Dividing Fractions Worksheets with Answer Key - Free Printable

Let's solve each of these fraction division problems step by step.

The general rule for dividing fractions is:

> $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

That is, multiply by the reciprocal of the second fraction.

We'll go through each problem one at a time.

---

1. $\frac{4}{3} \div \frac{9}{5}$

$$
= \frac{4}{3} \times \frac{5}{9} = \frac{4 \times 5}{3 \times 9} = \frac{20}{27}
$$

✔ Answer: $\frac{20}{27}$

---

2. $\frac{7}{2} \div \frac{17}{16}$

$$
= \frac{7}{2} \times \frac{16}{17} = \frac{7 \times 16}{2 \times 17} = \frac{112}{34}
$$

Simplify: divide numerator and denominator by 2:

$$
\frac{112 \div 2}{34 \div 2} = \frac{56}{17}
$$

✔ Answer: $\frac{56}{17}$ (or $3\frac{5}{17}$)

---

3. $\frac{20}{9} \div \frac{8}{24}$

First simplify $\frac{8}{24} = \frac{1}{3}$

So:
$$
\frac{20}{9} \div \frac{1}{3} = \frac{20}{9} \times \frac{3}{1} = \frac{60}{9} = \frac{20}{3}
$$

✔ Answer: $\frac{20}{3}$ (or $6\frac{2}{3}$)

---

4. $\frac{1}{4} \div \frac{7}{9}$

$$
= \frac{1}{4} \times \frac{9}{7} = \frac{9}{28}
$$

✔ Answer: $\frac{9}{28}$

---

5. $\frac{6}{5} \div \frac{3}{8}$

$$
= \frac{6}{5} \times \frac{8}{3} = \frac{48}{15}
$$

Simplify: divide numerator and denominator by 3:

$$
\frac{48 \div 3}{15 \div 3} = \frac{16}{5}
$$

✔ Answer: $\frac{16}{5}$ (or $3\frac{1}{5}$)

---

6. $\frac{1}{3} \div \frac{20}{9}$

$$
= \frac{1}{3} \times \frac{9}{20} = \frac{9}{60} = \frac{3}{20}
$$

✔ Answer: $\frac{3}{20}$

---

7. $\frac{11}{10} \div \frac{2}{7}$

$$
= \frac{11}{10} \times \frac{7}{2} = \frac{77}{20}
$$

✔ Answer: $\frac{77}{20}$ (or $3\frac{17}{20}$)

---

8. $\frac{4}{15} \div \frac{11}{5}$

$$
= \frac{4}{15} \times \frac{5}{11} = \frac{20}{165}
$$

Simplify: divide numerator and denominator by 5:

$$
\frac{20 \div 5}{165 \div 5} = \frac{4}{33}
$$

✔ Answer: $\frac{4}{33}$

---

9. $\frac{18}{22} \div \frac{3}{7}$

First simplify $\frac{18}{22} = \frac{9}{11}$

Then:
$$
\frac{9}{11} \div \frac{3}{7} = \frac{9}{11} \times \frac{7}{3} = \frac{63}{33}
$$

Simplify: divide numerator and denominator by 3:

$$
\frac{63 \div 3}{33 \div 3} = \frac{21}{11}
$$

✔ Answer: $\frac{21}{11}$ (or $1\frac{10}{11}$)

---

10. $\frac{10}{6} \div \frac{9}{12}$

Simplify both fractions:

- $\frac{10}{6} = \frac{5}{3}$
- $\frac{9}{12} = \frac{3}{4}$

Now:
$$
\frac{5}{3} \div \frac{3}{4} = \frac{5}{3} \times \frac{4}{3} = \frac{20}{9}
$$

✔ Answer: $\frac{20}{9}$ (or $2\frac{2}{9}$)

---

11. $\frac{2}{3} \div \frac{8}{20}$

Simplify $\frac{8}{20} = \frac{2}{5}$

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

✔ Answer: $\frac{5}{3}$ (or $1\frac{2}{3}$)

---

12. $\frac{5}{6} \div \frac{10}{12}$

Simplify $\frac{10}{12} = \frac{5}{6}$

So:
$$
\frac{5}{6} \div \frac{5}{6} = \frac{5}{6} \times \frac{6}{5} = \frac{30}{30} = 1
$$

✔ Answer: $1$

---

13. $\frac{6}{10} \div \frac{3}{7}$

Simplify $\frac{6}{10} = \frac{3}{5}$

Now:
$$
\frac{3}{5} \div \frac{3}{7} = \frac{3}{5} \times \frac{7}{3} = \frac{21}{15} = \frac{7}{5}
$$

✔ Answer: $\frac{7}{5}$ (or $1\frac{2}{5}$)

---

14. $\frac{22}{5} \div \frac{8}{14}$

Simplify $\frac{8}{14} = \frac{4}{7}$

Now:
$$
\frac{22}{5} \div \frac{4}{7} = \frac{22}{5} \times \frac{7}{4} = \frac{154}{20}
$$

Simplify: divide numerator and denominator by 2:

$$
\frac{77}{10}
$$

✔ Answer: $\frac{77}{10}$ (or $7\frac{7}{10}$)

---

15. $\frac{7}{5} \div \frac{21}{9}$

Simplify $\frac{21}{9} = \frac{7}{3}$

Now:
$$
\frac{7}{5} \div \frac{7}{3} = \frac{7}{5} \times \frac{3}{7} = \frac{21}{35} = \frac{3}{5}
$$

✔ Answer: $\frac{3}{5}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $\frac{20}{27}$ |
| 2 | $\frac{56}{17}$ |
| 3 | $\frac{20}{3}$ |
| 4 | $\frac{9}{28}$ |
| 5 | $\frac{16}{5}$ |
| 6 | $\frac{3}{20}$ |
| 7 | $\frac{77}{20}$ |
| 8 | $\frac{4}{33}$ |
| 9 | $\frac{21}{11}$ |
| 10 | $\frac{20}{9}$ |
| 11 | $\frac{5}{3}$ |
| 12 | $1$ |
| 13 | $\frac{7}{5}$ |
| 14 | $\frac{77}{10}$ |
| 15 | $\frac{3}{5}$ |

Let me know if you'd like them in mixed number form or simplified further!