Ratio, proportion and percentages – Year 6 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. Red to blue is 3 : 5.
   2. Blue to red is 5 : 3. The order matters, because the ratio is written in the order of the things it compares.
   3. There are 3 + 5 = 8 counters in the bag, so \(\frac{3}{8}\) are red.
   4. 12 : 18 divides by 6, so the ratio is 2 : 3.
   5. Write both in the same units: 40 cm to 100 cm. Divide by 20 to get 2 : 5.

2. Answer to Question 2

   1. The HCF of 45 and 60 is 15, so the ratio is 3 : 4.
   2. The HCF of 24, 36 and 60 is 12, so the ratio is 2 : 3 : 5.
   3. The HCF is 3, so the ratio is 2 : 3.
   4. 120p : 280p. The HCF is 40, so the ratio is 3 : 7.
   5. 2 kg = 2 000 g. 2 000 : 500 divides by 500 to give 4 : 1.

3. Answer to Question 3

   1. The multiplier is 12 ÷ 3 = 4, so 7 × 4 = 28.
   2. 12 ÷ 3 = 4, so the sugar is 1 × 4 = 4 g.
   3. 3 × 4 = 12, so the cost is 2.40 × 4 = £9.60.
   4. The multiplier is 40 ÷ 8 = 5, so 5 × 5 = 25.

4. Answer to Question 4

   1. 3 + 5 = 8 parts. £40 ÷ 8 = £5 a part. Shares: 3 × 5 = £15 and 5 × 5 = £25. Check: 15 + 25 = 40.
   2. 2 + 3 + 4 = 9 parts. 72 ÷ 9 = 8. Shares: 16, 24 and 32 sweets. Check: 16 + 24 + 32 = 72.
   3. 1 + 4 = 5 parts. 90 ÷ 5 = 18 kg. Shares: 18 kg and 72 kg.
   4. 3 + 4 = 7 parts. 56 ÷ 7 = 8. Shares: 24 and 32. The second friend gets 8 more stickers.

5. Answer to Question 5

   1. 3 × 4 = 12 cm and 5 × 4 = 20 cm. The new rectangle is 12 cm by 20 cm.
   2. The scale factor is 12 ÷ 4 = 3. The other sides are 6 × 3 = 18 cm and 8 × 3 = 24 cm.
   3. 6.5 × 5 = 32.5 km.
   4. 40 ÷ 5 = 8 cm on the map.

6. Answer to Question 6

   1. 10% = 35, so 20% = 70.
   2. 10% = £4.80 and 5% = £2.40, so 15% = £7.20.
   3. Class A: 18/24 = 3/4 = 75%. Class B: 21/30 = 7/10 = 70%. Class A is higher.
   4. 25% of £80 = £20. £80 + £20 = £100.

7. Answer to Question 7

   1. 3 parts = 450 g, so 1 part = 150 g. Bananas = 2 × 150 = 300 g.
   2. 450 + 300 = 750 g.
   3. \(\frac{2}{5}\) of the mixture is bananas, so \(\frac{2}{5}\).
   4. 2 parts = 600 g, so 1 part = 300 g. Strawberries = 3 × 300 = 900 g. The total is 900 + 600 = 1 500 g.

8. Answer to Question 8

   1. 3 parts = 15 tins, so 1 part = 5. Blue = 2 × 5 = 10 tins.
   2. 10 + 15 = 25 tins.
   3. 2 parts = 20 tins, so 1 part = 10. White = 3 × 10 = 30 tins. Total = 20 + 30 = 50 tins.
   4. Blue is 2 out of 5 parts, so \(\frac{2}{5}=\frac{40}{100}=\) 40%.

9. Answer to Question 9

   1. 3 + 4 = 7 parts. 28 ÷ 7 = 4. Boys: 3 × 4 = 12. Girls: 4 × 4 = 16.
   2. 28 + 7 = 35 pupils.
   3. There are 12 boys and 16 + 7 = 23 girls, so the ratio is 12 : 23. This cannot be simplified (12 and 23 have no common factor).
   4. 16 ÷ 28 = 4/7 = 0.571..., so about 57%.

10. Answer to Question 10

    1. Lake path: 6.5 × 5 = 32.5 km. River path: 4.2 × 5 = 21 km. Hill path: 2.8 × 5 = 14 km.
    2. The Lake path is the longest. 32.5 − 14 = 18.5 km longer than the Hill path.
    3. 32.5 ÷ 3.5 = 9.28..., so it takes about 9 hours 17 minutes (9.29 hours).
    4. 4.2 − 1.5 = 2.7 cm on the map, and 2.7 × 5 = 13.5 km.

11. Answer to Question 11

    1. 3 + 5 = 8 parts. £40 ÷ 8 = £5. Sam gets 3 × £5 = £15. Tia gets 5 × £5 = £25.
    2. Sam worked 3 hours, so 1 part is 1 hour. Tia worked 5 hours.
    3. £16 ÷ 8 = £2 a part. Sam gets £6. Tia gets £10.
    4. Sam: £15 + £6 = £21. Tia: £25 + £10 = £35. Check: 21 + 35 = 56 = 40 + 16.

12. Answer to Question 12

    1. 2 + 3 + 4 = 9 parts. 72 ÷ 9 = 8. Red: 16, green: 24, yellow: 32.
    2. 72 − 16 = 56 sweets.
    3. 24 : 32 divides by 8 to give 3 : 4.
    4. 24 ÷ 56 = 3/7 = 0.428..., so about 43%.

13. Answer to Question 13

    1. 4.8 m = 480 cm. 480 ÷ 24 = 20 cm.
    2. 3 × 24 = 72 cm, so the real wheel has a diameter of 72 cm.
    3. 1.68 m = 168 cm. 168 ÷ 24 = 7 cm.
    4. 5 × 24 = 120 cm = 1.2 m.

14. Answer to Question 14

    1. The multiplier is 10 ÷ 4 = 2.5.
    2. Rice: 200 × 2.5 = 500 g. Milk: 800 × 2.5 = 2 000 ml. Sugar: 60 × 2.5 = 150 g. Butter: 20 × 2.5 = 50 g.
    3. 800 ml serves 4 people, so 200 ml serves 1 person. 2 000 ÷ 200 = 10 people.
    4. 200 : 60 divides by 20 to give 10 : 3.

15. Answer to Question 15

    1. Rovers: 18/24 = 75%. United: 21/30 = 70%. Town: 14/20 = 70%. City: 20/25 = 80%.
    2. City has the best record, with 80%.
    3. United and Town both have 70%, because \(\frac{21}{30}=\frac{7}{10}\) and \(\frac{14}{20}=\frac{7}{10}\).
    4. Rovers: 23 out of 29 = 79.3%. Town: 19 out of 25 = 76%. (To the nearest 0.1%, Rovers 79.3% and Town 76.0%.)
    5. No. Rovers have played more matches, so the total number of wins is not a fair comparison. Percentages (or fractions) compare fairly: 75% for Rovers and 70% for Town.

16. Answer to Question 16

    1. 1 + 2 + 3 = 6 parts.
    2. 1.8 tonnes = 1 800 kg. 1 800 ÷ 6 = 300 kg a part. Cement: 300 kg. Sand: 600 kg. Gravel: 900 kg.
    3. 300 ÷ 25 = 12 bags.
    4. 2/6 = 1/3 = 33.3...%, so about 33%.
    5. Sand is 2 parts out of 6. 200 kg of sand is 2 parts, so 1 part = 100 kg. The total mass is 6 × 100 = 600 kg.

17. Answer to Question 17

    1. 3 × 2.5 = 7.5 m and 5 × 2.5 = 12.5 m.
    2. Small bed: 2 × (3 + 5) = 16 m. Large bed: 2 × (7.5 + 12.5) = 40 m. The perimeter is multiplied by the scale factor: 16 × 2.5 = 40.
    3. Small bed: 3 × 5 = 15 m². Large bed: 7.5 × 12.5 = 93.75 m². The area is 93.75 ÷ 15 = 6.25 times bigger, which is 2.5 × 2.5.
    4. 40 × 4.80 = £192.
    5. 150 ÷ 4.80 = 31.25, so she can buy 31.25 m (31 m of whole metres).

18. Answer to Question 18

    1. 10% of £240 = £24 and 5% = £12, so 15% = £36. Sale price = 240 − 36 = £204.
    2. 5% of £204 = £10.20. Price = 204 − 10.20 = £193.80.
    3. Saving = 240 − 193.80 = £46.20. Percentage = 46.20 ÷ 240 = 0.1925, which is 19.25%, so 19% to the nearest whole number (not 20%).
    4. 20% of £250 = £50, so the price is £200. The first shop (with the loyalty card) is cheaper: 200 − 193.80 = £6.20 cheaper.
    5. 193.80 + 18 = £211.80.

19. Answer to Question 19

    1. 3.50 ÷ 5 = 70p each.
    2. 8 × 70p = 560p = £5.60.
    3. Pack of 12: 780p ÷ 12 = 65p. Pack of 20: 1 200p ÷ 20 = 60p.
    4. The pack of 20 has the lowest cost for each pen (60p), so it is the best value.
    5. 60 ÷ 20 = 3 packs of 20, costing 3 × £12 = £36. (60 ÷ 12 = 5 packs would cost £39, and 12 packs of 5 would cost £42.)

20. Answer to Question 20

    1. Blue minus red is 3 − 2 = 1 part, and 1 part = 10 beads. Red = 20, blue = 30, so there are 50 beads altogether.
    2. For a ratio of 1 : 1 there must be 30 red beads, so 10 red beads are added. The total is now 60 beads.
    3. 3 + 2 = 5 parts. 60 ÷ 5 = 12. The friends get 36 beads and 24 beads.