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Fractions
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New Zealand
Level 5

Dividing whole numbers by unit fractions

Lesson
Practice
Lesson

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 $$1 as the numerator), it helps to imagine how many of those parts each whole ($$1) contains.

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

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Need more?

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

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Remember!

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

Worked Examples

Question 1

The number line below shows $$4 wholes split into $$13​ size pieces.

  1. If $$4 is divided into pieces that are $$13​ of a whole each, how many pieces are there in total?

    012345

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

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

Question 2

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

0123

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

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

  3. What is the result of $$2÷​13​?

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

Question 3

$$2÷​15​ can be visualised using the following model:

  1. How many $$15​ pieces are in $$2 wholes?

  2. How many $$15​ size pieces would be in $$9 wholes?

  3. How many $$15​ size pieces would be in $$17 wholes?

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