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Dividing whole numbers by non-unit fractions


The next step

Once you have mastered dividing whole numbers by unit fractions (they have a numerator of $1$1), it's just one more step to divide whole numbers by other fractions. If you can work out $8$8 ÷ $\frac{1}{5}$15, you only need to know one more step, and you'll be able to work out  $8$8 ÷ $\frac{2}{5}$25

Let's see how this works, and find out the simple rule that means we don't need to use number lines or fraction bars to help us. Oh, you'll also get to see why it's great to know how to find the reciprocal of a fraction!

Worked Examples

Question 1

The number line below shows $2$2 wholes split into $\frac{1}{5}$15 size pieces.



  1. If $2$2 is divided into pieces that are $\frac{1}{5}$15 of a whole each, how many pieces are there in total?

  2. How many $\frac{2}{5}$25 size pieces are in $2$2 wholes?

Question 2

Evaluate $8\div\frac{3}{8}$8÷​38. Write your answer as a mixed number.

The rule

Now you're ready to use the rule for dividing by fractions:

$a$a ÷ $\frac{b}{c}$bc = $a$a × $\frac{c}{b}$cb


Question 3

Evaluate $7\div\frac{3}{10}$7÷​310. Write your answer as an improper fraction.



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