Ratio and Proportion: Practice Set 2
Ratio and Proportion: Practice Set 2 is a second practice round for 11+ ratio and proportion, building on simplifying ratios and sharing amounts before pushing into problems given as a difference, combined ratios and best-value comparisons.
Method
- Simplify a ratio by dividing all of its parts by their highest common factor, exactly like simplifying a fraction to its lowest terms.
- To share an amount in a given ratio, add the ratio's parts to find the total number of parts, then divide the amount by this total to find the value of one part.
- When you are told the difference between two shares rather than the total, first find the value of one 'gap' part, then use it to work out the total or either share.
- To combine two ratios that share a common term, such as A : B and B : C, scale each ratio so the shared term matches in both before merging them into one three-part ratio.
- For best-value comparisons, convert each option to the cost (or amount) for one identical unit, then compare the unit values directly.
- When a ratio problem also involves a unit change, such as metres to centimetres, convert every quantity to the same unit before working with the ratio.
Worked example
A fruit drink is made by mixing orange juice and lemonade in the ratio 2 : 5. Sam makes 490 ml of the drink. How much lemonade does he need?
- Add the parts of the ratio to find the total number of parts: 2 + 5 = 7.
- Divide the total amount by the number of parts to find the value of one part: 490 / 7 = 70 ml.
- Multiply the lemonade's number of parts by the unit value: 5 x 70 = 350 ml.
- Final answer: 350 ml.
Practice questions
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Q1Simplify the ratio 24 : 36 to its simplest form.Show answer
Answer: 2 : 3
Q2A box contains red and green marbles in the ratio 3 : 8. There are 12 red marbles. How many green marbles are there?Show answer
Answer: 32 (12 / 3 = 4, 4 x 8 = 32)
Q3Complete the missing number: 5 : 9 = 15 : ___.Show answer
Answer: 27
Q472 stickers are shared between Jack and Mia in the ratio 5 : 7. How many stickers does Mia receive?Show answer
Answer: 42 (72 / 12 = 6, 6 x 7 = 42)
Q56 identical notebooks cost 6.90 pounds. Calculate the cost of 10 of these notebooks.Show answer
Answer: 11.50 pounds (6.90 / 6 = 1.15, 1.15 x 10 = 11.50)
Q6A scale drawing has a scale of 1 : 200. A wall on the drawing is 8 cm long. Work out the real length of the wall in metres.Show answer
Answer: 16 m (8 x 200 = 1600 cm = 16 m)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The ratio of boys to girls in a class is 4 : 5. Calculate what fraction of the class are boys.
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In a fruit basket, the ratio of apples to pears is 3 : 2. There are 15 more apples than pears. Calculate the total number of pieces of fruit in the basket.
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A recipe uses flour, sugar and butter in the ratio 6 : 2 : 3. A baker wants to make a larger batch using 900 g of flour, keeping the same ratio for all three ingredients. (a) Calculate the amount of sugar needed. (b) Calculate the total mass of the mixture.
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Free printable worksheet
Want more practice on paper? Download the ratio and proportion: practice set 2 worksheet pack - 11 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.
This topic is chapter 2 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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