Ratio and Proportion
Ratio and Proportion covers comparing two quantities using a ratio, sharing an amount into unequal parts according to a given ratio, scaling a recipe, model or map up or down using a scale factor, and solving problems about similar shapes where one measurement is known and another must be found.
Before you start
Make sure you're comfortable with these topics first:
Method
- Decide whether the problem is a ratio (comparing two or more quantities that make up a whole) or direct proportion (scaling one recipe, drawing or amount up or down by the same factor).
- For sharing in a given ratio, add the parts of the ratio to find the total number of parts, divide the total amount by this to find the value of one part, then multiply to find each share.
- For scaling problems, find the scale factor by dividing the new value by the original value, then multiply every quantity by that same factor.
- For similar shapes, find the scale factor from one pair of matching (corresponding) sides, then apply it to find any other missing side.
- Simplify a ratio in the same way as a fraction, by dividing every part by their highest common factor.
- For best-value or unit-price problems, divide the cost by the quantity to find a price per single unit, so that different pack sizes can be compared fairly.
- Show the value of one part or one unit as a clear step in your working, since it is usually the key method mark in a ratio question.
Worked example
Two brothers, Kwame and Reuben, share some money in the ratio 3:5. Kwame receives 18 pounds less than Reuben. Work out how much money they share in total.
- Find the difference in parts between the two shares: 5 parts - 3 parts = 2 parts.
- This difference of 2 parts is equal to 18 pounds, so divide to find the value of 1 part: 18 divided by 2 = 9 pounds.
- Find the total number of parts in the ratio: 3 + 5 = 8 parts.
- Multiply the value of one part by the total number of parts: 8 x 9 = 72.
- So Kwame and Reuben share 72 pounds in total (check: Kwame gets 3 x 9 = 27 pounds, Reuben gets 5 x 9 = 45 pounds, and 45 - 27 = 18, which matches).
Practice questions
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Q1Simplify the ratio 15:25.Show answer
Answer: 3:5
Q2Amaan mixes yellow and blue paint in the ratio 2:5 to make green paint. He uses 6 litres of yellow paint. How much blue paint does he need?Show answer
Answer: 15 litres
Q3A recipe for 8 flapjacks uses 240g of oats. How many grams of oats are needed for 20 flapjacks?Show answer
Answer: 600g
Q4Share 45 pounds between Elsie and Idris in the ratio 4:5. How much does Idris receive?Show answer
Answer: 25 pounds
Q5A 500g bag of rice costs 1.60 pounds. An 800g bag costs 2.40 pounds. Which bag is better value for money?Show answer
Answer: The 800g bag (30p per 100g, compared with 32p per 100g for the 500g bag)
Q6A model car is built at a scale of 1:24. The real car is 4.8 metres long. How long is the model car, in centimetres?Show answer
Answer: 20cm
Q7The ratio of teachers to pupils on a school trip is 1:12. There are 96 pupils going on the trip. How many teachers are needed?Show answer
Answer: 8 teachers
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A necklace is made using blue beads and white beads in the ratio 3:7. There are 21 white beads. How many blue beads are there?
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A fruit squash is made by mixing concentrate and water in the ratio 2:9. Priyanka wants to make 6.6 litres of squash in total. Work out how many litres of concentrate she needs.
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Two rectangles are mathematically similar. The smaller rectangle has a length of 8cm and a width of 5cm. The larger rectangle has a length of 22cm. Work out the width of the larger rectangle, giving your answer to 1 decimal place.
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Free printable worksheet
Want more practice on paper? Download the ratio and proportion worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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