Multiplying any integer by a fraction

Home learning focus

In this lesson you will learn how to multiply an integer (a whole number) by a fraction.

This lesson includes:

  • one slideshow lesson
  • two downloadable activities

Created in partnership with Numerise

Learn

Key vocabulary

  • Numerator - the number above the line in a fraction.
  • Denominator - the number below the line in a fraction.
  • Mixed number - a number with a whole part and a fraction part, eg 2½
  • Improper fraction - the fraction equivalent of a mixed number, where the numerator is larger than the denominator, eg 5⁄2

What does it mean to multiply by a fraction?

Firstly, let's think about multiplying whole numbers. We can think of 3 x 4 as meaning 3 lots of 4, or 4 + 4 + 4.

So what does it mean to multiply a fraction by an integer?

Imagine we are asked to work out 2 x ½. In the same way as multiplying integers, we can think of 2 x ½ as 2 lots of ½ or ½ + ½.

We can see from this diagram that two lots of ½ is equal to one.

How can we multiply integers by fractions?

We don’t always want to have to draw a picture to work out an integer multiplied by a fraction.

These slides from Numerise will show you the general method to multiply any integer by any fraction - simply multiply the integer (whole number) by the numerator (number above the line in the fraction) and keep the denominator (number below the line) the same.

Multiplying an integer and a fraction

Multiplying an integer and a fraction
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As you can see from this example, this method works if the fraction is first in the multiplication, too.

You can even use this method to solve 'fractions of amounts' problems. For example, working out ⅔ of 12 is the same as ⅔ x 12. (The answer is 24⁄3 = 8!)

How about mixed numbers and improper fractions?

It can be confusing to multiply mixed numbers by integers.

But you can quickly convert mixed numbers to improper fractions and, as you can see in this example, the method works for improper fractions too.

Remember: you can convert improper fractions to mixed numbers, so you could write this answer this way as well.

Practise

Activity 1

Multiplying an integer and a fraction

Download the activity below from Numerise on multiplying an integer and a fraction. You can print it out, or use a pen and paper to answer the questions. Make sure you clearly write down your workings as well as your answer!

Watch out, the answer might already be in its simplest form.

Multiplying an integer and a fraction

Click here to download the answer sheet.

Activity 2

Fractions of amounts

Download the activity below from Numerise on fractions of amounts. You can print it out, or use a pen and paper to answer the questions. Remember that to find a fraction of an amount you can multiply the amount by the fraction.

Fractions of amounts

Click here to download the answer sheet.

There's more to learn

Have a look at these other resources around the BBC and the web.

KS3 Maths
BBC Bitesize Daily
Simon Singh's Numbers
11-14 Maths
Bitesize Support
KS3 English