Dividing Fractions by Whole Numbers

Welcome to our Dividing Fractions by Whole Numbers page.

On this page, we have a range of free printable sheets to help your child learn to divide fractions by integers, or whole numbers.

Take a look at our worked examples or have a go at our practice sheets!

We also have a calculator which will not only give you the answer, but also show you all the working out along the way!

If you need support to divide fractions by other fractions, use the link below.

Dividing Fractions by Whole Numbers

On this page, you will learn how to divide a fraction by a whole number, and also some practice worksheets designed to help your child master this skill.

The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.

Before your child tackles dividing fractions, they should be confident with multiplying fractions, and also converting mixed fractions to improper fractions and reducing fractions to simplest form.

Using these sheets will help your child to:

  • divide a fraction by a whole number;
  • apply their understanding of simplest form;
  • convert an improper fraction to a mixed number.

Dividing Fractions Calculator

If you want to divide fractions, you can use our Free Divide Fractions calculator.

The calculator will help you dividing fractions by whole numbers, or fractions by other fractions or mixed numbers.

The best thing about the calculator is that it also shows you all the working out along the way.

Dividing Fractions by Whole Numbers Support

Frazer says "To divide a fraction by an integer, or whole numbers, follow these 4 easy steps."

Frazer the Fraction Salamander

Step 1

Change the whole number to a fraction by putting it over a denominator of 1.

If any of the fractions are mixed fractions (or mixed numbers), then first convert them into improper fractions.

Step 2

Swap the numerator and denominator of the dividend fraction (the fraction after the ÷ sign) and change the operator to a 'x' instead of a '÷ '

Step 3

Multiply the numerators of the fractions together, and the denominators of the fractions together. This will give you the answer.

Step 4 (Optional)

You may want to convert the fraction into its simplest form or convert it back to a mixed fraction (if it is an improper fraction).

How to Divide a Fraction by a Whole Number Printable Sheet

Examples of Dividing Fractions by Whole Numbers

Example 1) Work out: \[{3 \over 4} ÷ 6 \]

Step 1)

Put the integer over a denominator of 1.

So this gives us: \[{3 \over 4} ÷ 6\; = \; {3 \over 4} ÷ {6 \over 1} \]

Step 2)

Invert the dividend fraction and change the operation to multiplication.

So we now have \[{3 \over 4} ÷ {6 \over 1} \; = \; {3 \over 4} \times {1 \over 6}\]

Now multiply the fractions:

\[{3 \over 4} \times {1 \over 6} \; = \; {3 \times 1 \over 4 \times 6} \; = \; {3 \over 24} \]

Step 3)

Simplify the answer by dividing the numerator and denominator by 3.

\[ {3 \over 24} \; = \; {3 ÷ 3 \over 24 ÷ 3} \; = \; {1 \over 8}\]

Final answer: \[{3 \over 4} ÷ 6 \; = \; {1 \over 8} \]


Example 2) Work out: \[{5 \over 9} ÷ 4 \]

Step 1)

Put the integer over a denominator of 1.

So this gives us: \[{5 \over 9} ÷ 4 \; = \; {5 \over 9} ÷ {4 \over 1} \]

Step 2)

Invert the dividend fraction and change the operation to multiplication.

So we now have \[{5 \over 9} ÷ {4 \over 1} \; = \; {5 \over 9} \times {1 \over 4}\]

Now multiply the fractions:

\[{5 \over 9} \times {1 \over 4} \; = \; {5 \times 1 \over 9 \times 4} \; = \; {5 \over 36} \]

Step 3)

This fraction is already in simplest form.

Final answer: \[{5 \over 9} ÷ 4 \; = \; {5 \over 36} \]


Example 3) Work out: \[ 2 {2 \over 3} ÷ 7 \]

Step 1)

Convert the mixed number to an improper fraction and put the integer over a denominator of 1.

As an improper fraction: \[ 2 {2 \over 3} \; = \; {8 \over 3} \]

So this gives us: \[2 {2 \over 3} ÷ 7 \; = \; {8 \over 3} ÷ {7 \over 1} \]

Step 2)

Invert the dividend fraction and change the operation to multiplication.

So we now have \[{8 \over 3} ÷ {7 \over 1} \; = \; {8 \over 3} \times {1 \over 7}\]

Now multiply the fractions:

\[{8 \over 3} \times {1 \over 7} \; = \; {8 \times 1 \over 3 \times 7} \; = \; {8 \over 21} \]

Step 3)

This fraction is already in simplest form.

Final answer: \[2 {2 \over 3} ÷ 7 \; = \; {8 \over 21} \]


Dividing Fractions by whole numbers

Multiplying and Dividing Fractions Support Pages

The links below will take you to our support pages for multiplying and dividing fractions.

All the support pages contain detailed explanations and some worked examples.

Multiplying and Dividing Fractions Worksheets

The links below will take you to our worksheets for multiplying and dividing fractions.

The worksheets are all carefully graded and have different levels of support for students.

Converting Improper Fractions

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert an improper fraction to a mixed number.

Using these sheets will help your child to:

  • convert an improper fraction to a mixed number;
  • convert a mixed number to an improper fraction.

How to Convert to Simplest Form

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert a fraction to its simplest form.

Using these sheets will help your child to:

  • develop an understanding of equivalent fractions;
  • know when a fraction is in its simplest form;
  • convert a fraction to its simplest form.
 

How to Print or Save these sheets

how to print information image printer

Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!

How to Print or Save these sheets

how to print information image printer

Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!

Math-Salamanders.com

Math Salamanders Main Logo

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.


New! Comments

Have your say about the Math resources on this page! Leave me a comment in the box below.
 

Math Salamanders Shop

math salamanders shop logo

Looking for some fun printable math games?

We have some great games for you to play in our Math Games e-books!

NEW Online Age Calculator

Online Age Calculator image

Do you know how old you are...in weeks? days? hours?

Are you more than a million minutes old?

Find out how old you are to the nearest second!

NEW Fraction Calculators

We have updated and improved our fraction calculators to show you how to solve your fraction problems step-by-step!

Take a look and try them out!

Adding Fractions Calculator image Subtracting Fractions Calculator image Multiply Fractions Calculator image Divide Fractions Calculator image

Some of our TOP pages!

Have a look at some of our most popular pages to see different Math activities and ideas you could use with your child


Support Us

If you are a regular user of our site and appreciate what we do, please consider making a small donation to help us with our costs.

Get a free sample copy of our Math Salamanders Dice Games book with each donation!

FUN Math Games

Math Games Learning Games Captain Salamander

Looking for a fun and motivating way to learn and practice math skills?

Why not try one of our free printable math games with your students!