Equivalent Ratios worksheet for students to practice finding equivalent ratios and converting them to fractions.

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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💡 Tip:

To check your answers:
- Convert all ratios to fractions and see if they reduce to the same value (e.g., $ \frac{5}{10} = \frac{1}{2} $).

This method helps confirm that the ratios are truly equivalent.

Let me know if you'd like a printable version or explanation with visuals! 😊