comparing and ordering fractions problem solving

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Students typically study comparing fractions starting in 4th grade. Initially, students learn to compare fractions that have the same denominator (such as 5/12 and 9/12) and fractions with the same numerator (such as 5/9 and 5/7). They also learn to compare to 1/2 (such as 1/2 and 4/5). In grade 5, students learn how to compare any two fractions by first converting them so they have a common denominator.

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

You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then 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:

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".

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.

See more Math Made Easy books at Amazon

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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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• 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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This quick quiz tests your understanding and skill at comparing two or more fractions.

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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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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.

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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

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Comparing Fractions

Comparing fractions interactive.

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Comparing and Ordering Fractions

Description.

In this module students learn how to compare and order fractions. All examples shown involve fractions less than 1. Various strategies for comparing and ordering fractions are covered.

Specifically, students will learn the following strategies for comparing and ordering fractions:

• Comparing fractions to a benchmark fraction
• Graphing fractions on a number line and determining relative size and order based on their location on the number line
• Generating equivalent fractions to compare fractions with a common denominator

This module includes tutorials, multiple choice assessments, and an interactive drag-and-drop activity.

Math Concepts

• Graphing Numbers
• Number Concepts

Learning Objectives

• Compare fractions using various strategies
• Order fractions using various strategies

Prerequisite Skills

• Can generate equivalent fractions
• Knows how to use inequality symbols

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Writing & comparing fractions word problems

Comparing fractions in context.

Below are word problem worksheets involving the writing and comparing of fractions. Both "parts of whole" and "parts of group" are considered. If comparing fractions, either i) the fractions will have like denominators, or ii) the fractions will be significantly different (e.g 1/8 vs 3/4) so that students can recognize which fraction is larger without necessarily converting to like denominators.

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COMPARING AND ORDERING FRACTIONS

Comparing fractions.

Whenever we compare two fractions, first we have to check the denominators.

If the denominators are same, then we can decide that the fraction which is having the greater numerator is greater.

If the denominators are different, then we have to make the denominators same and compare the fractions as said in case 1.

To make the denominator same, we have to apply the concept of least common multiple.

Ordering Fractions

To order fractions from least to greatest or greatest to least, first we have to check the denominators.

If the denominators are same, then we can compare the values of the numerators and order the fractions.

If the denominators are different, then we have to make the denominators same and order the fractions as said in case 1.

Find which fraction is greater :

Example 1 :

6/19 and 16/19

In the fractions  6/19 and 16/19, the denominator is same. So, the fraction which has greater numerator will greater in value.

16/9 > 6/19

16/19 is greater than 6/19

Example 2 :

1/2 and 3/5

In the fractions 1 /2 and 3/5, the denominators are different.

Make the denominators same using least common multiple.

Least common multiple of (2, 5) = 10.

1/2 = (1  ⋅ 5)/(2 ⋅ 5) = 5/10

3/5 = (3 ⋅ 2)/(5 ⋅ 2) = 15/10

Compare the numerators of like fractions 5/10 and 15/10.

15/10 > 5/10

Substitute the corresponding original fractions.

3/5 > 1/2

3/5 is greater than 1/2

Example 3 :

7/12 and 11/18

In the fractions 7/12  and 11/18, the denominators are different.

Least common multiple of (12, 18) = 36.

7/12 = (7  ⋅ 3)/(12 ⋅ 3) = 21/36

11/18 = (11 ⋅ 2)/(18 ⋅ 2) = 22/36

Compare the numerators of like fractions 21/36 and 22/36.

22/36 > 21/36

11/18 > 7/12

11/18 is greater than 7/12

Order the fractions from least to greatest :

Example 4 :

5/19, 7/19, 2/19, 3/19

In all the given fractions, the denominator is same.

Compare the numerators and order them from least to greatest.

2/19, 3/19, 5/19, 7/19

Example 5 :

3/4, 2/5, 1/8

In the given fractions, the denominators are different.

Make the denominator same using least common multiple and order them from least to greatest.

Least common multiple of (4, 5, 8) = 40.

3/4 = (3  ⋅ 10)/(4 ⋅ 10) = 30/40

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

1/8 = (1 ⋅ 5)/(8 ⋅ 5) = 5/40

Compare the numerators of like fractions above and order them from least to greatest.

5/40, 16/40, 30/40

1/8, 2/5, 3/4

Example 6 :

5/6, 1/4, 3/8, 7/12

In the given fractions, the denominators are different. 

Least common multiple of (6, 4, 8, 12) = 24.

5/6 = (5  ⋅ 4)/(6 ⋅ 4) = 20/24

1/4 = (1 ⋅ 6)/(4 ⋅ 6) = 6/24

3/8 = (3 ⋅ 3)/(8 ⋅ 3) = 9/24

7/12 = (7 ⋅ 2)/(12 ⋅ 2) = 14/24

6/24, 9/24, 14/24, 20/24

1/4, 3/8, 7/12, 5/6

Order the fractions from greatest to least :

Example 7 :

3/4, 2/5, 5/8, 1/2

Make the denominator same using least common multiple and order them from greatest to least.

Least common multiple of  (4, 5, 8, 2) = 40.

2/5 = (2 ⋅ 8)/(5 ⋅ 8) = 16/40

5/8 = (5 ⋅ 5)/(8 ⋅ 5) = 25/40

1/2 = (1 ⋅ 20)/(2 ⋅ 20) = 20/40

Compare the numerators of like fractions above and order them from greatest to least.

30/40, 25/40, 20/40, 16/40

3/4, 5/8, 1/2, 2/5

Example 8 :

1/6, 1/3, 3/14, 2/7

Least common multiple of  (6, 3, 14, 7) = 42.

1/6 = (1 ⋅ 7)/(6 ⋅ 7) = 7/42

1/3 = (1  ⋅ 14)/(3 ⋅ 14) = 14/42

3/14 = (3 ⋅ 3)/(14 ⋅ 3) = 9/42

2/7 = (2 ⋅ 6)/(7 ⋅ 6) = 12/42

14/42, 12/42, 9/42, 7/42

1/3, 2/7, 3/14, 1/6

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Comparing and Ordering Fractions Word Problems Problem Solving Worksheets

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Description

Comparing and Ordering Fractions Problem Solving is an effective way to engage your students, with word problems for real-life situations.

This print-and-go fractions resource is perfect for:

• Partner practice
• Small group work
• Assessments

This easy-prep comparing and ordering fractions resource includes:

1) Six problem solving pages

• Each page presents a different situation
• Each situation has a set of 3-4 word problems

2) Detailed answer keys showing work for each problem

The comparing and ordering fractions word problems help students practice:

• Comparing fractions with different denominators
• Ordering fractions with different denominators
• Finding equivalent fractions

What teachers are saying about this resource:

⭐️⭐️⭐️⭐️⭐️ "Perfect way to challenge my high kiddos while I work with small groups. It kept them engaged and was so well done they were able to complete it without much assistance from me."

⭐️⭐️⭐️⭐️⭐️ "Great center activity. I'm always looking for interesting ways to get in more problem solving!"

⭐️⭐️⭐️⭐️⭐️" My students were engaged with this resource because of its real world context. Thank you! "

⭐️⭐️⭐️⭐️⭐️ "Great fraction problem solving, just what we needed!"

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Solve problems involving comparing and ordering unit fractions in a range of contexts

I can solve problems involving comparing and ordering unit fractions in a range of contexts.

Lesson details

Key learning points.

• When comparing unit fractions, the greater the denominator, the smaller the fraction.
• When comparing unit fractions, the smaller the denominator, the larger the fraction.
• Equal parts may not look the same.

Common misconception

When looking at fraction notation, children might still be prone to considering the greater denominator to signify a greater fraction.

Get the whole class on board with reminding one another that the greater the denominator, the smaller the fraction. You can model this by making this mistake as you teach and the children can call you out on it - they will enjoy that!

Whole - The whole is all of a group or number.

Part - A part is a section of the whole.

Denominator - A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.

Unit fraction - A unit fraction is a fraction where the numerator is 1

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 questions.

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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Home / United States / Math Classes / Ordering and Comparing Percents, Decimals and Fractions

Ordering and Comparing Percents, Decimals and Fractions

Percents are basically a different version of decimals and fractions. Here we will learn how to convert a percent into a decimal or a fraction and vice versa. We will also learn to compare and sort a percent, decimal, and a fraction with the help of some examples. ...Read More Read Less

About Comparing and Ordering Fractions

Introduction

Fraction, decimal and percent, comparing fractions, decimals and percents.

• Ordering Fractions, Decimals and Prcents
• Solved Examples
• Frequently Asked Questions

Joseph and John are at the pizza store and they buy a pizza each. They bet on who can eat the most in the shortest amount of time. Dinner will be decided by the winner. Joseph claims he had eaten\(\frac{1}{2}\) the pizza. According to John, he had eaten up 75% of the pizza. Who gets to choose the dinner menu? To answer this question we must compare a fraction with a decimal. As a result, you’ll learn how to compare and order fractions, percentages and decimals in the sections below. By the end of this lesson, you will be able to figure out who will get to choose the dinner menu.

Because fractions, decimals, and percentages all have equivalents, comparing and ordering them is simple. It’s just a matter of converting them to the same format.

Let’s write \(\frac{4}{5}\) , which is a fraction , in terms of a decimal and a percent.

• To convert a fraction to a decimal, we have to do division:

     \(\frac{4}{5}=4\div 5=0.8\) (using long division for 4 divided by 5).

• To get a percent value, multiply by 100:

     \(0.8\times 100=80%\)

So as you can see, \(\frac{4}{5}\) , 0.8 and 80% all represent the same value but they are in fraction, decimal and percent form respectively.

You can use the symbols of greater than, less than and equal to symbols to compare fractions , decimals and percents. To compare values, convert fractions, decimals and percents to the same form. 

For example, 

Find the least number from 35%, \(\frac{3}{5}\) ,0.8 .

Firstly, convert all three numbers into the same form. Let us first convert the number to a percentage.

To convert \(\frac{3}{5}\) into a percentage, multiply both the numerator and denominator by ‘20’.

\(\frac{3\times 20}{5\times 20}=\frac{60}{100}=60%\)

To convert 0.8 into percentage.

Multiply 0.8 by 100%.

\(0.8\times 100%=80%\)

From 35%, 60%, 80% . 35% is the least

What are Ordering Fractions, Decimals and Percents?

When ordering fractions, decimals and percents, write them as all fractions or decimals or all percents. Then order them according to the question.

For example; which is the least number; 21%, \(\frac{2}{5}\) or 0.5 ? Find which is greater using a number line.

First, convert all three numbers into the same form. Let’s convert the number to percentage.

To convert \(\frac{2}{5}\) to percentage, multiply both the numerator and denominator by ‘20’.

\(\frac{2\times 20}{5\times 20}=\frac{40}{100}=40%\)

To convert 0.5 to percentage, move the decimal point two places to the right and add the percent sign.

So now we have 21%, 40% and 50%.

Let’s order from least to greatest: 21% < 40% < 50%

We can also plot the values on a number line. Values to the right are greater than the values to the left of the number line.

Solved Ordering and Comparing Examples

Example 1:  Katie, Courteney and Chloe were drinking juice from a 1 gallon carton. Katie drank 50% of the carton and Courteney drank 0.2 gallon whereas Chloe drank \(\frac{11}{50}\) gallon. Who drank the most juice?

First, convert 50% and \(\frac{11}{50}\)  into the decimal form. 

Let’s convert 50% into a decimal.

Move the decimal point two places to the left.

\(50%=\frac{50}{100}=0.50\) gallon

Let’s convert \(\frac{11}{50}\) into a decimal.

Find the equivalent fraction of \(\frac{11}{50}\) as a fraction with denominator 100. Multiply both numerator and denominator by ‘2’.

\(\frac{11\times 2}{50\times 2}=\frac{22}{100}=0.22\) gallon.

We can plot 0.5, 0.22 and 0.2 on a number line and the number to the right-most would be the greatest, which is 0.5.

So out of 0.5 gallon, 0.22 gallon and 0.2 gallon we can identify that 0.5 gallons is the greatest amount and this means that Katie drank the most juice.

Example 2: Complete the table given below.  

Let’s convert \(\frac{15}{10}\) into a decimal and percentage .

To find the equivalent fraction of \(\frac{15}{10}\)  as a fraction with denominator 100, multiply both the numerator and denominator by ‘10’.

\(\frac{15\times 10}{10\times 10}=\frac{150}{100}=1.5\) .

To convert 1.5 to percentage, move the decimal point two places to the right and add the percentage sign.

1.5 = 150 %

Let’s convert \(\frac{4}{10}\) into a decimal .

To find the equivalent fraction of \(\frac{4}{10}\) as a fraction with denominator 100, multiply both the numerator and denominator by ‘10’.

\(\frac{4\times 10}{10\times 10}=\frac{40}{100}=0.4\).

Let’s convert \(\frac{11}{10}\) into a percent .

To find the equivalent fraction of \(\frac{11}{10}\) as a fraction with denominator 100, multiply both the numerator and denominator by ‘10’.

\(\frac{11\times 10}{10\times 10}=\frac{110}{100}=110%\).

The table is filled as below:

What does ascending or descending order mean?

Descending order is the process of arranging things such as numbers, quantities, lengths and so on from a higher to a lower value. The decreasing order is another name for it. 

Ascending order refers to the placement of numbers from smallest to largest.

Why is comparing fractions difficult?

Comparing fractions is difficult because there is an added step to convert fractions with common denominators. When comparing fractions with the same denominators, determining the greater or smaller fraction becomes easier as we can simply look for the fraction with the larger numerator. 

To compare fractions with unlike denominators, we must first convert them to like denominators.

Let’s look at \(\frac{1}{3}\) and \(\frac{3}{5}\) as an example.

• Step 1: Look at the denominators of the fractions given: \(\frac{1}{3}\) and \(\frac{3}{5}\) . They are distinct. 
• Step 2: Let’s now convert them so that the denominators are the same. Multiply the first fraction by \(\frac{5}{5}\) , which equals \(\frac{1}{3}\times \frac{5}{5}=\frac{5}{15}\).
• Step 3: Multiply the second fraction by \(\frac{3}{3}\) , which equals \(\frac{3}{5}\times \frac{3}{3}=\frac{9}{15}\)
• Step 4: Make a comparison between the fractions \(\frac{5}{15}\) and \(\frac{9}{15}\) . We can compare the numerators because the denominators are the same, and we can see that 5 < 9
• Step 5: The fraction with the larger numerator, \(\frac{5}{15}\) < \(\frac{9}{15}\) , is the larger fraction. As a result,\(\frac{1}{3}\) < \(\frac{3}{5}\)

It’s worth noting that if the denominators differ but the numerators are the same, we can compare fractions by comparing their denominators.

For example in \(\frac{1}{3}\) and \(\frac{1}{9}\)

3 < 9 So \(\frac{1}{9}\) < \(\frac{1}{3}\)

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