Dividing Fractions by Whole Numbers

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).

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