# Dividing Fractions by Whole Numbers (Integers)

Welcome to our Dividing Fractions by Whole Numbers page.

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

## Dividing Fractions by Whole Numbers

### How to Divide Fractions 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 Integers

#### 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

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