LCM of 6 and 9 is 18. So, we will multiply 4/6 with 3/3, (4/6) × (3/3) = 12/18, and 6/9 with 2/2, (6/9) × (2/2) = 12/18, which will convert them to like fractions with the same denominators. The new fractions with the same denominators will be 12/18 and 12/18. Hence, both the fractions are equal: 4/6 = 6/9. Therefore, 4/6 = 6/9.

Example 3: Compare the fractions 5/8 and 7/12.

Solution: For comparing fractions with different denominators, we need to find the LCM of the denominators. The LCM of 8 and 12 is 24. So, let us multiply 5/8 with 3/3, that is, 5/8 × 3/3 = 15/24. Now, let us multiply 7/12 with 2/2, that is, 14/24. Now that we have like fractions 15/24 and 14/24, we can easily compare them. Since 15 > 14, 5/8 > 7/12. Therefore, 5/8 > 7/12.

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Practice Questions on Comparing Fractions

Faqs on comparing fractions, what does comparing fractions mean.

Comparing fractions means comparing the given fractions in order to tell if one fraction is less than, greater than, or equal to the other fraction. Like whole numbers , we can compare fractions using the same symbols: <,> and =. There are various methods and rules to compare fractions, depending upon the numerator and the denominator and the kind of fractions given.

What is the Rule of Comparing Fractions with the Same Denominator?

When the denominators of the given set of fractions are the same, the fraction with the smaller numerator is the smaller fraction and the fraction with the larger numerator is the larger fraction. When the numerators are equal, the fractions are considered to be equal. For example, if we need to compare 2/5 and 4/5, we just need to check and compare the numerators. Since 2 < 4, it can be said that 2/5 < 4/5.

What is the Rule when Comparing Fractions with the Same Numerator?

When the fractions have the same numerator, the fraction with the smaller denominator is greater. For example, let us compare fractions with the same numerator. The given fractions are 1/2, and 1/6. Now out of these, the fraction with the smaller denominator is 1/2. Thus, 1/2 is the larger of the given fractions.

What are Equivalent Fractions?

The fractions that have different numerators and denominators but are equal in their values are called equivalent fractions . For example, 5/10, and 6/12 are equivalent fractions since both of them are equal to 1/2 when simplified.

What is the Easiest Way of Comparing Fractions?

The easiest and fastest way to compare fractions is to convert them into decimal numbers. The fraction with the larger decimal value is the larger fraction.

Why do we Need to Compare Fractions?

Comparing fractions is an important component, which helps students develop their number sense about the fraction size. This helps them realize that the strategies they use to compare whole numbers do not necessarily apply while comparing fractions. For example, 1/4 is greater than 1/8 even though the whole number 8 is greater than 4.

How to Compare Fractions with Different Denominators?

In order to compare fractions with different denominators, we need to find the Least Common Multiple (LCM) of the denominators and convert the given fractions to like fractions by making their denominators the same and then the numerators can be easily compared. For example, let us compare 7/12 and 9/16.

• Step 1: Since the given fractions have different denominators, we will find the LCM of the denominators. The LCM of 12 and 16 = 48.
• Step 2: Now, we will convert the fractions in such a way that the denominators become the same. Let us multiply the first fraction with 4/4, that is, 7/12 × 4/4 = 28/48.
• Step 3: Now, let us multiply the second fraction with 3/3 that is, 9/16 × 3/3 = 27/48.
• Step 4: Compare the fractions: 28/48 and 27/48. Since the denominators are the same, we will compare the numerators, and we can see that 28 > 27.
• Step 5: The fraction with the larger numerator is the larger fraction, that is, 28/48 > 27/48. Therefore, 7/12 > 9/16

Calcworkshop

Comparing Fractions Hands-On Practice w/ 17 Examples!

// Last Updated: November 8, 2020 - Watch Video //

Did you want to know the trick for comparing fractions?

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Equivalent fractions!

Now equivalent fractions may have different numerators and denominators, but they represent the same value or proportion of the whole.

Let’s quickly remind ourselves of how we create equivalent fractions and simplify them using the two examples below.

Notice how four-fifths is equivalent to eight-tenths and twenty-five thirtieths is equivalent to five-sixth.

Multiply to Find Equivalent Fractions

Divide to Find an Equivalent Fraction

But how does knowing how to create equivalent fractions help us compare fractions?

Well, to compare fractions , we have to ensure that we have common denominators . In other words, we can only compare fractions if the denominators are the same.

And the way we get common denominators is by creating fractions that have the same part to whole, as noted by Monterey Institute .

Finding Common Denominators

How do we determine the common denominators?

By using the Least Common Denominator (LCD)!

What’s cool is that the LCD uses the same process for finding the least common multiple (LCM), but only for the numbers in the denominator. This means we already know what to do.

Solved Example

For instance, let’s find common denominators for:

• First, we find the LCM of the denominators 5 and 4 by either listing multiples or using prime factorization .

How To Find LCM Using Prime Factorization

• Then we create equivalent fractions for each using our new LCM.

Equivalent Fractions with LCD

How To Compare Fractions

And now that we’ve found common denominators, we are ready to do a comparison of the fractions!

Because our denominators are the same, all we have to do is analyze our numerators to determine or =.

Worked Example

So, let’s compare our two fractions of:

Thankfully, we already transformed these two fractions into equivalent fractions of 5/20 and 8/20 after finding common denominators, so all we have to do now is study their numerators.

Compare Equivalent Fractions

That’s all there is to comparing fractions:

• Write each fraction with common denominators.
• Then compare their numerators.

Mixed Number vs. Improper Fraction

But what if we are working with an improper fraction with a mixed number?

You first want to change the mixed number into an improper fraction by multiplying the denominator by the whole number and adding the numerator, and then follow the steps listed above.

Detailed Example

For example, let’s work on the following problem:

First, we write the mixed number of 5 and 1/2 as an improper fraction of 11/2 using the technique we learned in our improper fraction mixed number video .

Compare Mixed Numbers and Improper Fractions

Next, we find the LCD by first finding the LCM of our denominators in order to create common denominators.

Because the LCM of 3 and 2 is 6, our least common denominator is 6.

So, now it’s time to create equivalent fractions.

Comparing Improper Fractions

And since 28 is less than 33, then 28/6 is less than 33/6, which means 14/3 is less than 5 and 1/2.

Improper Fractions — Comparison

How To Compare More Than 2 Fractions

Okay, so what do we do when we want to equate more than two fractions?

Whenever this happens, you are asked to list each fraction in order from least to greatest ( ascending ) or greatest to least ( descending ), just like we did in our decimals lesson.

Key Example

Once again, the key to listing fractions in order is to first get common denominators!

List of Fractions in Order

Worksheet (PDF) — Hands on Practice

Put that pencil to paper in these easy to follow worksheets — expand your knowledge!

Comparing Fractions — Practice Problems Comparing Fractions — Step-by-Step Solutions

In the video below, we will look at additional examples of how to compare fractions by finding the least common denominator and how to order fractions from least to greatest, as well as looking at some helpful tricks and tips along the way.

Let’s do it!

Video Tutorial — Full Lesson w/ Detailed Examples

1 hr 12 min

• Introduction to Video
• 00:00:39 – Least Common Denominator and Equivalent Fractions (Examples #1-3)
• 00:09:20 – Compare fractions by finding the LCD (Examples #4-7)
• 00:25:59 – Tips and Tricks for mixed numbers and improper fractions
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• 00:38:22 – Compare each fraction using ,or = (Examples #11-14)
• 00:54:43 – Order the fractions from least to greatest (Examples #15-17)
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Comparing Fractions

Sometimes we need to compare two fractions to discover which is larger or smaller.

There are two main ways to compare fractions: using decimals , or using the same denominator .

The Decimal Method of Comparing Fractions

Convert each fraction to decimals, and then compare the decimals.

Example: which is bigger: 3 8 or 5 12 ?

Convert each fraction to a decimal.

We can use a calculator (3÷8 and 5÷12), or the method on Converting Fractions to Decimals .

Anyway, these are the answers I get:

3 8 = 0.375, and 5 12 = 0.4166...

So 5 12 is bigger.

The Same Denominator Method

The denominator is the bottom number in a fraction.

It shows how many equal parts the item is divided into

When two fractions have the same denominator they are easy to compare:

Example:   4 9 is less than 5 9 (because 4 is less than 5)

But when the denominators are not the same we need to make them the same (using Equivalent Fractions ).

Example: Which is larger: 3 8 or 5 12 ?

Look at this:

• When we multiply 8 × 3 we get 24,
• and when we multiply 12 × 2 we also get 24,

so let's try that ( important: what we do to the bottom we must also do to the top ):

We can now see that 9 24 is smaller than 10 24 (because 9 is smaller than 10).

Making the Denominators the Same

There are two main methods to make the denominator the same:

• Common Denominator Method , or the
• Least Common Denominator Method

They both work, use which one you prefer!

Example: Which is larger: 5 6 or 11 15 ?

Using the Common Denominator method we multiply each fraction by the denominator of the other:

We can see that 75 90 is the larger fraction (because 75 is more than 66)

Ordering Fractions

If denominators are the same , then we only need to compare the numerators, for example:

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Comparing and Ordering Fractions

Compare and order fractions and mixed numbers. Includes "greater than," "less than," and "equal to" symbols. This page has printable task cards, learning center games, and worksheets.

Comparing Fractions

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Comparing Mixed Numbers

Comparing measurements, fraction counting, ordering fractions, ordering mixed numbers, reference chart.

Learn about equivalent fractions, simplifying fractions, and fractions of sets. There are also links to fraction addition, multiplication, subtraction, and division.

Learn all about mixed numbers with these printable lesson activities.

From this index page, you can jump to worksheets on comparing 4-digit numbers, 5-digit numbers, or 6-digit numbers. Also includes links to STW resources on comparing decimals and money.

Here are some learning resources for teaching ordering and comparing of decimal numbers.

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Exploring Fractions

• The first group  gives you some starting points to explore with your class, which are applicable to a wide range of ages.  The tasks in this first group will build on children's current understanding of fractions and will help them get to grips with the concept of the part-whole relationship. 
• The second group of tasks  focuses on the progression of ideas associated with fractions, through a problem-solving lens.  So, the tasks in this second group are curriculum-linked but crucially also offer opportunities for learners to develop their problem-solving and reasoning skills.   

• are applicable to a range of ages;
• provide contexts in which to explore the part-whole relationship in depth;
• offer opportunities to develop conceptual understanding through talk.

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Comparing Fractions Reasoning and Problem Solving

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 April 2022

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This is a sample resource containing reasoning and problem solving when comparing fractions in Year 6.

For a full year’s worth of reasoning and problem solving for Year 6 please see:

https://www.tes.com/teaching-resource/reasoning-and-problem-solving-for-year-6-12201133

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5 Fun Activities for Teaching Comparing and Ordering Fractions

When you hear pizza and baking, which math unit comes to mind? If it’s comparing and ordering fractions, then we’re totally on the same wave length! I generally LOVE pizza and baking. However, a lot of kiddos don’t love fractions. That’s why today I am sharing five fun activities that you can add to your comparing and ordering fractions unit.

1) Introduce Students to a Variety of Strategies

With a concept as tricky as comparing and ordering fractions, kids need to be exposed to a variety of strategies they can use to solve problems.

I suggest introducing students to one new strategy each day. Then giving them a TON of practice opportunities so that they can test the strategy out and see if it works for them.

Here is the anchor chart that I use when introducing new comparing and ordering fractions strategies. You can get a FREE copy of this chart sent to your inbox by clicking HERE !

2) Practice with BOOM Cards

When students are first learning a new math concept, immediate and specific feedback is crucial! That’s why I love to use BOOM cards in my math classroom. These digital, self checking task cards give kids that speedy feedback that they need! Plus I love that this is an alternative to working in a workbook or on a worksheet. After all, sometimes we need to change things up a bit!

You can click to check out my comparing and ordering fractions BOOM cards .

3) Incorporate Digital Activities

Digital Activities are essentially worksheets on steroids. I love using them because kiddos are SO much more motivated by a digital activity than a traditional worksheet. I created this fun set of problems that have a pizza theme so that students could practice comparing and ordering fractions. Click HERE to check it out!

4) Problem Solving!

Problem solving is such an integral part of any math unit. I like to start each class with one word problem. This gives kiddos a ton of good practice.

Remember to let your students solve word problems on individual whiteboards! They are often so much more willing to try new strategies and step outside of their comfort zones if they know that they can easily wipe away their mistakes. Plus… who doesn’t love a fun pink marker?

Here are some comparing and ordering fractions word problems that you might consider incorporating into your unit:

5) Review with a Digital Escape Room

Virtual Breakout Rooms are seriously so much fun! Best of all, they require kids to use problem solving skills and critical thinking in order to complete the challenges. 

But if we’re being honest, my favourite part about digital escape rooms is that they require almost no prep and literally zero marking! This makes them a fantastic activity for weeks that are super busy because you can get some work done while the kids enjoy their math challenge.

This Comparing and Ordering Fractions Digital Escape Room has a fun pizza theme. Your kiddos will literally be cheering that it’s time for math! 

So there you have it, 5 great activities that you can use when teaching your upper elementary math students about comparing and ordering fractions.

Want to learn more about teaching equivalent fractions? Check out that blog post by clicking HERE !

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Comparing and Ordering Numbers: Definition with Examples

What are comparing and ordering numbers, what is ordering numbers, comparing and ordering real numbers using a number line, solved examples on comparing and ordering, practice problems on comparing and ordering, frequently asked questions on comparing and ordering.

Have you ever compared your height and your friend’s height to decide who is taller? Or has the teacher ever asked your class to stand in increasing order of height? 

This type of situation can be answered by comparing and ordering numbers. “Comparing” in math is the process in which we observe similar properties of different persons or objects or things. Ordering a list of numbers means stating the numbers from the least to the greatest or from the greatest to the least. Before we learn how to compare and order numbers, let us first introduce the meaning of comparing numbers.

Comparing Numbers Meaning

Comparing in math refers to viewing something in relation to another. So, what is comparing numbers? Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to its values. 

The definition of comparison in math is all about identifying a quantity greater, smaller, or equal in relation with the given number.

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Symbols for Comparing Numbers

The symbols used for comparing numbers are $\gt,\; \lt,$ or $=$.

• $“\gt”$ means “greater than”
• $“\lt”$ means “less than”
• $“=”$ means “equal to”

We also use the following symbols for comparing two quantities.

means “less than or equal to”

means “greater than or equal to”

Example: Let’s understand this visually using vertical bars composed of blocks. Each small block is of the same size. We can compare the numbers by comparing the heights of the bars.

On comparing two numbers, we can find out by how much a number is greater or smaller. 

• In the first example, $7 \gt 3$ since the green bar is taller than the pink bar. We can also say that 7 is more or greater than 3 by $7 \;−\; 3 = 4$.
• In the second part, $3 \lt 6$ since the red bar is shorter than the yellow bar.  We can also say that 3 is less or smaller than 6 by $6 \;−\; 3 = 3$.

Steps for Comparing Numbers

Step 1: Compare the number of digits. The number with the more digits, is greater. Note that 0 placed at the beginning of a number is insignificant.

Example: $358 \lt 9104$

Step 2: If the number of digits are the same, we start by comparing the highest place values.

Example: In the following example, $312521 \lt 312712$ since $5 \lt 7$ at the hundreds place.

Ordering a list of numbers means arranging the numbers from least to greatest or greatest to least. In other words, we can say that ordering numbers means arranging numbers either in increasing order or decreasing order.

• Ascending order

Arrangement of numbers in increasing order, from the smallest to the greatest, is called ascending order.

For example $2 \lt 4 \lt 6 \lt 8 \lt 10$

• Descending order

Arrangement of numbers in decreasing order, from the greatest to smallest, is called descending order.

For example, $10 \gt 8 \gt 6 \gt 4 \gt 2$ 

On a number line, the numbers increase as we go from left to right. Thus, the number on the right is always greater than the number on the left. Thus, any two real numbers can be compared based on their position on the number line.

Example: Compare – 9 and 8 on the number line. 

-9 lies on the left side of 8.

Thus, -9 < 8.

We can order the integers in increasing order as shown below

$…\; \lt -9 \lt -8 \lt -7 \lt -6 \lt …\lt -2 \lt -1 \lt 0 \lt 1 \lt 2 \lt 3 \lt 4 \lt …$

Similarly, $0.5 \lt 1.4$ since 0.5 lies on the left side of 1.4.

Comparing Rational Numbers

Comparing two or more rational numbers is similar to comparing fractions. We just need to keep in mind that:

• All negative rational numbers are smaller than 0.
• All positive rational numbers are greater than 0.
• All positive rational numbers are greater than all negative rational numbers.

As we know that rational numbers include whole numbers, integers, fractional, and decimal numbers in it, hence comparing two or more rational numbers can be categorized as

Comparing Whole Numbers

Comparing integers, comparing fractions, comparing decimals.

Let’s discuss steps for comparing numbers for each category one by one.

There are some steps through which we can compare two or more whole numbers:

Step 1: We should compare the number of digits. If there are more digits, it means the number is greater. For example $15 \gt 9,\; 125 \gt 32$, etc.

Step 2: If the number of digits is the same in both numbers, then we should compare the highest place values or the digit to the extreme left of the numbers. For example, $65 \gt 57,\; 243 \gt 127$, etc.

Step 3: If the digits at the highest place value are the same, we should compare the digits in the next digits to the right or the second highest place value. For example $76 \gt 72,\; 358 \gt 348$, etc.

Step 4: We keep comparing digits with the same place value until we find digits that are different. The number with the greater face value is the greater number. $109 \gt 102,\; 557 \gt 552$ etc.

• Comparing two positive integers is the same as comparing whole numbers except comparing with a negative integer.
• A positive integer is always greater or more than a negative integer. 

For example $5 \gt \;−\;5,\; 80 \gt \;−\; 80$, etc.

For comparing two negative numbers, we say that the greater number with a negative sign is the smallest of two negative integers.

For example $−\;80 \lt \;−\;75,\; −\;15 \lt \;−\;5$, etc.

• Negative integers are less than 0 and positive integers are greater than 0.

For example $−\;5 \lt 0, \;−\;12 \lt 0,\; 8 \gt 0$, etc.

When two or more fractions share the same denominator, the fractions are called “like fractions.” When two or more fractions have different denominators, they are called “unlike fractions.”

Comparing Like Fractions

To compare two or more like fractions, we just have to compare the numerators.

In the above figure, since $7 \gt 5$, hence $78\gt58$.

Comparing Unlike Fractions

To compare two or more unlike fractions, we can use different methods.

• Cross Multiplication Method

We multiply the numerator of the first fraction by the denominator of the second fraction and write the answer.

For example, we have to compare $\frac{5}{8}$ and $\frac{6}{11}$.

So, we multiply 5 and 11 together and 8 and 6 together, and we get

$5 \times 11 = 55$ and $6 \times 8 = 48$

After that, we can compare them like two whole numbers.

$55 \gt 48$

Finally, we replace the numbers with fractions. 

$\frac{5}{8} \gt \frac{6}{11}$

• Making the Denominators the Same 

In this method, we first find the LCM of both denominators. 

Let us take the above example, i.e., compare $\frac{5}{8}$ and $\frac{6}{11}$.

LCM $(8,\; 11) = 88$

To make the denominator the same, multiply the numerator and denominator by a relevant number. 

$\frac{5 \times 11}{8 \times 11} = \frac{55}{88}$ and $\frac{6\times8}{11\times8} = \frac{48}{88}$

After the denominators become the same, we compare the numerator. 

$55 > 48$

Finally, we replace the numbers with fractions.

$\frac{55}{88} \gt \frac{48}{88} \Rightarrow \frac{5}{8}\gt\frac{6}{11}$

We can compare two or more decimals by using the following steps:

Step 1: Firstly, compare the whole number part (i.e., compare the digits before the decimal). If they are different, you can compare the numbers as you would for any whole number. If they are the same, then follow the next step.

Step 2: Compare the tenth place. If they are different, then compare the numbers as you would for whole numbers. If they match, then move on to the next digit.

Step 3: Compare the hundredths place. If they are different, then compare those digits as you would for whole numbers. If they match, then move on to the next digit.

Example: Compare 23.56 and 23.289.

The numbers before the decimal are the same. So, we move to the next step, i.e., comparing the tenth place. Since $5 \gt 3,\; 23.56 \gt 23.289$.

In this article, we have discussed the meaning and symbols of comparing numbers, the method of comparing numbers, ordering, ascending and descending order as well as some important facts, and problems based on comparing and ordering numbers.

• Compare the numbers 425 and 412.

Given numbers 425 and 412.

Since the number of digits is the same in both numbers and the first digit is also the same, i.e., 4. But the digit at tens places 2 > 1.

Therefore, $425 \gt 412$

Hence, 425 is greater than 412.

• Which number is smaller out of $−612$ and $−625$ ?

Therefore, $−625 \lt −612$

Hence, $−625$ is smaller than $−612$.

• Compare $\frac{3}{5}$ and $\frac{5}{9}$ .

We have to compare $\frac{3}{5}$ and $\frac{5}{9}$.

Using the cross multiplication method,

$\frac{3}{5} = \frac{3 \times 9}{5 \times 9} = \frac{27}{45}$

$\frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45}$

Here, $27 \gt 25$

So, $\frac{27}{45} \gt \frac{25}{45}$

Finally, we replace the numbers with fractions $\frac{3}{5} \gt \frac{5}{9}$ .

• Compare the numbers 5, 0, 10, and $−15$ . Also, arrange them in ascending order.

Given a list of numbers $5, 0, 10,$ and $−15$.

Since a positive integer is always greater than a negative integer, $−15$ is smaller than all of the given numbers.

Also, negative integers are less than 0 and positive integers are greater than 0.

Hence, $−15 \lt 0 \lt 5 \lt 10$ (ascending order).

• Which is greater: 3.025 or 3.003?

Since the ones and tenth place of both the numbers are the same. So, we will see the hundredth place. Since $2 \gt 0$.

Hence, $3.025 \gt 3.003$.

Attend this quiz & Test your knowledge.

Which of the following is not a sign of comparing two numbers?

Which of the following is greater than $−5$, choose the correct sign for blank space: $\frac{13}{19}$ ——— $\frac{17}{19}$., ordering of a list of numbers in increasing order is called _________ order..

Why is comparing numbers important in our daily lives?

We compare numbers in our daily lives. For example, for comparing weights, for comparing the prices of everyday items, comparing the height of two or more people, etc.

How is comparing numbers different from ordering numbers?

Comparing numbers is a method of identifying greater, smaller, or equal numbers. Ordering numbers means arranging them in an ascending or descending order.

What is a quick way of comparing numbers?

The easiest way to compare numbers is by marking the numbers on a number line.

What are the different ways to compare numbers?

We can use different approaches to compare numbers, such as comparing numbers on a number line, by counting the number of digits, using place values of the numbers, etc.

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