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.

$$
\frac{2}{9} = \frac{\square}{36} = \frac{\square}{54}
$$

- First, find how many times 9 goes into 36:
$$
36 ÷ 9 = 4
$$
So multiply numerator and denominator by 4:
$$
\frac{2 × 4}{9 × 4} = \frac{8}{36}
$$

- Now for 54:
$$
54 ÷ 9 = 6
$$
Multiply numerator and denominator by 6:
$$
\frac{2 × 6}{9 × 6} = \frac{12}{54}
$$

✔ Answer:
$$
\frac{2}{9} = \frac{8}{36} = \frac{12}{54}
$$

---

2.

$$
\frac{1}{7} = \frac{\square}{28} = \frac{\square}{42}
$$

- 28 ÷ 7 = 4 → Multiply by 4:
$$
\frac{1 × 4}{7 × 4} = \frac{4}{28}
$$

- 42 ÷ 7 = 6 → Multiply by 6:
$$
\frac{1 × 6}{7 × 6} = \frac{6}{42}
$$

✔ Answer:
$$
\frac{1}{7} = \frac{4}{28} = \frac{6}{42}
$$

---

3.

$$
\frac{3}{5} = \frac{\square}{15} = \frac{\square}{30}
$$

- 15 ÷ 5 = 3 → Multiply by 3:
$$
\frac{3 × 3}{5 × 3} = \frac{9}{15}
$$

- 30 ÷ 5 = 6 → Multiply by 6:
$$
\frac{3 × 6}{5 × 6} = \frac{18}{30}
$$

✔ Answer:
$$
\frac{3}{5} = \frac{9}{15} = \frac{18}{30}
$$

---

4.

$$
\frac{1}{6} = \frac{\square}{24} = \frac{\square}{36}
$$

- 24 ÷ 6 = 4 → Multiply by 4:
$$
\frac{1 × 4}{6 × 4} = \frac{4}{24}
$$

- 36 ÷ 6 = 6 → Multiply by 6:
$$
\frac{1 × 6}{6 × 6} = \frac{6}{36}
$$

✔ Answer:
$$
\frac{1}{6} = \frac{4}{24} = \frac{6}{36}
$$

---

5.

$$
\frac{2}{5} = \frac{\square}{25} = \frac{\square}{40}
$$

- 25 ÷ 5 = 5 → Multiply by 5:
$$
\frac{2 × 5}{5 × 5} = \frac{10}{25}
$$

- 40 ÷ 5 = 8 → Multiply by 8:
$$
\frac{2 × 8}{5 × 8} = \frac{16}{40}
$$

✔ Answer:
$$
\frac{2}{5} = \frac{10}{25} = \frac{16}{40}
$$

---

6.

$$
\frac{3}{11} = \frac{\square}{22} = \frac{\square}{55}
$$

- 22 ÷ 11 = 2 → Multiply by 2:
$$
\frac{3 × 2}{11 × 2} = \frac{6}{22}
$$

- 55 ÷ 11 = 5 → Multiply by 5:
$$
\frac{3 × 5}{11 × 5} = \frac{15}{55}
$$

✔ Answer:
$$
\frac{3}{11} = \frac{6}{22} = \frac{15}{55}
$$

---

7.

$$
\frac{5}{8} = \frac{\square}{48} = \frac{\square}{56}
$$

- 48 ÷ 8 = 6 → Multiply by 6:
$$
\frac{5 × 6}{8 × 6} = \frac{30}{48}
$$

- 56 ÷ 8 = 7 → Multiply by 7:
$$
\frac{5 × 7}{8 × 7} = \frac{35}{56}
$$

✔ Answer:
$$
\frac{5}{8} = \frac{30}{48} = \frac{35}{56}
$$

---

8.

$$
\frac{9}{10} = \frac{\square}{30} = \frac{\square}{60}
$$

- 30 ÷ 10 = 3 → Multiply by 3:
$$
\frac{9 × 3}{10 × 3} = \frac{27}{30}
$$

- 60 ÷ 10 = 6 → Multiply by 6:
$$
\frac{9 × 6}{10 × 6} = \frac{54}{60}
$$

✔ Answer:
$$
\frac{9}{10} = \frac{27}{30} = \frac{54}{60}
$$

---

9.

$$
\frac{8}{9} = \frac{\square}{18} = \frac{\square}{36}
$$

- 18 ÷ 9 = 2 → Multiply by 2:
$$
\frac{8 × 2}{9 × 2} = \frac{16}{18}
$$

- 36 ÷ 9 = 4 → Multiply by 4:
$$
\frac{8 × 4}{9 × 4} = \frac{32}{36}
$$

✔ Answer:
$$
\frac{8}{9} = \frac{16}{18} = \frac{32}{36}
$$

---

10.

$$
\frac{10}{11} = \frac{\square}{33} = \frac{\square}{44}
$$

- 33 ÷ 11 = 3 → Multiply by 3:
$$
\frac{10 × 3}{11 × 3} = \frac{30}{33}
$$

- 44 ÷ 11 = 4 → Multiply by 4:
$$
\frac{10 × 4}{11 × 4} = \frac{40}{44}
$$

✔ Answer:
$$
\frac{10}{11} = \frac{30}{33} = \frac{40}{44}
$$

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✔ Final Answers:

1. $\frac{2}{9} = \frac{8}{36} = \frac{12}{54}$
2. $\frac{1}{7} = \frac{4}{28} = \frac{6}{42}$
3. $\frac{3}{5} = \frac{9}{15} = \frac{18}{30}$
4. $\frac{1}{6} = \frac{4}{24} = \frac{6}{36}$
5. $\frac{2}{5} = \frac{10}{25} = \frac{16}{40}$
6. $\frac{3}{11} = \frac{6}{22} = \frac{15}{55}$
7. $\frac{5}{8} = \frac{30}{48} = \frac{35}{56}$
8. $\frac{9}{10} = \frac{27}{30} = \frac{54}{60}$
9. $\frac{8}{9} = \frac{16}{18} = \frac{32}{36}$
10. $\frac{10}{11} = \frac{30}{33} = \frac{40}{44}$

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🔍 How to Check:

To verify any equivalent fraction, you can cross-multiply:
For example, check if $\frac{2}{9} = \frac{8}{36}$:
$2 × 36 = 72$, $9 × 8 = 72$ → Equal! ✔️

All answers are correct!

Let me know if you'd like this in a printable format or with explanations for kids!