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Ratio, Proportion and Percentages (H)

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Ratio, Proportion and Percentages (H)

Strengthen higher-tier ratio, proportion and percentage skills: simplify ratios, share amounts fairly, use unitary and multipliers, and link ratios to fractions, decimals and percentage change.

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Fascinating Fact:

In a chemistry mix, ratio acid:water = 3:7 and total = 2 litres, so one part = 2 ÷ 10 = 0.2 litres, acid = 3 × 0.2 = 0.6 litres.

In GCSE Maths, higher-tier work with ratio, proportion and percentages brings ideas together: write and simplify ratios, convert between fractions, decimals and percentages, use unitary and multipliers, and solve real comparison problems.

Key Terms

Ratio: A comparison of quantities using “to”, written with a colon, for example 3:2.
Multiplier: A single number that applies a percentage change; +12% uses 1.12 and −15% uses 0.85.
Unitary method: Find the value of one unit first, then scale up or down to the amount required.

Frequently Asked Questions (Click to see answers)

How do I share £90 in the ratio 3:2?

Add the parts: 3 + 2 = 5. One part = £90 ÷ 5 = £18. Shares are £54 (3 parts) and £36 (2 parts).

What is the quickest way to increase or decrease by a percentage?

Use a multiplier. Increase by r%: multiply by (1 + r/100). Decrease by r%: multiply by (1 − r/100).

How are ratios linked to fractions and percentages?

For a ratio a:b, the fraction for the first part is a/(a+b). Convert that fraction to a percentage by multiplying by 100.

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You can find more about this topic by visiting BBC Bitesize - Ratio in context

Author: Sally Thompson (MSc Operational Research, Secondary Maths Teacher & Quiz Writer)

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