Equivalent Ratios worksheet for students to practice converting ratios into 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 → all are equivalent because they represent the same fraction: $ \frac{1}{2} $

We can also write ratios as fractions:
$ 1:2 = \frac{1}{2} $

So, to find missing values, we use cross-multiplication or scaling.

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Let’s go through each problem:

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1. 1 : 2 = ___ : 10 = 9 : ___

- First blank:
$ 1:2 = x:10 $
Multiply both sides by 5:
$ 1 \times 5 = 5 $, $ 2 \times 5 = 10 $ → So, 5:10

- Second blank:
$ 1:2 = 9:x $
Multiply both sides by 9:
$ 1 \times 9 = 9 $, $ 2 \times 9 = 18 $ → So, 9:18

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

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2. 1 : 3 = ___ : 15 = 2 : ___

- First blank:
$ 1:3 = x:15 $
Multiply by 5: $ 1 \times 5 = 5 $, $ 3 \times 5 = 15 $ → 5:15

- Second blank:
$ 1:3 = 2:x $
Multiply by 2: $ 1 \times 2 = 2 $, $ 3 \times 2 = 6 $ → 2:6

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

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3. 1 : 4 = ___ : 24 = 5 : ___

- First blank:
$ 1:4 = x:24 $
Multiply by 6: $ 1 \times 6 = 6 $, $ 4 \times 6 = 24 $ → 6:24

- Second blank:
$ 1:4 = 5:x $
Multiply by 5: $ 1 \times 5 = 5 $, $ 4 \times 5 = 20 $ → 5:20

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

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4. 1 : 5 = ___ : 35 = 3 : ___

- First blank:
$ 1:5 = x:35 $
Multiply by 7: $ 1 \times 7 = 7 $, $ 5 \times 7 = 35 $ → 7:35

- Second blank:
$ 1:5 = 3:x $
Multiply by 3: $ 1 \times 3 = 3 $, $ 5 \times 3 = 15 $ → 3:15

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

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5. 1 : 6 = ___ : 12 = 4 : ___

- First blank:
$ 1:6 = x:12 $
Multiply by 2: $ 1 \times 2 = 2 $, $ 6 \times 2 = 12 $ → 2:12

- Second blank:
$ 1:6 = 4:x $
Multiply by 4: $ 1 \times 4 = 4 $, $ 6 \times 4 = 24 $ → 4:24

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

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6. 1 : 7 = ___ : 21 = 6 : ___

- First blank:
$ 1:7 = x:21 $
Multiply by 3: $ 1 \times 3 = 3 $, $ 7 \times 3 = 21 $ → 3:21

- Second blank:
$ 1:7 = 6:x $
Multiply by 6: $ 1 \times 6 = 6 $, $ 7 \times 6 = 42 $ → 6:42

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

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7. 1 : 8 = ___ : 16 = 7 : ___

- First blank:
$ 1:8 = x:16 $
Multiply by 2: $ 1 \times 2 = 2 $, $ 8 \times 2 = 16 $ → 2:16

- Second blank:
$ 1:8 = 7:x $
Multiply by 7: $ 1 \times 7 = 7 $, $ 8 \times 7 = 56 $ → 7:56

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

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8. 1 : 9 = ___ : 72 = 6 : ___

- First blank:
$ 1:9 = x:72 $
Multiply by 8: $ 1 \times 8 = 8 $, $ 9 \times 8 = 72 $ → 8:72

- Second blank:
$ 1:9 = 6:x $
Multiply by 6: $ 1 \times 6 = 6 $, $ 9 \times 6 = 54 $ → 6:54

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

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✔ Final Answers:

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

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📝 Tips for Solving:

- Always think: What number do I multiply the first term by to get the second?
- Use multiplication or division consistently on both sides.
- You can check your answer by simplifying the final ratio back to the original (e.g., 5:10 → 1:2).

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