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1.4 Fractions, decimals, percentages and ratio

Ratio and proportion

Everything on ratio and proportion that can come up in the WJEC GCSE Mathematics and Numeracy, in all three units. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.

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A worked example

Simplifying ratios · [1 mark]

Write the ratio 30 : 24 in its simplest form.

  1. B15 : 4

The exam skills (8)

Simplifying ratios

  1. Find the HCF of the numbers.
  2. Divide every part by it.
  3. Keep the same order and use whole numbers.

Watch out: Swapping the order. 2 : 4 simplifies to 1 : 2, not 2 : 1.

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Sharing in a ratio

  1. Add the ratio parts to get the total number of parts.
  2. Total amount ÷ total parts = one part.
  3. Multiply one part by each number in the ratio.

Watch out: Dividing by one side of the ratio instead of the total parts.

Worked example · Practise this skill free

Proportion

  1. Work out how much for one (one person, one item).
  2. Multiply by how many you need.
  3. Check it makes sense: more people means more ingredients.

Watch out: Adding the difference instead of scaling.

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Ratio problem

  1. Find the difference in the ratio parts.
  2. The difference in amounts ÷ the difference in parts = one part.
  3. Multiply one part by the total parts.

Watch out: Dividing by the total parts. The difference is shared between the difference in parts only.

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Inverse proportion

  1. More workers means less time: that is inverse proportion.
  2. Multiply to find the total work, e.g. builders × days.
  3. Divide the total work by the new number of workers.

Watch out: Doubling the time when you double the workers. It should halve.

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Ratio and fractions

  1. Add the parts to get the total.
  2. The fraction is one part over the total: 1 : 2 means 1/3 and 2/3.
  3. Simplify if you can.

Watch out: Writing 1 : 2 as 1/2. That ignores the total.

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Ratio and algebra

  1. Write the ratios as fractions and set them equal.
  2. Cross-multiply to get rid of the fractions.
  3. Solve the equation.

Watch out: Cross-multiplying the wrong way round. Top of one × bottom of the other.

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Combining ratios

  1. Find the part that is in both ratios (here, blue).
  2. Scale the ratios so that part is the same number in both.
  3. Write the three-part ratio.

Watch out: Just writing the numbers next to each other without matching the shared part.

Worked example · Practise this skill free

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