Succeed with maths – Part 1
Succeed with maths – Part 1

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Succeed with maths – Part 1

1.4 Converting between percentages, decimals and fractions

In the next activity you’ll get some practice in converting between percentages, decimals and fractions. You may wish to do your working out on paper then put your answers in the boxes provided. Show fractions on one line using the ‘/’ symbol, so one half would be entered as ‘1/2’.

Activity _unit6.1.1 Activity 1 Converting between percentages, decimals and fractions

Timing: Allow approximately 10 minutes
  • a.Turn each of these percentages into a decimal and a fraction in its simplest form.
    • i.10%
    • ii.25%
    • iii.50%
    • iv.125%
    • v.0.5%


  • a. 

    • i.Decimal: 10% = 0.1 Fraction: 10 percent equation sequence equals 10 divided by 100 equals one divided by 10
    • ii.Decimal: 25% = 0.25 Fraction: 25 percent equation sequence equals 25 divided by 100 equals one divided by four
    • iii.Decimal: 50% = 0.5 Fraction: 50 percent equation sequence equals 50 divided by 100 equals one divided by two
    • iv.Decimal: 125% = 1.25 Fraction: 125 percent equation sequence equals 125 divided by 100 equals five divided by four
    • v.Decimal: 0.5% = 0.005 Fraction: 0.5 percent equation sequence equals 0.5 divided by 100 equals 0.5 multiplication two divided by 100 multiplication two equals one divided by 200
  • b.Write each of the following fractions and decimals as percentages.
    • i.three divided by four
    • ii.five divided by eight
    • divided by three
    • iv.0.4
    • v.0.0075
    • vi.1.2


  • b.Multiplying each fraction or decimal by 100% gives the following answers:
    • i.equation left hand side three divided by four equals right hand side three divided by four multiplication 100 percent equals 75 percent
    • ii.equation left hand side five divided by eight equals right hand side five divided by eight multiplication 100 percent equals 62.5 percent
    • iii.equation left hand side one divided by three equals right hand side one divided by three multiplication 100 percent equals percent
    • iv.0.4 equals 0.4 multiplication 100 percent equals 40 percent
    • v.0.0075 equals 0.0075 multiplication 100 percent equals 0.75 percent
    • vi.1.2 equals 1.2 multiplication 100 percent equals 120 percent

By no means did you have to do it this way, but don’t forget that your answer must include a per cent symbol.

Now it is time to turn your attention to using percentages and find out how useful these techniques you’ve just covered are.

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