Dividing Fractions Worksheet with 12 Practice Problems

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. $\frac{1}{2} \div \frac{8}{9}$

$$
= \frac{1}{2} \times \frac{9}{8} = \frac{9}{16}
$$

✔ Answer: $\boxed{\frac{9}{16}}$

---

2. $\frac{2}{3} \div \frac{1}{5}$

$$
= \frac{2}{3} \times \frac{5}{1} = \frac{10}{3} = 3\frac{1}{3}
$$

✔ Answer: $\boxed{\frac{10}{3}}$ or $\boxed{3\frac{1}{3}}$

---

3. $\frac{1}{4} \div \frac{1}{2}$

$$
= \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2}
$$

✔ Answer: $\boxed{\frac{1}{2}}$

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4. $\frac{2}{3} \div \frac{1}{18}$

$$
= \frac{2}{3} \times \frac{18}{1} = \frac{36}{3} = 12
$$

✔ Answer: $\boxed{12}$

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5. $\frac{4}{6} \div \frac{2}{9}$

First simplify $\frac{4}{6} = \frac{2}{3}$

$$
= \frac{2}{3} \div \frac{2}{9} = \frac{2}{3} \times \frac{9}{2} = \frac{18}{6} = 3
$$

✔ Answer: $\boxed{3}$

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6. $\frac{1}{9} \div \frac{1}{5}$

$$
= \frac{1}{9} \times \frac{5}{1} = \frac{5}{9}
$$

✔ Answer: $\boxed{\frac{5}{9}}$

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7. $\frac{5}{6} \div \frac{10}{6}$

$$
= \frac{5}{6} \times \frac{6}{10} = \frac{30}{60} = \frac{1}{2}
$$

✔ Answer: $\boxed{\frac{1}{2}}$

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8. $\frac{9}{11} \div \frac{9}{6}$

Simplify $\frac{9}{6} = \frac{3}{2}$

$$
= \frac{9}{11} \div \frac{3}{2} = \frac{9}{11} \times \frac{2}{3} = \frac{18}{33} = \frac{6}{11}
$$

✔ Answer: $\boxed{\frac{6}{11}}$

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9. $\frac{1}{6} \div \frac{2}{10}$

Simplify $\frac{2}{10} = \frac{1}{5}$

$$
= \frac{1}{6} \div \frac{1}{5} = \frac{1}{6} \times \frac{5}{1} = \frac{5}{6}
$$

✔ Answer: $\boxed{\frac{5}{6}}$

---

10. $\frac{2}{3} \div \frac{8}{9}$

$$
= \frac{2}{3} \times \frac{9}{8} = \frac{18}{24} = \frac{3}{4}
$$

✔ Answer: $\boxed{\frac{3}{4}}$

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11. $\frac{3}{4} \div \frac{11}{12}$

$$
= \frac{3}{4} \times \frac{12}{11} = \frac{36}{44} = \frac{9}{11}
$$

✔ Answer: $\boxed{\frac{9}{11}}$

---

12. $\frac{4}{10} \div \frac{4}{5}$

Simplify $\frac{4}{10} = \frac{2}{5}$

$$
= \frac{2}{5} \div \frac{4}{5} = \frac{2}{5} \times \frac{5}{4} = \frac{10}{20} = \frac{1}{2}
$$

✔ Answer: $\boxed{\frac{1}{2}}$

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✔ Final Answers:

1. $\frac{9}{16}$
2. $\frac{10}{3}$ or $3\frac{1}{3}$
3. $\frac{1}{2}$
4. $12$
5. $3$
6. $\frac{5}{9}$
7. $\frac{1}{2}$
8. $\frac{6}{11}$
9. $\frac{5}{6}$
10. $\frac{3}{4}$
11. $\frac{9}{11}$
12. $\frac{1}{2}$

Let me know if you'd like a printable version or explanation in simpler terms!