Proportion Conversions: Ratios Worksheets - Free Printable

Let's solve the Ratio Conversions worksheet step by step. For each ratio given, we need to convert it into:

1. Fraction – write the ratio as a fraction (e.g., 1:8 → 1/8)
2. Percent – convert the fraction to a percent (multiply by 100 and round if needed)
3. Decimal – divide the numerator by the denominator

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🔢 General Steps:

- Fraction: Just write the ratio as a fraction.
- Decimal: Divide numerator by denominator.
- Percent: Multiply the decimal by 100.

Let’s go through each one.

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a. 1:8

- Fraction: $ \frac{1}{8} $
- Decimal: $ 1 ÷ 8 = 0.125 $
- Percent: $ 0.125 × 100 = 12.5\% $

✔ Answer:
| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| 1:8 | 1/8 | 12.5% | 0.125 |

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b. 1:2

- Fraction: $ \frac{1}{2} $
- Decimal: $ 1 ÷ 2 = 0.5 $
- Percent: $ 0.5 × 100 = 50\% $

✔
| 1:2 | 1/2 | 50% | 0.5 |

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c. 1:3

- Fraction: $ \frac{1}{3} $
- Decimal: $ 1 ÷ 3 ≈ 0.333... $
- Percent: $ 0.333... × 100 ≈ 33.3\% $

✔
| 1:3 | 1/3 | 33.3% | 0.333 |

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d. 5:8

- Fraction: $ \frac{5}{8} $
- Decimal: $ 5 ÷ 8 = 0.625 $
- Percent: $ 0.625 × 100 = 62.5\% $

✔
| 5:8 | 5/8 | 62.5% | 0.625 |

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e. 5:9

- Fraction: $ \frac{5}{9} $
- Decimal: $ 5 ÷ 9 ≈ 0.555... $
- Percent: $ 0.555... × 100 ≈ 55.6\% $

✔
| 5:9 | 5/9 | 55.6% | 0.556 |

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f. 2:5

- Fraction: $ \frac{2}{5} $
- Decimal: $ 2 ÷ 5 = 0.4 $
- Percent: $ 0.4 × 100 = 40\% $

✔
| 2:5 | 2/5 | 40% | 0.4 |

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g. 1:1

- Fraction: $ \frac{1}{1} $
- Decimal: $ 1 ÷ 1 = 1 $
- Percent: $ 1 × 100 = 100\% $

✔
| 1:1 | 1/1 | 100% | 1.0 |

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h. 2:9

- Fraction: $ \frac{2}{9} $
- Decimal: $ 2 ÷ 9 ≈ 0.222... $
- Percent: $ 0.222... × 100 ≈ 22.2\% $

✔
| 2:9 | 2/9 | 22.2% | 0.222 |

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i. 3:4

- Fraction: $ \frac{3}{4} $
- Decimal: $ 3 ÷ 4 = 0.75 $
- Percent: $ 0.75 × 100 = 75\% $

✔
| 3:4 | 3/4 | 75% | 0.75 |

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j. 5:6

- Fraction: $ \frac{5}{6} $
- Decimal: $ 5 ÷ 6 ≈ 0.833... $
- Percent: $ 0.833... × 100 ≈ 83.3\% $

✔
| 5:6 | 5/6 | 83.3% | 0.833 |

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k. 2:3

- Fraction: $ \frac{2}{3} $
- Decimal: $ 2 ÷ 3 ≈ 0.666... $
- Percent: $ 0.666... × 100 ≈ 66.7\% $

✔
| 2:3 | 2/3 | 66.7% | 0.667 |

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l. 2:7

- Fraction: $ \frac{2}{7} $
- Decimal: $ 2 ÷ 7 ≈ 0.2857 $
- Percent: $ 0.2857 × 100 ≈ 28.6\% $

✔
| 2:7 | 2/7 | 28.6% | 0.286 |

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m. 8:9

- Fraction: $ \frac{8}{9} $
- Decimal: $ 8 ÷ 9 ≈ 0.888... $
- Percent: $ 0.888... × 100 ≈ 88.9\% $

✔
| 8:9 | 8/9 | 88.9% | 0.889 |

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n. 7:8

- Fraction: $ \frac{7}{8} $
- Decimal: $ 7 ÷ 8 = 0.875 $
- Percent: $ 0.875 × 100 = 87.5\% $

✔
| 7:8 | 7/8 | 87.5% | 0.875 |

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o. 1:7

- Fraction: $ \frac{1}{7} $
- Decimal: $ 1 ÷ 7 ≈ 0.1429 $
- Percent: $ 0.1429 × 100 ≈ 14.3\% $

✔
| 1:7 | 1/7 | 14.3% | 0.143 |

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p. 4:5

- Fraction: $ \frac{4}{5} $
- Decimal: $ 4 ÷ 5 = 0.8 $
- Percent: $ 0.8 × 100 = 80\% $

✔
| 4:5 | 4/5 | 80% | 0.8 |

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q. 1:10

- Fraction: $ \frac{1}{10} $
- Decimal: $ 1 ÷ 10 = 0.1 $
- Percent: $ 0.1 × 100 = 10\% $

✔
| 1:10 | 1/10 | 10% | 0.1 |

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r. 1:4

- Fraction: $ \frac{1}{4} $
- Decimal: $ 1 ÷ 4 = 0.25 $
- Percent: $ 0.25 × 100 = 25\% $

✔
| 1:4 | 1/4 | 25% | 0.25 |

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s. 1:9

- Fraction: $ \frac{1}{9} $
- Decimal: $ 1 ÷ 9 ≈ 0.111... $
- Percent: $ 0.111... × 100 ≈ 11.1\% $

✔
| 1:9 | 1/9 | 11.1% | 0.111 |

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t. 3:8

- Fraction: $ \frac{3}{8} $
- Decimal: $ 3 ÷ 8 = 0.375 $
- Percent: $ 0.375 × 100 = 37.5\% $

✔
| 3:8 | 3/8 | 37.5% | 0.375 |

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## ✔ Final Answer Table:

| Ratio | Fraction | Percent | Decimal |
|-------|----------|---------|---------|
| a. 1:8 | 1/8 | 12.5% | 0.125 |
| b. 1:2 | 1/2 | 50% | 0.5 |
| c. 1:3 | 1/3 | 33.3% | 0.333 |
| d. 5:8 | 5/8 | 62.5% | 0.625 |
| e. 5:9 | 5/9 | 55.6% | 0.556 |
| f. 2:5 | 2/5 | 40% | 0.4 |
| g. 1:1 | 1/1 | 100% | 1.0 |
| h. 2:9 | 2/9 | 22.2% | 0.222 |
| i. 3:4 | 3/4 | 75% | 0.75 |
| j. 5:6 | 5/6 | 83.3% | 0.833 |
| k. 2:3 | 2/3 | 66.7% | 0.667 |
| l. 2:7 | 2/7 | 28.6% | 0.286 |
| m. 8:9 | 8/9 | 88.9% | 0.889 |
| n. 7:8 | 7/8 | 87.5% | 0.875 |
| o. 1:7 | 1/7 | 14.3% | 0.143 |
| p. 4:5 | 4/5 | 80% | 0.8 |
| q. 1:10 | 1/10 | 10% | 0.1 |
| r. 1:4 | 1/4 | 25% | 0.25 |
| s. 1:9 | 1/9 | 11.1% | 0.111 |
| t. 3:8 | 3/8 | 37.5% | 0.375 |

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📝 Notes:

- Percents are rounded to one decimal place unless exact (like 50%, 75%).
- Decimals are rounded to three decimal places for consistency.
- Fractions are left in simplest form.

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