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

Let's solve the 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(3, 12) = 3 → $ \frac{3}{3} : \frac{12}{3} = 1 : 4 $

#### 2) 5 : 30
GCD(5, 30) = 5 → $ \frac{5}{5} : \frac{30}{5} = 1 : 6 $

#### 3) 2 : 14
GCD(2, 14) = 2 → $ \frac{2}{2} : \frac{14}{2} = 1 : 7 $

#### 4) 3 : 15
GCD(3, 15) = 3 → $ \frac{3}{3} : \frac{15}{3} = 1 : 5 $

#### 5) 10 : 30
GCD(10, 30) = 10 → $ \frac{10}{10} : \frac{30}{10} = 1 : 3 $

#### 6) 6 : 60
GCD(6, 60) = 6 → $ \frac{6}{6} : \frac{60}{6} = 1 : 10 $

#### 7) 2 : 16
GCD(2, 16) = 2 → $ \frac{2}{2} : \frac{16}{2} = 1 : 8 $

#### 8) 4 : 24
GCD(4, 24) = 4 → $ \frac{4}{4} : \frac{24}{4} = 1 : 6 $

#### 9) 8 : 24
GCD(8, 24) = 8 → $ \frac{8}{8} : \frac{24}{8} = 1 : 3 $

#### 10) 9 : 27
GCD(9, 27) = 9 → $ \frac{9}{9} : \frac{27}{9} = 1 : 3 $

#### 11) 11 : 55
GCD(11, 55) = 11 → $ \frac{11}{11} : \frac{55}{11} = 1 : 5 $

#### 12) 7 : 42
GCD(7, 42) = 7 → $ \frac{7}{7} : \frac{42}{7} = 1 : 6 $

#### 13) 10 : 15
GCD(10, 15) = 5 → $ \frac{10}{5} : \frac{15}{5} = 2 : 3 $

#### 14) 8 : 12
GCD(8, 12) = 4 → $ \frac{8}{4} : \frac{12}{4} = 2 : 3 $

#### 15) 55 : 66
GCD(55, 66) = 11 → $ \frac{55}{11} : \frac{66}{11} = 5 : 6 $

#### 16) 14 : 21
GCD(14, 21) = 7 → $ \frac{14}{7} : \frac{21}{7} = 2 : 3 $

#### 17) 10 : 25
GCD(10, 25) = 5 → $ \frac{10}{5} : \frac{25}{5} = 2 : 5 $

#### 18) 8 : 10
GCD(8, 10) = 2 → $ \frac{8}{2} : \frac{10}{2} = 4 : 5 $

#### 19) 12 : 16
GCD(12, 16) = 4 → $ \frac{12}{4} : \frac{16}{4} = 3 : 4 $

#### 20) 9 : 15
GCD(9, 15) = 3 → $ \frac{9}{3} : \frac{15}{3} = 3 : 5 $

#### 21) 36 : 60
GCD(36, 60) = 12 → $ \frac{36}{12} : \frac{60}{12} = 3 : 5 $

#### 22) 27 : 36
GCD(27, 36) = 9 → $ \frac{27}{9} : \frac{36}{9} = 3 : 4 $

#### 23) 20 : 50
GCD(20, 50) = 10 → $ \frac{20}{10} : \frac{50}{10} = 2 : 5 $

#### 24) 6 : 21
GCD(6, 21) = 3 → $ \frac{6}{3} : \frac{21}{3} = 2 : 7 $

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✔ Section B: Share the amounts into the following ratios

We use this method:
- Add the parts of the ratio.
- Divide the total amount by the total number of parts.
- Multiply each part of the ratio by the value of one part.

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#### 1) $100 into the ratio 3:7
Total parts = 3 + 7 = 10
Each part = $100 ÷ 10 = $10
→ 3 parts = 3 × $10 = $30
→ 7 parts = 7 × $10 = $70
✔ Answer: $30 : $70

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

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

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#### 4) $25 into the ratio 2:3
Total parts = 2 + 3 = 5
Each part = $25 ÷ 5 = $5
→ 2 parts = 2 × $5 = $10
→ 3 parts = 3 × $5 = $15
✔ Answer: $10 : $15

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#### 5) $56 into the ratio 3:5
Total parts = 3 + 5 = 8
Each part = $56 ÷ 8 = $7
→ 3 parts = 3 × $7 = $21
→ 5 parts = 5 × $7 = $35
✔ Answer: $21 : $35

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

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

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

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

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✔ Final Answers Summary

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🔹 Section A – Simplified Ratios:

| Problem | Simplified Ratio |
|--------|------------------|
| 1) | 1 : 4 |
| 2) | 1 : 6 |
| 3) | 1 : 7 |
| 4) | 1 : 5 |
| 5) | 1 : 3 |
| 6) | 1 : 10 |
| 7) | 1 : 8 |
| 8) | 1 : 6 |
| 9) | 1 : 3 |
| 10) | 1 : 3 |
| 11) | 1 : 5 |
| 12) | 1 : 6 |
| 13) | 2 : 3 |
| 14) | 2 : 3 |
| 15) | 5 : 6 |
| 16) | 2 : 3 |
| 17) | 2 : 5 |
| 18) | 4 : 5 |
| 19) | 3 : 4 |
| 20) | 3 : 5 |
| 21) | 3 : 5 |
| 22) | 3 : 4 |
| 23) | 2 : 5 |
| 24) | 2 : 7 |

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🔹 Section B – Shared Amounts:

| Problem | Answer |
|--------|--------|
| 1) | $30 : $70 |
| 2) | $24 : $24 |
| 3) | $2 : $6 : $16 |
| 4) | $10 : $15 |
| 5) | $21 : $35 |
| 6) | $24 : $16 : $20 |
| 7) | $8 : $10 |
| 8) | $55 : $22 |
| 9) | $8 : $6 : $14 |

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