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

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Everyday maths 1 (Wales)

3.3 Simplifying fractions

You may need to simplify a fraction. The following terms may also be used for this:

  • cancelling
  • express in the lowest terms
  • express in the simplest form.

For example, eight divided by 12 is equivalent to (the same as) two divided by three, which is the simplest way of writing this fraction.

Example: Simplifying fractions

  1. Simplify five divided by 20.
  2. Simplify 20 divided by 30.

Method

To simplify a fraction, you need to divide the top and bottom numbers by the same value. You keep dividing down until you cannot get the fraction any smaller. Each time you divide, you must divide the top and bottom numbers by the same value.

  1. In order to simplify five divided by 20, you need to find out what number will divide into 5 and 20. The only number that will divide into both 5 and 20 is 5:
    • 5 ÷ 5 = 1
    • 20 ÷ 5 = 4

    So five divided by 20 = one divided by four.

  2. There are different ways to simplify 20 divided by 30 to the lowest form. For example, you can divide both numbers in 20 divided by 30 by 2:
    • 20 ÷ 2 = 10
    • 30 ÷ 2 = 15

    However, 10 divided by 15 not the simplest form of the fraction. You can simplify the fraction further by dividing the top and bottom numbers by 5:

    • 10 ÷ 5 = 2
    • 15 ÷ 5 = 3

    two divided by three is the simplest form of 20 divided by 30.

    However, you may have recognised that 10 will go into both 20 and 30, so you may have divided by 10 straightaway:

    • 20 ÷ 10 = 2
    • 30 ÷ 10 = 3

    The answer is the same, but dividing by 10 would have got you to the answer more quickly.

Now try the following activity.

Activity 21: Simplifying fractions

Simplify the following fractions:

  1. five divided by 10
  2. 20 divided by 25
  3. three divided by six
  4. two divided by eight
  5. three divided by nine

Answer

  1. five divided by 10 = one divided by two (the top and bottom numbers are divided by 5)
  2. 20 divided by 25 = four divided by five (the top and bottom numbers are divided by 5)
  3. three divided by six = one divided by two (the top and bottom numbers are divided 2)
  4. two divided by eight = one divided by four (the top and bottom numbers are divided 2)
  5. three divided by nine = one divided by three (the top and bottom numbers are divided 3)
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