Ratio Problems With Answers
Practice ratio problems with answers - simplifying ratios, equivalent ratios and proportions, sharing in a ratio, and word problems.
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Simplifying Ratios
| # | Problem |
|---|---|
| 1 | Simplify 6 : 9 |
| 2 | Simplify 10 : 25 |
| 3 | Simplify 12 : 18 |
| 4 | Simplify 21 : 14 |
| 5 | Simplify 40 : 24 |
Equivalent Ratios and Proportions
| # | Problem |
|---|---|
| 6 | 2 : 3 = 8 : ? |
| 7 | 5 : 4 = ? : 16 |
| 8 | 3 : 7 = 12 : ? |
| 9 | 1 : 6 = 4 : ? |
| 10 | 9 : 5 = ? : 20 |
Sharing in a Ratio
| # | Problem |
|---|---|
| 11 | Share 20 sweets in the ratio 2 : 3. |
| 12 | Share 35 in the ratio 3 : 4. |
| 13 | Share 48 in the ratio 5 : 3. |
| 14 | Share 50 in the ratio 1 : 4. |
| 15 | Share 60 in the ratio 7 : 5. |
Word Problems
| # | Problem |
|---|---|
| 16 | A recipe mixes flour and sugar in the ratio 3 : 1. With 9 cups of flour, how much sugar? |
| 17 | The ratio of boys to girls in a class is 4 : 5. If there are 12 boys, how many girls? |
| 18 | A map scale is 1 : 100. A wall is 3 cm on the map. How long is it in real life, in cm? |
| 19 | Paint is mixed red to blue in the ratio 2 : 5. For 10 litres of red, how much blue? |
| 20 | Two numbers are in the ratio 3 : 8 and the smaller is 9. What is the larger? |
Answer Key
| # | Answer |
|---|---|
| 1 | 2 : 3 |
| 2 | 2 : 5 |
| 3 | 2 : 3 |
| 4 | 3 : 2 |
| 5 | 5 : 3 |
| 6 | 12 |
| 7 | 20 |
| 8 | 28 |
| 9 | 24 |
| 10 | 36 |
| 11 | 8 and 12 |
| 12 | 15 and 20 |
| 13 | 30 and 18 |
| 14 | 10 and 40 |
| 15 | 35 and 25 |
| 16 | 3 cups |
| 17 | 15 |
| 18 | 300 cm |
| 19 | 25 litres |
| 20 | 24 |
Step-by-Step Solutions
Problem 5: the greatest common factor of 40 and 24 is 8, so 40 : 24 = 5 : 3.
Problem 13: there are 5 + 3 = 8 parts, and 48 ÷ 8 = 6 per part, so the shares are 5 × 6 = 30 and 3 × 6 = 18.
Problem 17: 12 boys make up 4 parts, so 1 part is 3, and the girls are 5 parts = 15.
Problem 20: the smaller number (3 parts) is 9, so 1 part is 3, and the larger (8 parts) is 24.