Math worksheet for reducing ratios of practical units to their simplest forms.

Let's solve each ratio and express it in its simplest form. We'll reduce each ratio by dividing both numbers by their greatest common divisor (GCD) or simplifying decimals and fractions appropriately.

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1. 14 grapes to 140 grapes

$$
\frac{14}{140} = \frac{1}{10}
$$

✔ Answer: 1:10

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2. 45 goals to 405 goals

$$
\frac{45}{405} = \frac{1}{9} \quad (\text{divide numerator and denominator by } 45)
$$

✔ Answer: 1:9

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3. 2.5 buns out of 10 buns

Convert to fractions:

$$
\frac{2.5}{10} = \frac{25}{100} = \frac{1}{4}
$$

✔ Answer: 1:4

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4. 12 tigers out of 264 cats

$$
\frac{12}{264} = \frac{1}{22} \quad (\text{divide by } 12)
$$

✔ Answer: 1:22

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5. 8 goals out of 96 goals

$$
\frac{8}{96} = \frac{1}{12}
$$

✔ Answer: 1:12

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6. 30 cars out of 160 cars

$$
\frac{30}{160} = \frac{3}{16} \quad (\text{divide by } 10, \text{ then } 3/16)
$$

✔ Answer: 3:16

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7. 125 girls to 375 boys

$$
\frac{125}{375} = \frac{1}{3} \quad (\text{divide by } 125)
$$

✔ Answer: 1:3

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8. 4.5 liters to 8.1 liters

Convert to fractions:

$$
\frac{4.5}{8.1} = \frac{45}{81} = \frac{5}{9} \quad (\text{multiply numerator and denominator by 10, then divide by 9})
$$

✔ Answer: 5:9

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9. 75 errors out of 200 errors

$$
\frac{75}{200} = \frac{3}{8} \quad (\text{divide by } 25)
$$

✔ Answer: 3:8

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10. 15 cups out of 35 cups

$$
\frac{15}{35} = \frac{3}{7}
$$

✔ Answer: 3:7

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11. $24 out of $204

$$
\frac{24}{204} = \frac{2}{17} \quad (\text{divide by } 12)
$$

✔ Answer: 2:17

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12. 104 glasses out of 13 bottles

This is 104 glasses per 13 bottles, so:

$$
\frac{104}{13} = 8 \quad \Rightarrow \text{8 glasses per bottle}
$$

But since the ratio is glasses to bottles, we write:

$$
\frac{104}{13} = \frac{8}{1}
$$

✔ Answer: 8:1

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13. 425 cents to 500 cents

$$
\frac{425}{500} = \frac{17}{20} \quad (\text{divide by } 25)
$$

✔ Answer: 17:20

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14. 121 ships to 143 ships

Check GCD of 121 and 143:

- 121 = 11²
- 143 = 11 × 13

So GCD = 11

$$
\frac{121}{143} = \frac{11}{13}
$$

✔ Answer: 11:13

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✔ Final Answers:

| Original Ratio | Simplified Ratio |
|----------------|------------------|
| 14 grapes to 140 grapes | 1:10 |
| 45 goals to 405 goals | 1:9 |
| 2.5 buns out of 10 buns | 1:4 |
| 12 tigers out of 264 cats | 1:22 |
| 8 goals out of 96 goals | 1:12 |
| 30 cars out of 160 cars | 3:16 |
| 125 girls to 375 boys | 1:3 |
| 4.5 liters to 8.1 liters | 5:9 |
| 75 errors out of 200 errors | 3:8 |
| 15 cups out of 35 cups | 3:7 |
| $24 out of $204 | 2:17 |
| 104 glasses out of 13 bottles | 8:1 |
| 425 cents to 500 cents | 17:20 |
| 121 ships to 143 ships | 11:13 |

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Let me know if you'd like this formatted as a printable answer sheet!