Grade 6 Equivalent Fractions Worksheets | Math Worksheets - Free Printable

Let's solve each problem step by step to find the equivalent fractions. We'll use multiplication or division to scale the original fraction so that it matches the given denominators.

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1.

$$
\frac{2}{3} = \frac{\square}{9} = \frac{\square}{12}
$$

- To go from 3 → 9: multiply by 3
So, $2 \times 3 = 6$ → $\frac{6}{9}$

- To go from 3 → 12: multiply by 4
So, $2 \times 4 = 8$ → $\frac{8}{12}$

✔ Answer: $\frac{2}{3} = \frac{6}{9} = \frac{8}{12}$

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2.

$$
\frac{3}{7} = \frac{\square}{21} = \frac{\square}{35}
$$

- 7 → 21: ×3 → $3 \times 3 = 9$ → $\frac{9}{21}$

- 7 → 35: ×5 → $3 \times 5 = 15$ → $\frac{15}{35}$

✔ Answer: $\frac{3}{7} = \frac{9}{21} = \frac{15}{35}$

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3.

$$
\frac{5}{7} = \frac{\square}{14} = \frac{\square}{28}
$$

- 7 → 14: ×2 → $5 \times 2 = 10$ → $\frac{10}{14}$

- 7 → 28: ×4 → $5 \times 4 = 20$ → $\frac{20}{28}$

✔ Answer: $\frac{5}{7} = \frac{10}{14} = \frac{20}{28}$

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4.

$$
\frac{3}{10} = \frac{\square}{20} = \frac{\square}{30}
$$

- 10 → 20: ×2 → $3 \times 2 = 6$ → $\frac{6}{20}$

- 10 → 30: ×3 → $3 \times 3 = 9$ → $\frac{9}{30}$

✔ Answer: $\frac{3}{10} = \frac{6}{20} = \frac{9}{30}$

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5.

$$
\frac{5}{9} = \frac{\square}{27} = \frac{\square}{36}
$$

- 9 → 27: ×3 → $5 \times 3 = 15$ → $\frac{15}{27}$

- 9 → 36: ×4 → $5 \times 4 = 20$ → $\frac{20}{36}$

✔ Answer: $\frac{5}{9} = \frac{15}{27} = \frac{20}{36}$

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6.

$$
\frac{3}{8} = \frac{\square}{16} = \frac{\square}{40}
$$

- 8 → 16: ×2 → $3 \times 2 = 6$ → $\frac{6}{16}$

- 8 → 40: ×5 → $3 \times 5 = 15$ → $\frac{15}{40}$

✔ Answer: $\frac{3}{8} = \frac{6}{16} = \frac{15}{40}$

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7.

$$
\frac{4}{5} = \frac{\square}{45} = \frac{\square}{50}
$$

- 5 → 45: ×9 → $4 \times 9 = 36$ → $\frac{36}{45}$

- 5 → 50: ×10 → $4 \times 10 = 40$ → $\frac{40}{50}$

✔ Answer: $\frac{4}{5} = \frac{36}{45} = \frac{40}{50}$

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8.

$$
\frac{1}{11} = \frac{\square}{33} = \frac{\square}{44}
$$

- 11 → 33: ×3 → $1 \times 3 = 3$ → $\frac{3}{33}$

- 11 → 44: ×4 → $1 \times 4 = 4$ → $\frac{4}{44}$

✔ Answer: $\frac{1}{11} = \frac{3}{33} = \frac{4}{44}$

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9.

$$
\frac{2}{9} = \frac{\square}{54} = \frac{\square}{63}
$$

- 9 → 54: ×6 → $2 \times 6 = 12$ → $\frac{12}{54}$

- 9 → 63: ×7 → $2 \times 7 = 14$ → $\frac{14}{63}$

✔ Answer: $\frac{2}{9} = \frac{12}{54} = \frac{14}{63}$

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10.

$$
\frac{7}{10} = \frac{\square}{20} = \frac{\square}{70}
$$

- 10 → 20: ×2 → $7 \times 2 = 14$ → $\frac{14}{20}$

- 10 → 70: ×7 → $7 \times 7 = 49$ → $\frac{49}{70}$

✔ Answer: $\frac{7}{10} = \frac{14}{20} = \frac{49}{70}$

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✔ Final Answers:

| Problem | Equivalent Fractions |
|--------|------------------------|
| 1. | $\frac{2}{3} = \frac{6}{9} = \frac{8}{12}$ |
| 2. | $\frac{3}{7} = \frac{9}{21} = \frac{15}{35}$ |
| 3. | $\frac{5}{7} = \frac{10}{14} = \frac{20}{28}$ |
| 4. | $\frac{3}{10} = \frac{6}{20} = \frac{9}{30}$ |
| 5. | $\frac{5}{9} = \frac{15}{27} = \frac{20}{36}$ |
| 6. | $\frac{3}{8} = \frac{6}{16} = \frac{15}{40}$ |
| 7. | $\frac{4}{5} = \frac{36}{45} = \frac{40}{50}$ |
| 8. | $\frac{1}{11} = \frac{3}{33} = \frac{4}{44}$ |
| 9. | $\frac{2}{9} = \frac{12}{54} = \frac{14}{63}$ |
| 10. | $\frac{7}{10} = \frac{14}{20} = \frac{49}{70}$ |

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🔍 How It Works:

To find equivalent fractions:
- Multiply both numerator and denominator by the same number.
- This keeps the value of the fraction unchanged.

For example:
$\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$

You can always check your answer by simplifying the new fraction back to the original.

Let me know if you'd like a printable version or visual models! 😊