Ratio and Proportion Worksheets | Definitions, Examples, Activities - Free Printable

Let's solve the Equivalent Ratios worksheet step by step. The goal is to find equivalent ratios for each given ratio and express them in fraction form.

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🔷 Understanding Equivalent Ratios

A ratio like $1:2$ means "1 part to 2 parts." To find an equivalent ratio, we multiply or divide both numbers by the same value.

For example:
- $1:2 = 2:4 = 3:6 = 5:10$, etc.
- This is because $ \frac{1}{2} = \frac{2}{4} = \frac{5}{10} $

We’ll use this idea to fill in the blanks.

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✔ Problem 1: $1 : 2 = \_\_ : 10 = 9 : \_\_$

- First: $1:2 = ? : 10$

Since $2 \times 5 = 10$, then $1 \times 5 = 5$

→ So, $1:2 = 5:10$

- Second: $1:2 = 9 : ?$

Since $1 \times 9 = 9$, then $2 \times 9 = 18$

→ So, $1:2 = 9:18$

- Fraction: $ \frac{1}{2} $

✔ Answer:
5 : 10 = 9 : 18, Fraction: $ \frac{1}{2} $

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✔ Problem 2: $1 : 3 = \_\_ : 15 = 2 : \_\_$

- $1:3 = ? : 15$

$3 \times 5 = 15$, so $1 \times 5 = 5$

→ $5:15$

- $1:3 = 2 : ?$

$1 \times 2 = 2$, so $3 \times 2 = 6$

→ $2:6$

- Fraction: $ \frac{1}{3} $

✔ Answer:
5 : 15 = 2 : 6, Fraction: $ \frac{1}{3} $

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✔ Problem 3: $1 : 4 = \_\_ : 24 = 5 : \_\_$

- $1:4 = ? : 24$

$4 \times 6 = 24$, so $1 \times 6 = 6$

→ $6:24$

- $1:4 = 5 : ?$

$1 \times 5 = 5$, so $4 \times 5 = 20$

→ $5:20$

- Fraction: $ \frac{1}{4} $

✔ Answer:
6 : 24 = 5 : 20, Fraction: $ \frac{1}{4} $

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✔ Problem 4: $1 : 5 = \_\_ : 35 = 3 : \_\_$

- $1:5 = ? : 35$

$5 \times 7 = 35$, so $1 \times 7 = 7$

→ $7:35$

- $1:5 = 3 : ?$

$1 \times 3 = 3$, so $5 \times 3 = 15$

→ $3:15$

- Fraction: $ \frac{1}{5} $

✔ Answer:
7 : 35 = 3 : 15, Fraction: $ \frac{1}{5} $

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✔ Problem 5: $1 : 6 = \_\_ : 12 = 4 : \_\_$

- $1:6 = ? : 12$

$6 \times 2 = 12$, so $1 \times 2 = 2$

→ $2:12$

- $1:6 = 4 : ?$

$1 \times 4 = 4$, so $6 \times 4 = 24$

→ $4:24$

- Fraction: $ \frac{1}{6} $

✔ Answer:
2 : 12 = 4 : 24, Fraction: $ \frac{1}{6} $

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✔ Problem 6: $1 : 7 = \_\_ : 21 = 6 : \_\_$

- $1:7 = ? : 21$

$7 \times 3 = 21$, so $1 \times 3 = 3$

→ $3:21$

- $1:7 = 6 : ?$

$1 \times 6 = 6$, so $7 \times 6 = 42$

→ $6:42$

- Fraction: $ \frac{1}{7} $

✔ Answer:
3 : 21 = 6 : 42, Fraction: $ \frac{1}{7} $

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✔ Problem 7: $1 : 8 = \_\_ : 16 = 7 : \_\_$

- $1:8 = ? : 16$

$8 \times 2 = 16$, so $1 \times 2 = 2$

→ $2:16$

- $1:8 = 7 : ?$

$1 \times 7 = 7$, so $8 \times 7 = 56$

→ $7:56$

- Fraction: $ \frac{1}{8} $

✔ Answer:
2 : 16 = 7 : 56, Fraction: $ \frac{1}{8} $

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✔ Problem 8: $1 : 9 = \_\_ : 72 = 6 : \_\_$

- $1:9 = ? : 72$

$9 \times 8 = 72$, so $1 \times 8 = 8$

→ $8:72$

- $1:9 = 6 : ?$

$1 \times 6 = 6$, so $9 \times 6 = 54$

→ $6:54$

- Fraction: $ \frac{1}{9} $

✔ Answer:
8 : 72 = 6 : 54, Fraction: $ \frac{1}{9} $

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📝 Final Answers:

| # | Ratio | Equivalent Ratios | Fraction |
|---|-------|-------------------|----------|
| 1 | 1:2 | 5:10 = 9:18 | $ \frac{1}{2} $ |
| 2 | 1:3 | 5:15 = 2:6 | $ \frac{1}{3} $ |
| 3 | 1:4 | 6:24 = 5:20 | $ \frac{1}{4} $ |
| 4 | 1:5 | 7:35 = 3:15 | $ \frac{1}{5} $ |
| 5 | 1:6 | 2:12 = 4:24 | $ \frac{1}{6} $ |
| 6 | 1:7 | 3:21 = 6:42 | $ \frac{1}{7} $ |
| 7 | 1:8 | 2:16 = 7:56 | $ \frac{1}{8} $ |
| 8 | 1:9 | 8:72 = 6:54 | $ \frac{1}{9} $ |

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✔ Key Concept Recap:

To find equivalent ratios:
- Multiply or divide both terms of the ratio by the same number.
- Think of the ratio as a fraction: $ \frac{a}{b} $
- Then scale numerator and denominator equally.

This helps in comparing ratios and solving proportion problems.

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