# Dividing Fractions by Whole Numbers

Welcome to our Dividing Fractions by Whole Numbers page.

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

### Dividing Fractions by Whole Numbers Support

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

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).

### 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: $2 {2 \over 3} ÷ 7 \; = \; {8 \over 21}$

### How to Convert to Simplest Form

How to Print or Save these sheets

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

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

### Math Salamanders Shop

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

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!

### New Math Sheets & Resources

Check out our LATEST webpages.

### 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

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!