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Dividing whole numbers by unit fractions


Picturing things

A good way to understand what a question is asking us, is to imagine using pictures. We can use things like area models and number lines to picture things like division. When we want to divide a whole number by a unit fraction (a fraction with $1$1 as the numerator), it helps to imagine how many of those parts each whole ($1$1) contains.

Let's take a look at how we can visualise this, using number lines and fraction bars.

Need more?

If you're still a little unsure, watch this video using a clock. By thinking about how many $\frac{1}{4}$14 hour blocks there are in $1$1 hour, we see that multiplying the denominator of the unit fraction by the whole number works!


If we see a problem like $5$5 ÷ $\frac{1}{6}$16, it helps to think of how many sixths there are in $1$1 whole. Then, we can think about how many there are in 5 wholes.

Worked Examples

Question 1

The number line below shows $4$4 wholes split into $\frac{1}{3}$13 size pieces.

  1. If $4$4 is divided into pieces that are $\frac{1}{3}$13 of a whole each, how many pieces are there in total?


  2. How many pieces would there be if we had $5$5 wholes?

  3. How many pieces would there be if we split up $10$10 wholes?

Question 2

This number line shows that each whole is divided up into thirds.


  1. Write the fraction that shows how big each division is:

  2. How many divisions are in $2$2 wholes?

  3. What is the result of $2\div\frac{1}{3}$2÷​13?

  4. How many third size pieces are there in $5$5 wholes?

Question 3

$2\div\frac{1}{5}$2÷​15 can be visualised using the following model:

  1. How many $\frac{1}{5}$15 pieces are in $2$2 wholes?

  2. How many $\frac{1}{5}$15 size pieces would be in $9$9 wholes?

  3. How many $\frac{1}{5}$15 size pieces would be in $17$17 wholes?

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