Ratio and Proportion - Free resources about circles and their ... - Free Printable

Let's solve each problem step by step, explaining the method and reasoning clearly.

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1. Split £150 into the following ratios:

#### a) 2:1
- Total parts = 2 + 1 = 3
- Each part = £150 ÷ 3 = £50
- First share (2 parts) = 2 × £50 = £100
- Second share (1 part) = 1 × £50 = £50

✔ Answer: £100 : £50

#### b) 1:4
- Total parts = 1 + 4 = 5
- Each part = £150 ÷ 5 = £30
- First share = 1 × £30 = £30
- Second share = 4 × £30 = £120

✔ Answer: £30 : £120

#### c) 3:7
- Total parts = 3 + 7 = 10
- Each part = £150 ÷ 10 = £15
- First share = 3 × £15 = £45
- Second share = 7 × £15 = £105

✔ Answer: £45 : £105

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2. Split 360g into the following ratios:

#### a) 3:1
- Total parts = 3 + 1 = 4
- Each part = 360g ÷ 4 = 90g
- First share = 3 × 90g = 270g
- Second share = 1 × 90g = 90g

✔ Answer: 270g : 90g

#### b) 5:7
- Total parts = 5 + 7 = 12
- Each part = 360g ÷ 12 = 30g
- First share = 5 × 30g = 150g
- Second share = 7 × 30g = 210g

✔ Answer: 150g : 210g

#### c) 2:4:3
- Total parts = 2 + 4 + 3 = 9
- Each part = 360g ÷ 9 = 40g
- Shares:
- 2 parts = 2 × 40g = 80g
- 4 parts = 4 × 40g = 160g
- 3 parts = 3 × 40g = 120g

✔ Answer: 80g : 160g : 120g

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3. Split 225m into the following ratios:

#### a) 11:4
- Total parts = 11 + 4 = 15
- Each part = 225m ÷ 15 = 15m
- First share = 11 × 15m = 165m
- Second share = 4 × 15m = 60m

✔ Answer: 165m : 60m

#### b) 5:1:3
- Total parts = 5 + 1 + 3 = 9
- Each part = 225m ÷ 9 = 25m
- Shares:
- 5 parts = 5 × 25m = 125m
- 1 part = 1 × 25m = 25m
- 3 parts = 3 × 25m = 75m

✔ Answer: 125m : 25m : 75m

#### d) 10:9:6
- Total parts = 10 + 9 + 6 = 25
- Each part = 225m ÷ 25 = 9m
- Shares:
- 10 parts = 10 × 9m = 90m
- 9 parts = 9 × 9m = 81m
- 6 parts = 6 × 9m = 54m

✔ Answer: 90m : 81m : 54m

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4. Karen and Priti are sharing sweets in ratio 2:3. Karen gets 10 sweets. How many does Priti get?

- Ratio 2:3 means for every 2 sweets Karen gets, Priti gets 3.
- Karen’s 2 parts = 10 sweets → So 1 part = 10 ÷ 2 = 5 sweets
- Priti gets 3 parts = 3 × 5 = 15 sweets

✔ Answer: 15 sweets

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5. Tom, Phil and Ali deliver newspapers in ratio 1:4:3. Total delivered = 120. How many did Ali deliver?

- Total parts = 1 + 4 + 3 = 8
- Each part = 120 ÷ 8 = 15
- Ali’s share = 3 parts = 3 × 15 = 45 newspapers

✔ Answer: 45 newspapers

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6. Ando is 13, Hiro is 15. They share £112 in ratio of their ages. How much each?

- Ratio of ages = 13:15
- Total parts = 13 + 15 = 28
- Each part = £112 ÷ 28 = £4
- Ando gets = 13 × £4 = £52
- Hiro gets = 15 × £4 = £60

✔ Answer: Ando: £52, Hiro: £60

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7. Book club: 12 people, men:women = 1:2. Two more men join. New ratio?

- Original ratio: 1:2 → total parts = 3
- Total people = 12 → so each part = 12 ÷ 3 = 4
- Men = 1 × 4 = 4
- Women = 2 × 4 = 8
- After 2 more men join: men = 4 + 2 = 6, women = 8
- New ratio = 6:8 = simplify by dividing by 2 → 3:4

✔ Answer: 3:4

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8. Tennis club: 3 times as many right-handed as left-handed. Total players = 36. How many left-handed?

Let:
- Left-handed = x
- Right-handed = 3x

Total:
x + 3x = 36
4x = 36
x = 9

✔ Answer: 9 left-handed players

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✔ Final Answers Summary:

1. a) £100 : £50 b) £30 : £120 c) £45 : £105
2. a) 270g : 90g b) 150g : 210g c) 80g : 160g : 120g
3. a) 165m : 60m b) 125m : 25m : 75m d) 90m : 81m : 54m
4. Priti gets 15 sweets
5. Ali delivered 45 newspapers
6. Ando: £52, Hiro: £60
7. New ratio: 3:4
8. 9 left-handed players

Let me know if you'd like these explained visually or with diagrams!