Grade 6 Equivalent Fractions Worksheets | Math Worksheets - Free Printable

Let's solve each of these fraction division problems step by step. The rule for dividing fractions is:

> To divide by a fraction, multiply by its reciprocal.

That is:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$

We'll apply this rule to each problem.

---

1. $\frac{1}{3} \div \frac{7}{9}$

$$
= \frac{1}{3} \times \frac{9}{7} = \frac{1 \times 9}{3 \times 7} = \frac{9}{21} = \frac{3}{7}
$$

✔ Answer: $\boxed{\frac{3}{7}}$

---

2. $\frac{1}{5} \div \frac{5}{8}$

$$
= \frac{1}{5} \times \frac{8}{5} = \frac{8}{25}
$$

✔ Answer: $\boxed{\frac{8}{25}}$

---

3. $\frac{10}{11} \div \frac{20}{22}$

First simplify $\frac{20}{22} = \frac{10}{11}$

So:
$$
\frac{10}{11} \div \frac{10}{11} = 1
$$

✔ Answer: $\boxed{1}$

---

4. $\frac{2}{3} \div \frac{18}{15}$

Simplify $\frac{18}{15} = \frac{6}{5}$

Now:
$$
\frac{2}{3} \div \frac{6}{5} = \frac{2}{3} \times \frac{5}{6} = \frac{10}{18} = \frac{5}{9}
$$

✔ Answer: $\boxed{\frac{5}{9}}$

---

5. $\frac{1}{9} \div \frac{3}{10}$

$$
= \frac{1}{9} \times \frac{10}{3} = \frac{10}{27}
$$

✔ Answer: $\boxed{\frac{10}{27}}$

---

6. $\frac{7}{16} \div \frac{9}{8}$

$$
= \frac{7}{16} \times \frac{8}{9} = \frac{56}{144} = \frac{7}{18}
$$

(Simplify: divide numerator and denominator by 8 → $56 \div 8 = 7$, $144 \div 8 = 18$)

✔ Answer: $\boxed{\frac{7}{18}}$

---

7. $\frac{4}{5} \div \frac{1}{10}$

$$
= \frac{4}{5} \times \frac{10}{1} = \frac{40}{5} = 8
$$

✔ Answer: $\boxed{8}$

---

8. $\frac{1}{11} \div \frac{4}{44}$

Simplify $\frac{4}{44} = \frac{1}{11}$

So:
$$
\frac{1}{11} \div \frac{1}{11} = 1
$$

✔ Answer: $\boxed{1}$

---

9. $\frac{3}{13} \div \frac{2}{3}$

$$
= \frac{3}{13} \times \frac{3}{2} = \frac{9}{26}
$$

✔ Answer: $\boxed{\frac{9}{26}}$

---

10. $\frac{8}{25} \div \frac{16}{32}$

Simplify $\frac{16}{32} = \frac{1}{2}$

So:
$$
\frac{8}{25} \div \frac{1}{2} = \frac{8}{25} \times \frac{2}{1} = \frac{16}{25}
$$

✔ Answer: $\boxed{\frac{16}{25}}$

---

11. $\frac{1}{7} \div \frac{3}{42}$

Simplify $\frac{3}{42} = \frac{1}{14}$

So:
$$
\frac{1}{7} \div \frac{1}{14} = \frac{1}{7} \times \frac{14}{1} = \frac{14}{7} = 2
$$

✔ Answer: $\boxed{2}$

---

12. $\frac{8}{9} \div \frac{32}{45}$

$$
= \frac{8}{9} \times \frac{45}{32} = \frac{360}{288}
$$

Simplify:
- Divide numerator and denominator by 72:
$360 \div 72 = 5$, $288 \div 72 = 4$ → $\frac{5}{4}$

Or step-by-step:
- $360 \div 24 = 15$, $288 \div 24 = 12$ → $\frac{15}{12}$
- Then $\frac{15}{12} = \frac{5}{4}$

✔ Answer: $\boxed{\frac{5}{4}}$ or $1\frac{1}{4}$

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✔ Final Answers:

1. $\frac{3}{7}$
2. $\frac{8}{25}$
3. $1$
4. $\frac{5}{9}$
5. $\frac{10}{27}$
6. $\frac{7}{18}$
7. $8$
8. $1$
9. $\frac{9}{26}$
10. $\frac{16}{25}$
11. $2$
12. $\frac{5}{4}$ (or $1\frac{1}{4}$)

Let me know if you'd like this printed out or explained further!