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 find the greatest common divisor (GCD) of the two numbers and divide both by it.

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

✔ Answer: 1 : 4

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#### 2) 5 : 30
- GCD of 5 and 30 is 5.
- $ \frac{5}{5} : \frac{30}{5} = 1 : 6 $

✔ Answer: 1 : 6

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#### 3) 2 : 14
- GCD of 2 and 14 is 2.
- $ \frac{2}{2} : \frac{14}{2} = 1 : 7 $

✔ Answer: 1 : 7

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#### 4) 3 : 15
- GCD of 3 and 15 is 3.
- $ \frac{3}{3} : \frac{15}{3} = 1 : 5 $

✔ Answer: 1 : 5

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#### 5) 10 : 30
- GCD of 10 and 30 is 10.
- $ \frac{10}{10} : \frac{30}{10} = 1 : 3 $

✔ Answer: 1 : 3

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#### 6) 6 : 60
- GCD of 6 and 60 is 6.
- $ \frac{6}{6} : \frac{60}{6} = 1 : 10 $

✔ Answer: 1 : 10

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#### 7) 2 : 16
- GCD of 2 and 16 is 2.
- $ \frac{2}{2} : \frac{16}{2} = 1 : 8 $

✔ Answer: 1 : 8

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#### 8) 4 : 24
- GCD of 4 and 24 is 4.
- $ \frac{4}{4} : \frac{24}{4} = 1 : 6 $

✔ Answer: 1 : 6

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#### 9) 8 : 24
- GCD of 8 and 24 is 8.
- $ \frac{8}{8} : \frac{24}{8} = 1 : 3 $

✔ Answer: 1 : 3

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#### 10) 9 : 27
- GCD of 9 and 27 is 9.
- $ \frac{9}{9} : \frac{27}{9} = 1 : 3 $

✔ Answer: 1 : 3

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#### 11) 11 : 55
- GCD of 11 and 55 is 11.
- $ \frac{11}{11} : \frac{55}{11} = 1 : 5 $

✔ Answer: 1 : 5

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#### 12) 7 : 42
- GCD of 7 and 42 is 7.
- $ \frac{7}{7} : \frac{42}{7} = 1 : 6 $

✔ Answer: 1 : 6

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#### 13) 10 : 15
- GCD of 10 and 15 is 5.
- $ \frac{10}{5} : \frac{15}{5} = 2 : 3 $

✔ Answer: 2 : 3

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#### 14) 8 : 12
- GCD of 8 and 12 is 4.
- $ \frac{8}{4} : \frac{12}{4} = 2 : 3 $

✔ Answer: 2 : 3

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#### 15) 55 : 66
- GCD of 55 and 66 is 11.
- $ \frac{55}{11} : \frac{66}{11} = 5 : 6 $

✔ Answer: 5 : 6

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#### 16) 14 : 21
- GCD of 14 and 21 is 7.
- $ \frac{14}{7} : \frac{21}{7} = 2 : 3 $

✔ Answer: 2 : 3

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#### 17) 10 : 25
- GCD of 10 and 25 is 5.
- $ \frac{10}{5} : \frac{25}{5} = 2 : 5 $

✔ Answer: 2 : 5

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#### 18) 8 : 10
- GCD of 8 and 10 is 2.
- $ \frac{8}{2} : \frac{10}{2} = 4 : 5 $

✔ Answer: 4 : 5

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#### 19) 12 : 16
- GCD of 12 and 16 is 4.
- $ \frac{12}{4} : \frac{16}{4} = 3 : 4 $

✔ Answer: 3 : 4

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#### 20) 9 : 15
- GCD of 9 and 15 is 3.
- $ \frac{9}{3} : \frac{15}{3} = 3 : 5 $

✔ Answer: 3 : 5

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#### 21) 36 : 60
- GCD of 36 and 60 is 12.
- $ \frac{36}{12} : \frac{60}{12} = 3 : 5 $

✔ Answer: 3 : 5

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#### 22) 27 : 36
- GCD of 27 and 36 is 9.
- $ \frac{27}{9} : \frac{36}{9} = 3 : 4 $

✔ Answer: 3 : 4

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#### 23) 20 : 50
- GCD of 20 and 50 is 10.
- $ \frac{20}{10} : \frac{50}{10} = 2 : 5 $

✔ Answer: 2 : 5

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#### 24) 6 : 21
- GCD of 6 and 21 is 3.
- $ \frac{6}{3} : \frac{21}{3} = 2 : 7 $

✔ Answer: 2 : 7

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## 🔁 Summary – Section A Answers:

| # | Original Ratio | Simplified |
|---|----------------|------------|
| 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: Share the amounts into the following ratios

We use the method:
1. Add parts of the ratio.
2. Divide total amount by total parts → value per part.
3. Multiply each part by value per part.

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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
- Value 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
- Value 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
- Value per part = $25 ÷ 5 = $5
- Shares:
- 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
- Value per part = $56 ÷ 8 = $7
- Shares:
- 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
- Value 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
- Value per part = $18 ÷ 9 = $2
- Shares:
- 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
- Value per part = $77 ÷ 7 = $11
- Shares:
- 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
- Value per part = $28 ÷ 14 = $2
- Shares:
- 4 × $2 = $8
- 3 × $2 = $6
- 7 × $2 = $14

✔ Answer: $8, $6, $14

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## 🔁 Summary – Section B Answers:

| # | Amount | Ratio | Shares |
|----|--------|-------|--------|
| 1 | $100 | 3:7 | $30, $70 |
| 2 | $48 | 2:2 | $24, $24 |
| 3 | $24 | 1:3:8 | $2, $6, $16 |
| 4 | $25 | 2:3 | $10, $15 |
| 5 | $56 | 3:5 | $21, $35 |
| 6 | $60 | 6:4:5 | $24, $16, $20 |
| 7 | $18 | 4:5 | $8, $10 |
| 8 | $77 | 5:2 | $55, $22 |
| 9 | $28 | 4:3:7 | $8, $6, $14 |

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✔ Final Notes:

- Always simplify ratios using GCD.
- When sharing amounts in a ratio:
- Add the parts.
- Divide total by total parts to get "value per part".
- Multiply each part by that value.

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