Ratio problems
Objective. Solve recipes, maps and comparison problems using ratio.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Ratio problems apply the sharing and scaling skills of ratio to real contexts such as recipes, maps and comparing mixtures. For a recipe scaled by ratio, if a recipe for 4 people needs ingredients in a certain ratio, the same ratio applies when scaling up for 12 people by multiplying every quantity by 3. For a map scale given as a ratio like 1:25000, every 1 cm on the map represents 25000 cm, or 250 m, in real life. Comparing mixtures using ratio means converting both to the same units before comparing the proportion of one ingredient to the total.
Worked example
A recipe for 6 people uses flour and sugar in the ratio 3:1, with 240 g of flour. Use ratio methods to find how much sugar is needed for 6 people.
- 1Identify the ratio 3:1, where flour corresponds to 3 parts and sugar to 1 part.
- 2Find the value of one part using the flour amount: 240÷3=80.
- 3Multiply the sugar's part by this value: 1×80=80.
- 4Check the ratio of 240:80 simplifies back to 3:1.
Answer: 80 g of sugar
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes scale a recipe ratio by adding a fixed amount rather than multiplying, turning doubling 2 eggs for twice the people into 2+2 eggs correctly but then wrongly adding flour amounts inconsistently. Always multiply every quantity by the same scale factor.
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