Everyday maths 1 (Wales)
Everyday maths 1 (Wales)

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Everyday maths 1 (Wales)

3.1 Using equivalent fractions

Equivalent fractions are fractions that are the same as each other, but are expressed in different ways. The BBC Skillswise website has an explanation of equivalent fractions. [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

To make an equivalent fraction, you multiply or divide the numerator (top) and denominator (bottom) by the same number. The size of the fraction is not altered. For example:

In the fraction four divided by six, the numerator is 4 and the denominator is 6.

4 × 2 = 8

6 × 2 = 12

So four divided by six = eight divided by 12

In the fraction 10 divided by 15, the numerator is 10 and the denominator is 15.

10 ÷ 5 = 2

15 ÷ 5 = 3

So 10 divided by 15 = two divided by three

Example: Looking at equivalent fractions

Arrange the following fractions in order of size, starting with the smallest:

  • three divided by six, one divided by three, two divided by 12

Method

You need to look at the bottom number in each fraction (the denominator) and find the lowest common multiple. In this case, the bottom numbers are 6, 3 and 12, so the lowest common multiple is 12:

  • 6 × 2 = 12
  • 3 × 4 = 12
  • 12 × 1 = 12

Whatever you do to the bottom of the fraction you must also do to the top of the fraction, so that it holds the equivalent value. The third fraction, two divided by 12, already has 12 as its denominator, so we don’t need to make any further calculations for this fraction. But what about three divided by six and one divided by three?

  • 2 × three divided by six means calculating (2 × 3 = 6) and (2 × 6 = 12), so the equivalent fraction is six divided by 12
  • 4 × one divided by three means calculating (4 × 1 = 4) and (4 × 3 = 12), so the equivalent fraction is four divided by 12

Now you can now see the size order of the fractions clearly:

  • two divided by 12, four divided by 12, six divided by 12

So the answer is:

  • two divided by 12, one divided by three, three divided by six

Use the examples above to help you with the following activity. Remember to check your answers once you have completed the questions.

Activity 19: Fractions in order of size

  1. Put these fractions in order of size, with the smallest first:
  • one divided by five, one divided by three, one divided by four, one divided by 10, one divided by two

Answer

Remember that when the numerator of a fraction is 1, the larger the denominator, the smaller the fraction.

From smallest to largest, the order is:

  • one divided by 10, one divided by five, one divided by four, one divided by three, one divided by two
  1. What should you replace the question marks with to make these fractions equivalent?
  • one divided by three = question mark divided by six
  • one divided by four = question mark divided by eight
  • one divided by five = question mark divided by 10
  • one divided by two = question mark divided by 10

Answer

  • one divided by three = two divided by six
  • one divided by four = two divided by eight
  • one divided by five = two divided by 10
  • one divided by two = five divided by 10
  1. Put these fractions in order of size, with the smallest first:
  • two divided by three, three divided by five, three divided by 10

Answer

You need to change to equivalent fractions to compare like-for-like. To do this, you need to look at the bottom numbers of the fractions (3, 5 and 10) and find the lowest common multiple. The lowest common multiple of 3, 5 and 10 is 30:

3 × 10 = 30

5 × 6 = 30

10 × 3 = 30

Whatever you do to the bottom of each fraction, you must also do to the top:

With two divided by three, you need to multiply the top and bottom numbers by 10 to make 20 divided by 30.

With three divided by five, you need to multiply the top and bottom number by 6 to equal 18 divided by 30.

With three divided by 10, you need to multiply the top and bottom number by 3 to equalnine divided by 30.

The order of the fractions from smallest to largest is therefore:

three divided by 10 (nine divided by 30)

three divided by five (18 divided by 30)

two divided by three (20 divided by 30)

FSM_1_CYMRU

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