Year 8 ratio and proportion worksheet answers to download as PDF

These Year 8 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
Divide every part by the highest common factor. Clear decimals or fractions first by multiplying all parts by the same number, and use the same units before simplifying.
1. Divide by 6: \(3:4\)
2. Divide by 15: \(3:4:5\)
3. Multiply by 2: \(5:20\), divide by 5: \(1:4\)
4. Multiply by 4: \(2:3\), so \(2:3\)
5. 1.5 kg = 1500 g, so \(200:1500\), divide by 100: \(2:15\)
Answer to Question 2
1. Divide both parts by 4 to get \(1:2.5\); divide both by 10 to get \(0.4:1\).
2. Divide by 5: \(1:2.4\); divide by 12: \(0.417:1\) (to 3 d.p.).
3. Divide by 8: \(1:2.5\); divide by 20: \(0.4:1\).
4. Divide by 3: \(1:5\); divide by 15: \(0.2:1\).
To write a ratio as \(1:n\) divide both parts by the first number; for \(n:1\) divide both by the second number.
Answer to Question 3
1. 5 parts, one part \(=60\div5=12\). Shares: £24 and £36
2. 7 parts, one part \(=12\). Shares: £48 and £36
3. 9 parts, one part \(=20\). Shares: 100 kg, 60 kg and 20 kg
4. 5 parts, one part \(=1.50\). Shares: £1.50 and £6.00
Answer to Question 4
1. 3 parts = 24, so 1 part \(=8\) and girls \(=5\times8=\) 40
2. 7 parts = 35 L, so 1 part \(=5\) and red \(=4\times5=\) 20 litres
3. 7 parts = 63, so 1 part \(=9\). Cats 45 and dogs 18.
4. \(B-A\) is \(3\) parts \(=36\), so 1 part \(=12\). \(A=\) 24 and \(B=\) 60.
Answer to Question 5
The unitary method has two steps: divide to find the value for one item, then multiply by the number you need.
1. 1 pen \(=3.20\div5=£0.64\), so 8 pens \(=\) £5.12
2. 1 mile \(=18\div150=0.12\) litres, so 400 miles \(=\) 48 litres
3. 1 biscuit \(=70\) cal, so 7 biscuits \(=\) 490 cal
4. 1 minute \(=75\) bottles, so 14 minutes \(=\) 1050 bottles
Answer to Question 6
1. Total work \(4\times9=36\) worker-days; 6 workers share it: \(36\div6=\)6 days.
2. \(3\times40=120\) pipe-minutes; \(120\div5=\)24 minutes.
3. The number of sweets is fixed: \(12\times8=96\). \(96\div16=\)6 each.
4. \(6\times10=60\) pump-hours; to finish in 4 hours: \(60\div4=\)15 pumps.
In each case more workers, pipes or pumps means less time, so the answers get smaller as the number increases.
Answer to Question 7
1. \(300:150:90=10:5:3\)
2. Multiplier \(30\div12=2.5\): oats 750 g, butter 375 g, syrup 225 g, sugar 187.5 g.
3. Butter per flapjack \(=150\div12=12.5\) g. \(200\div12.5=16\), so 16 flapjacks.
4. Oats per flapjack \(=25\) g. \(28\times25=700\) g, so 700 g.
Answer to Question 8
1. \(1+2+4=\) 7 parts
2. 1 part \(=0.7\div7=0.1\) m³: cement 0.1 m³, sand 0.2 m³, gravel 0.4 m³.
3. \(0.1\times48+0.2\times30+0.4\times36=4.80+6.00+14.40=\) £25.20
4. \(1+3+5=9\) parts, 1 part \(=0.7\div9=0.0778\) m³, sand \(=3\times0.0778=0.2333\) m³. That is \(0.2333-0.2=\) 0.033 m³ more.
Answer to Question 9
1. \(6.4\times50000=320000\) cm. Divide by 100 000 to change to km: 3.2 km.
2. 3.5 km \(=350000\) cm, and \(350000\div50000=\)7 cm on the map.
3. 50 000 cm \(=500\) m \(=0.5\) km, so 1 cm represents 0.5 km.
4. Time = distance ÷ speed: \(3.2\div4=0.8\) hours, and \(0.8\times60=\)48 minutes.
Answer to Question 10
1. \(350\times1.15=\) €402.50
2. Left \(=402.50-280=122.50\) euros. \(122.50\div1.25=\) £98
3. \(60\div1.15=\) £52.17
4. At £1 = €1.15 one euro is worth £0.870. At £1 = €1.25 one euro is worth only £0.800. The first rate is better for changing euros into pounds.
Answer to Question 11
1. Small: \(85\div5=17.0\)p. Medium: \(210\div15=14.0\)p. Large: \(375\div25=15.0\)p per 100 ml.
2. Medium at 14p per 100 ml.
3. 3 medium bottles give 4.5 litres for \(3\times2.10=\) £6.30. (A large and a medium would give 4 litres for £5.85; two larges and a small give 5.5 litres for £8.35.)
4. A small bottle has the lowest price but the highest price per 100 ml. Value for money depends on the price for the same amount.
Answer to Question 12
1. 5 parts, 1 part \(=0.5\) L. Blue 1.5 L, yellow 1.0 L.
2. Blue is \(\frac35\) of the mix: \(\frac35\times12=\) 7.2 L
3. 1 part of yellow \(=0.4\) L, so the total is \(5\times0.4=\) 2 litres.
4. \(1.5\times6+1.0\times8=9+8=\) £17
Check (a): \(1.5+1.0=2.5\) litres and \(1.5:1.0=3:2\).
Answer to Question 13
1. Work needed = workers × days: \(4\times6=\)24 caretaker-days.
2. \(24\div3=\)8 days, longer because there are fewer people.
3. \(24\div2=\)12 caretakers.
4. In 2 days alone he does 2 caretaker-days, leaving 22. Four people then take \(22\div4=5.5\) days. Total \(2+5.5=\)7.5 days.
Answer to Question 14
1. \(14:18:8=\) \(7:9:4\)
2. 20 parts, 1 part \(=14\). Jo £98, Kai £126, Lee £56.
3. Equal share: \(280\div3=93.33\), so Lee would receive about £37.33 more.
4. 1 part \(=420\div20=21\). Jo £147, Kai £189, Lee £84.
Answer to Question 15
1. 10 parts, 1 part \(=45\). Library £225, sports club £135, food bank £90.
2. The rest is \(450-150=300\), in 8 parts, so 1 part \(=37.50\). Library £187.50, sports club £112.50, food bank £150.
3. Income \(=150\times4=600\). Costs : income \(=120:600=\) \(1:5\).
4. Profit \(=4n-120=450\Rightarrow n=142.5\), so 143 tickets.
Answer to Question 16
1. Length: \(3600\div72=\) 50 cm. Wingspan: \(3840\div72=\) 53.3 cm.
2. \(7.5\times72=540\) cm \(=\) 5.4 m
3. \(180\div12=\) 15 figures
4. The scale factor for areas is \(72^2=5184\). \(90\) m² \(=900000\) cm², and \(900000\div5184=\) 173.6 cm².
Lengths are divided by 72, but areas are divided by \(72^{2}\), because an area has two dimensions that are both scaled.
Answer to Question 17
1. \(12:20=\) \(3:5\)
2. 8 parts, 1 part \(=6\). Ali £18, Beth £30.
3. \(48\times1.15=\) £55.20. 1 part \(=6.90\). Ali £20.70, Beth £34.50.
4. Yes: \(30\times1.15=34.50\). The ratio does not change, so each share rises by the same 15%.
Answer to Question 18
1. Gran: \(240:400=1:1.67\). Cookbook: \(300:450=1:1.5\).
2. The cookbook recipe has more flour for each ml of milk (0.667 g/ml against 0.6 g/ml), so it is thicker.
3. 6 eggs is twice 3 eggs, so double everything: flour 480 g and milk 800 ml.
4. \(600:1000:7.5\), which is \(240:400:3\), simplest form \(240:400:3\) (no common factor).
Answer to Question 19
1. \(1120\div8=\) £140
2. \(1120\div12=\) £93.33
3. If the number of people goes up, the share per person goes down, and the product (people × share = £1120) is constant.
4. \(1120\times0.9=1008\), and \(1008\div12=\) £84
5. Second: \(1500\div10=£150\) per person. The first villa costs £140, so the first is cheaper per person.
Answer to Question 20
1. Green is 3 in the first ratio and 4 in the second. Use the LCM 12: red:green \(=8:12\) and green:blue \(=12:15\). So \(8:12:15\).
2. \(8+12+15=35\) parts, 1 part \(=6\). Red 48, green 72, blue 90.
3. \(2:3\) (the original red : green ratio is unchanged).
4. \(\dfrac{15}{35}=\) 42.9%

How to use these Year 8 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 8 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 8 ratio and proportion worksheet answers show every step, so nothing is left unexplained.