Ratios and Proportions Synthesis Worksheet | Fun and Engaging 6th ... - Free Printable

Let's solve this "Ratios and Proportions Synthesis" worksheet step by step.

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✔ Section A: Simplify the Ratios

To simplify a ratio, we divide both numbers by their greatest common divisor (GCD).

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#### 1) $ 3 : 12 $
- GCD of 3 and 12 is 3
- $ \frac{3}{3} : \frac{12}{3} = 1 : 4 $

#### 2) $ 5 : 30 $
- GCD = 5 → $ 1 : 6 $

#### 3) $ 2 : 14 $
- GCD = 2 → $ 1 : 7 $

#### 4) $ 3 : 15 $
- GCD = 3 → $ 1 : 5 $

#### 5) $ 10 : 30 $
- GCD = 10 → $ 1 : 3 $

#### 6) $ 6 : 60 $
- GCD = 6 → $ 1 : 10 $

#### 7) $ 2 : 16 $
- GCD = 2 → $ 1 : 8 $

#### 8) $ 4 : 24 $
- GCD = 4 → $ 1 : 6 $

#### 9) $ 8 : 24 $
- GCD = 8 → $ 1 : 3 $

#### 10) $ 9 : 27 $
- GCD = 9 → $ 1 : 3 $

#### 11) $ 11 : 55 $
- GCD = 11 → $ 1 : 5 $

#### 12) $ 7 : 42 $
- GCD = 7 → $ 1 : 6 $

#### 13) $ 10 : 15 $
- GCD = 5 → $ 2 : 3 $

#### 14) $ 8 : 12 $
- GCD = 4 → $ 2 : 3 $

#### 15) $ 55 : 66 $
- GCD = 11 → $ 5 : 6 $

#### 16) $ 14 : 21 $
- GCD = 7 → $ 2 : 3 $

#### 17) $ 10 : 25 $
- GCD = 5 → $ 2 : 5 $

#### 18) $ 8 : 10 $
- GCD = 2 → $ 4 : 5 $

#### 19) $ 12 : 16 $
- GCD = 4 → $ 3 : 4 $

#### 20) $ 9 : 15 $
- GCD = 3 → $ 3 : 5 $

#### 21) $ 36 : 60 $
- GCD = 12 → $ 3 : 5 $

#### 22) $ 27 : 36 $
- GCD = 9 → $ 3 : 4 $

#### 23) $ 20 : 50 $
- GCD = 10 → $ 2 : 5 $

#### 24) $ 6 : 21 $
- GCD = 3 → $ 2 : 7 $

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✔ Section B: Share the amounts into the following ratios

We use the method:
1. Add up the parts of the ratio.
2. Divide the total amount by the sum to get the value of one part.
3. Multiply each part of the ratio by this value.

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#### 1) $100 into the ratio 3:7
- Total parts = 3 + 7 = 10
- Value per part = $100 ÷ 10 = $10
- First share = 3 × $10 = $30
- Second share = 7 × $10 = $70
✔ Answer: $30 and $70

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#### 2) $48 into the ratio 2:2
- Total parts = 2 + 2 = 4
- Per part = $48 ÷ 4 = $12
- Each share = 2 × $12 = $24
✔ Answer: $24 and $24

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#### 3) $24 into the ratio 1:3:8
- Total parts = 1 + 3 + 8 = 12
- Per part = $24 ÷ 12 = $2
- Shares:
- 1 × $2 = $2
- 3 × $2 = $6
- 8 × $2 = $16
✔ Answer: $2, $6, $16

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#### 4) $25 into the ratio 2:3
- Total parts = 2 + 3 = 5
- Per part = $25 ÷ 5 = $5
- 2 × $5 = $10, 3 × $5 = $15
✔ Answer: $10 and $15

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#### 5) $56 into the ratio 3:5
- Total parts = 3 + 5 = 8
- Per part = $56 ÷ 8 = $7
- 3 × $7 = $21, 5 × $7 = $35
✔ Answer: $21 and $35

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#### 6) $60 into the ratio 6:4:5
- Total parts = 6 + 4 + 5 = 15
- Per part = $60 ÷ 15 = $4
- Shares:
- 6 × $4 = $24
- 4 × $4 = $16
- 5 × $4 = $20
✔ Answer: $24, $16, $20

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#### 7) $18 into the ratio 4:5
- Total parts = 4 + 5 = 9
- Per part = $18 ÷ 9 = $2
- 4 × $2 = $8, 5 × $2 = $10
✔ Answer: $8 and $10

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#### 8) $77 into the ratio 5:2
- Total parts = 5 + 2 = 7
- Per part = $77 ÷ 7 = $11
- 5 × $11 = $55, 2 × $11 = $22
✔ Answer: $55 and $22

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#### 9) $28 into the ratio 4:3:7
- Total parts = 4 + 3 + 7 = 14
- Per part = $28 ÷ 14 = $2
- Shares:
- 4 × $2 = $8
- 3 × $2 = $6
- 7 × $2 = $14
✔ Answer: $8, $6, $14

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✔ Final Answers:

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Section A: Simplified Ratios

| Problem | Answer |
|--------|--------|
| 1) 3:12 | 1:4 |
| 2) 5:30 | 1:6 |
| 3) 2:14 | 1:7 |
| 4) 3:15 | 1:5 |
| 5) 10:30 | 1:3 |
| 6) 6:60 | 1:10 |
| 7) 2:16 | 1:8 |
| 8) 4:24 | 1:6 |
| 9) 8:24 | 1:3 |
| 10) 9:27 | 1:3 |
| 11) 11:55 | 1:5 |
| 12) 7:42 | 1:6 |
| 13) 10:15 | 2:3 |
| 14) 8:12 | 2:3 |
| 15) 55:66 | 5:6 |
| 16) 14:21 | 2:3 |
| 17) 10:25 | 2:5 |
| 18) 8:10 | 4:5 |
| 19) 12:16 | 3:4 |
| 20) 9:15 | 3:5 |
| 21) 36:60 | 3:5 |
| 22) 27:36 | 3:4 |
| 23) 20:50 | 2:5 |
| 24) 6:21 | 2:7 |

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Section B: Sharing Amounts

| Problem | Answer |
|--------|--------|
| 1) $100 in 3:7 | $30 and $70 |
| 2) $48 in 2:2 | $24 and $24 |
| 3) $24 in 1:3:8 | $2, $6, $16 |
| 4) $25 in 2:3 | $10 and $15 |
| 5) $56 in 3:5 | $21 and $35 |
| 6) $60 in 6:4:5 | $24, $16, $20 |
| 7) $18 in 4:5 | $8 and $10 |
| 8) $77 in 5:2 | $55 and $22 |
| 9) $28 in 4:3:7 | $8, $6, $14 |

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