Year 7 ratio and proportion worksheet answers to download as PDF

These Year 7 ratio and proportion worksheet answers give a full worked solution to all 20 questions of the ratio and proportion worksheet. Try each question yourself first, then check your method step by step.

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Answer to Question 1
To simplify a ratio, divide every part by the highest common factor. If there are decimals, multiply first to make whole numbers, and if there are units, make them the same before simplifying.
1. 2 : 3
2. 3 : 4 : 5
3. 1 : 4
4. 1 kg = 1000 g. 150 : 1000 = 3 : 20.
5. 1.2 m = 120 cm. 40 : 120 = 1 : 3.
Answer to Question 2
In each case add the parts of the ratio, divide the amount by this total to find one part, then multiply by each number in the ratio. The shares must add up to the original amount.
1. 3 parts, £20 per part: £20 and £40.
2. 9 parts, £10 per part: £20, £30, £40.
3. 12 parts, £7 per part: £35 and £49.
4. 4 parts, 18 per part: 54 and 18 sweets.
Answer to Question 3
Equivalent ratios are made by multiplying (or dividing) every part by the same number, just like equivalent fractions.
1. Multiply by 4: 20.
2. Multiply by 4: 16.
3. Multiply by 3: 9 : 15.
4. 5 parts = 30, so 1 part = 6 and blue = \(2\times6=\)12.
Answer to Question 4
1. 1 pen = 70p. 8 pens = £5.60.
2. 1 apple = 0.15 kg. 20 apples = 3 kg.
3. 1 litre = 12 km. 10 litres = 120 km.
4. 1 hour = £7.80. 15 hours = £117.
The unitary method always works in two steps: divide to find the value for one, then multiply to find the value for the number you need.
Answer to Question 5
1. Small: \(120\div500=0.24\)p per gram. Large:\(440\div2000=0.22\)p per gram. The 2 kg pack is better value.
2. Small: \(150\div250=0.6\)p per ml. Large: \(420\div750=0.56\)p per ml. The 750 ml bottle is better value.
3. 1.5 litres: \(210\div1.5=140\)p per litre. 2 litres: \(260\div2=130\)p per litre. The 2 litre bottle is better value.
Answer to Question 6
1. 1 cm on the map is 50 000 cm on the ground. Divide by 100 to change to metres: 500 m.
2. \(6\times50000=300000\) cm. Divide by 100 to get 3 000 m, then by 1 000: 3 km.
3. Change 2.5 km into centimetres: \(2.5\times100000=250000\) cm. Divide by the scale: \(250000\div50000=\)5 cm.
Answer to Question 7
1. 10 parts = 5 litres, so 1 part = 0.5 litres: orange 1.5 litres, pineapple 1 litre, lemonade 2.5 litres.
2. 2 parts = 1.2 litres, so 1 part = 0.6 litres, and 10 parts = 6 litres.
3. Orange: \(3\times0.6=\)1.8 litres. Lemonade: \(5\times0.6=\)3 litres.
4. Cost: \(1.5\times1.5+1\times2+2.5\times0.6=2.25+2+1.5=\)£5.75.
Answer to Question 8
1. 2 bags = \(2\times25=50\) kg of cement, which is 1 part. Sand is 2 parts: 100 kg. Gravel is 4 parts: 200 kg.
2. Add the three amounts: \(50+100+200=\)350 kg.
3. There are \(1+2+4=7\) parts and cement is 1 of them: \(\dfrac{1}{7}\).
4. 700 kg is 7 parts, so 1 part (the cement) is \(700\div7=100\) kg. \(100\div25=\)4 bags.
Answer to Question 9
1. Small: \(225\div3.75=60\)p. Medium: \(330\div6=55\)p. Large: \(600\div12=50\)p.
2. The large pack (50p per 100 g).
3. Twice the medium pack costs £6.60 for 1.2 kg. The large pack costs £6.00, so it is cheaper by 60p.
4. \(1200\div150=\)8 days.
Comparing the price for the same mass (100 g) is the fairest way to decide which pack is the best buy.
Answer to Question 10
1. 9 parts = £45, 1 part = £5: Ali £20, Ben £25.
2. 12 parts = £72, 1 part = £6: Ali £24, Ben £30, Cara £18.
3. \(24-20=\)£4.
4. Ali \(\dfrac{4}{12}=\dfrac{1}{3}\), Ben \(\dfrac{5}{12}\), Cara \(\dfrac{3}{12}=\dfrac{1}{4}\).
Check: \(24+30+18=72\), so the three shares make the whole prize.
Answer to Question 11
1. Divide distance by time: \(195\div3=\)65 km in one hour.
2. Multiply by 5: \(65\times5=\)325 km.
3. Each hour covers 65 km, and \(130\div65=\)2 hours.
4. The second coach covers \(280\div4=70\) km each hour, more than 65 km, so the second coach is faster.
Answer to Question 12
1. 6 people: 300 g, 3 eggs, 450 ml. 10 people: 500 g, 5 eggs, 750 ml. 15 people: 750 g, 7.5 eggs, 1 125 ml.
2. 5 eggs feed 10 people, with 500 g flour and 750 ml milk.
3. Flour 0.5 kg = 60p. Eggs 5 × 25p = £1.25. Milk 0.75 litre = 60p. Total: \(60+125+60=245\)p = £2.45.
Answer to Question 13
1. \(330\div200=\)1.65 m
2. \(0.6\times200=\)120 m.
3. No. When lengths are scaled by 1 : 200, volume (and weight) is scaled by \(1:200^{3}\), which is 1 : 8 000 000. So the model weighs far less than the ratio of heights suggests.
A scale of 1 : 200 means every real length is 200 times the matching model length, so we divide to go from real to model and multiply to go from model to real.
Answer to Question 14
1. 9 parts = 135, 1 part = 15: 75 boys and 60 girls.
2. Girls: 70. Ratio \(75:70=\)15 : 14.
3. \(\dfrac{60}{135}\times100=44.4\), so about 44%.
4. \(135\times2.50\times4=\)£1 350.
Check: \(75+60=135\) members, and after ten girls join the club has 145 members.
Answer to Question 15
1. \(2:3:5\) is already in its simplest form (the total is 10 parts).
2. 1 part = £40: Amy £80, Ben £120, Cara £200.
3. \(400\div4=100\), so they have £300 left.
4. 1 part = £30: Amy £60, Cara £150. Difference £90.
Check: \(80+120+200=400\) and \(60+90+150=300\).
Answer to Question 16
1. 8 parts = 1600 g, 1 part = 200 g: flour 1000 g, water 600 g.
2. Water is 700 g. Ratio \(1000:700=\)10 : 7.
3. For 700 g of water the flour should be \(700\div3\times5=1166.67\) g, so add about 167 g of flour.
4. Flour 1167 g plus water 700 g = about 1 867 g.
Answer to Question 17
1. 5 parts, 2 litres per part: yellow 6 litres, blue 4 litres.
2. Yellow 4 litres, blue 6 litres.
3. Yellow \(6+4=10\) litres, blue \(4+6=10\) litres.
4. Yellow: 2 tins = £25. Blue: 4 tins = £28. Total £53.
Buying exactly enough would need 2 tins of yellow (10 litres) and 4 tins of blue (10 litres), so there is no cheaper combination.
Answer to Question 18
1. Each part is \(50\div5=10\), so the shares are £20 and £30.
2. The last number is wrong: \(24\div6=4\), so the answer is 2 : 3 : 4.
3. Carl added 6 pens at the wrong price. One pen costs 75p, so 10 pens cost £7.50.
4. Ratio 3 : 1 has 4 parts, so sugar is one quarter, not a third.
Answer to Question 19
1. 5 packs of 500 sheets make 2 500 sheets: \(5\times3.50=\)£17.50.
2. 10% off leaves 90%: \(17.50\times0.9=\)£15.75.
3. Shop A costs £15.75 and shop B costs £16.00, so shop A is cheaper by \(16-15.75=\)25p.
4. 10 000 sheets is 4 lots of 2 500, so the saving is \(4\times25\)p = £1.00.
Answer to Question 20
1. 7 parts = 42, 1 part = 6, so the daughter is \(2\times6=\)12.
2. Mother 47, daughter 17.
3. \(47:17\) cannot be simplified, so the ratio is 47 : 17.
4. Let t be years: \(42+t=2(12+t)\), \(42+t=24+2t\), \(t=\)18. In 18 years: mother 60, daughter 30.

How to use these Year 7 ratio and proportion worksheet answers

First, try every question on the worksheet without looking. Then compare your working with the solution line by line, not only the final answer. When your answer is different, find the first step that changes, because that is where the mistake is. After that, read the matching part of the ratio and proportion lesson again. Finally, check that the method is secure with the quiz or the test.

Also, the Year 7 ratio and proportion worksheet answers are available as a PDF, so you can mark printed work quickly. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, these Year 7 ratio and proportion worksheet answers show every step, so nothing is left unexplained.