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Ratio and Proportion (F)

Master GCSE ratios and proportion: simplify ratios, share amounts in a given ratio, and use the unitary method to scale recipes, maps, and real-life problems.

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Fascinating Fact:

At a smoothie bar, 750 ml shared in ratio 2:1 means total parts = 3, one part = 750 ÷ 3 = 250 ml, so amounts = 500 ml and 250 ml.

In GCSE Maths, ratio and proportion help you compare quantities and scale them fairly. You’ll simplify ratios, divide an amount into parts, use the unitary method, and solve proportional problems such as maps, recipes, and best buys.

Key Terms

Ratio: A way to compare quantities, written with a colon, e.g., 2:3.
Proportion: A statement that two ratios are equal, used to scale amounts up or down.
Unitary method: Finding the value of one unit first, then multiplying to get the required amount.

Frequently Asked Questions (Click to see answers)

How do I share an amount in a given ratio?

Add the parts, divide the total by this sum to get one part, then multiply. Example: split £90 in ratio 2:1, so parts = 3, one part = £30, shares = £60 and £30.

What is the unitary method in proportion?

Find the value for one unit, then scale. If 5 books cost £24, one book costs £24 ÷ 5 = £4.80, so 8 books cost 8 × £4.80 = £38.40.

How do I scale a recipe using ratio and proportion?

Work out the scale factor = new servings ÷ original servings, then multiply each ingredient by that factor. Keep all units consistent.