Simplifying Ratios worksheet for math practice, featuring various ratio problems to reduce to simplest form.

Let's solve each ratio by simplifying it to its simplest form. To simplify a ratio, we divide both numbers by their greatest common divisor (GCD). For decimals, we can convert them to fractions or multiply to eliminate decimals first.

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1. 35 : 42

- GCD of 35 and 42 is 7
- $ \frac{35}{7} = 5 $, $ \frac{42}{7} = 6 $
- Answer: 5 : 6

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2. 30 : 45

- GCD of 30 and 45 is 15
- $ \frac{30}{15} = 2 $, $ \frac{45}{15} = 3 $
- Answer: 2 : 3

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3. 35 : 105

- GCD of 35 and 105 is 35
- $ \frac{35}{35} = 1 $, $ \frac{105}{35} = 3 $
- Answer: 1 : 3

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4. 156 : 208

- GCD of 156 and 208 is 52
- $ \frac{156}{52} = 3 $, $ \frac{208}{52} = 4 $
- Answer: 3 : 4

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5. 95 : 475

- GCD of 95 and 475 is 95
- $ \frac{95}{95} = 1 $, $ \frac{475}{95} = 5 $
- Answer: 1 : 5

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6. 54 : 27

- GCD of 54 and 27 is 27
- $ \frac{54}{27} = 2 $, $ \frac{27}{27} = 1 $
- Answer: 2 : 1

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7. 117 : 260

- GCD of 117 and 260:
- 117 = 3×3×13
- 260 = 2×2×5×13
- Common factor: 13
- $ \frac{117}{13} = 9 $, $ \frac{260}{13} = 20 $
- Answer: 9 : 20

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8. 2.1 : 5.6

- Multiply both by 10 to eliminate decimals: 21 : 56
- GCD of 21 and 56 is 7
- $ \frac{21}{7} = 3 $, $ \frac{56}{7} = 8 $
- Answer: 3 : 8

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9. 36 : 1,200

- GCD of 36 and 1200:
- 36 = 2²×3²
- 1200 = 2⁴×3×5²
- Common: 2²×3 = 12
- $ \frac{36}{12} = 3 $, $ \frac{1200}{12} = 100 $
- Answer: 3 : 100

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10. 7.2 : 6.4

- Multiply both by 10: 72 : 64
- GCD of 72 and 64 is 8
- $ \frac{72}{8} = 9 $, $ \frac{64}{8} = 8 $
- Answer: 9 : 8

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11. 126 : 105

- GCD of 126 and 105:
- 126 = 2×3²×7
- 105 = 3×5×7
- Common: 3×7 = 21
- $ \frac{126}{21} = 6 $, $ \frac{105}{21} = 5 $
- Answer: 6 : 5

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12. 1.5 : 2.1

- Multiply by 10: 15 : 21
- GCD of 15 and 21 is 3
- $ \frac{15}{3} = 5 $, $ \frac{21}{3} = 7 $
- Answer: 5 : 7

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13. 11 : 330

- GCD of 11 and 330 is 11
- $ \frac{11}{11} = 1 $, $ \frac{330}{11} = 30 $
- Answer: 1 : 30

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14. 132 : 108

- GCD of 132 and 108:
- 132 = 2²×3×11
- 108 = 2²×3³
- Common: 2²×3 = 12
- $ \frac{132}{12} = 11 $, $ \frac{108}{12} = 9 $
- Answer: 11 : 9

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15. 112 : 240

- GCD of 112 and 240:
- 112 = 2⁴×7
- 240 = 2⁴×3×5
- Common: 2⁴ = 16
- $ \frac{112}{16} = 7 $, $ \frac{240}{16} = 15 $
- Answer: 7 : 15

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16. 90 : 65

- GCD of 90 and 65:
- 90 = 2×3²×5
- 65 = 5×13
- Common: 5
- $ \frac{90}{5} = 18 $, $ \frac{65}{5} = 13 $
- Answer: 18 : 13

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17. 200 : 800

- GCD of 200 and 800 is 200
- $ \frac{200}{200} = 1 $, $ \frac{800}{200} = 4 $
- Answer: 1 : 4

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18. 33 : 23.1

- Multiply by 10: 330 : 231
- GCD of 330 and 231:
- 330 = 2×3×5×11
- 231 = 3×7×11
- Common: 3×11 = 33
- $ \frac{330}{33} = 10 $, $ \frac{231}{33} = 7 $
- Answer: 10 : 7

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19. 2.8 : 2.1

- Multiply by 10: 28 : 21
- GCD of 28 and 21 is 7
- $ \frac{28}{7} = 4 $, $ \frac{21}{7} = 3 $
- Answer: 4 : 3

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20. 84 : 108

- GCD of 84 and 108:
- 84 = 2²×3×7
- 108 = 2²×3³
- Common: 2²×3 = 12
- $ \frac{84}{12} = 7 $, $ \frac{108}{12} = 9 $
- Answer: 7 : 9

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✔ Final Answers:

| Ratio | Simplified Form |
|--------------|------------------|
| 35 : 42 | 5 : 6 |
| 30 : 45 | 2 : 3 |
| 35 : 105 | 1 : 3 |
| 156 : 208 | 3 : 4 |
| 95 : 475 | 1 : 5 |
| 54 : 27 | 2 : 1 |
| 117 : 260 | 9 : 20 |
| 2.1 : 5.6 | 3 : 8 |
| 36 : 1,200 | 3 : 100 |
| 7.2 : 6.4 | 9 : 8 |
| 126 : 105 | 6 : 5 |
| 1.5 : 2.1 | 5 : 7 |
| 11 : 330 | 1 : 30 |
| 132 : 108 | 11 : 9 |
| 112 : 240 | 7 : 15 |
| 90 : 65 | 18 : 13 |
| 200 : 800 | 1 : 4 |
| 33 : 23.1 | 10 : 7 |
| 2.8 : 2.1 | 4 : 3 |
| 84 : 108 | 7 : 9 |

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