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, $1:2 = 9:18$

✔ Answer:
5 : 10 = 9 : 18
In fraction: $ \frac{5}{10} = \frac{9}{18} $ (both simplify to $ \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 $3 \times 2 = 6$

→ $2:6$

✔ Answer:
5 : 15 = 2 : 6
Fraction: $ \frac{5}{15} = \frac{2}{6} = \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 $4 \times 5 = 20$

→ $5:20$

✔ Answer:
6 : 24 = 5 : 20
Fraction: $ \frac{6}{24} = \frac{5}{20} = \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 $5 \times 3 = 15$

→ $3:15$

✔ Answer:
7 : 35 = 3 : 15
Fraction: $ \frac{7}{35} = \frac{3}{15} = \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 $6 \times 4 = 24$

→ $4:24$

✔ Answer:
2 : 12 = 4 : 24
Fraction: $ \frac{2}{12} = \frac{4}{24} = \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 $7 \times 6 = 42$

→ $6:42$

✔ Answer:
3 : 21 = 6 : 42
Fraction: $ \frac{3}{21} = \frac{6}{42} = \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 $8 \times 7 = 56$

→ $7:56$

✔ Answer:
2 : 16 = 7 : 56
Fraction: $ \frac{2}{16} = \frac{7}{56} = \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 $9 \times 6 = 54$

→ $6:54$

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

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📝 Final Answers:

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

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💡 Tips:

- Always think: What number do I multiply the first term by to get the second?
- Then apply that multiplier to the other term.
- Check if fractions reduce to the original ratio (e.g., $ \frac{5}{10} = \frac{1}{2} $).

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