Dividing Fractions Worksheet - Free Printable

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

> To divide by a fraction, multiply by its reciprocal (invert the divisor).

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

We’ll apply this rule to each problem and fill in the blanks.

---

1)

$$
\frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1} = \frac{8}{5}
$$

✔ Answer: $\boxed{\frac{8}{5}}$

---

2)

$$
\frac{3}{7} \div \frac{2}{3} = \frac{3}{7} \times \frac{3}{2} = \frac{9}{14}
$$

✔ Answer: $\boxed{\frac{9}{14}}$

---

3)

$$
\frac{4}{9} \div \frac{3}{4} = \frac{4}{9} \times \frac{4}{3} = \frac{16}{27}
$$

✔ Answer: $\boxed{\frac{16}{27}}$

---

4)

$$
\frac{5}{8} \div \frac{1}{3} = \frac{5}{8} \times \frac{3}{1} = \frac{15}{8}
$$

✔ Answer: $\boxed{\frac{15}{8}}$

---

5)

$$
\frac{4}{7} \div \frac{2}{9} = \frac{4}{7} \times \frac{9}{2} = \frac{36}{14} = \frac{18}{7} \quad (\text{but we don't need to simplify})
$$

✔ Answer: $\boxed{\frac{36}{14}}$ (or $\frac{18}{7}$ if simplified, but keep as $\frac{36}{14}$ since not required)

But let’s keep it as $\frac{36}{14}$ unless asked to reduce.

Wait — the instruction says: *"Your answer can be left as an improper fraction and does not need to be in simplest form."* So we can leave it as $\frac{36}{14}$.

✔ Answer: $\boxed{\frac{36}{14}}$

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6)

$$
\frac{5}{6} \div \frac{3}{10} = \frac{5}{6} \times \frac{10}{3} = \frac{50}{18}
$$

✔ Answer: $\boxed{\frac{50}{18}}$

---

7)

$$
\frac{3}{5} \div \frac{7}{4} = \frac{3}{5} \times \frac{4}{7} = \frac{12}{35}
$$

✔ Answer: $\boxed{\frac{12}{35}}$

---

8)

$$
\frac{5}{2} \div \frac{6}{7} = \frac{5}{2} \times \frac{7}{6} = \frac{35}{12}
$$

✔ Answer: $\boxed{\frac{35}{12}}$

---

9)

$$
\frac{4}{11} \div \frac{1}{8} = \frac{4}{11} \times \frac{8}{1} = \frac{32}{11}
$$

✔ Answer: $\boxed{\frac{32}{11}}$

---

10)

$$
\frac{7}{15} \div \frac{2}{5} = \frac{7}{15} \times \frac{5}{2} = \frac{35}{30}
$$

✔ Answer: $\boxed{\frac{35}{30}}$

---

11)

$$
\frac{5}{8} \div \frac{2}{9} = \frac{5}{8} \times \frac{9}{2} = \frac{45}{16}
$$

✔ Answer: $\boxed{\frac{45}{16}}$

---

12)

$$
\frac{7}{3} \div \frac{11}{4} = \frac{7}{3} \times \frac{4}{11} = \frac{28}{33}
$$

✔ Answer: $\boxed{\frac{28}{33}}$

---

13)

$$
\frac{7}{8} \div \frac{1}{5} = \frac{7}{8} \times \frac{5}{1} = \frac{35}{8}
$$

✔ Answer: $\boxed{\frac{35}{8}}$

---

14)

$$
\frac{7}{10} \div \frac{4}{9} = \frac{7}{10} \times \frac{9}{4} = \frac{63}{40}
$$

✔ Answer: $\boxed{\frac{63}{40}}$

---

15)

$$
\frac{2}{15} \div \frac{3}{8} = \frac{2}{15} \times \frac{8}{3} = \frac{16}{45}
$$

✔ Answer: $\boxed{\frac{16}{45}}$

---

16)

$$
\frac{5}{14} \div \frac{3}{11} = \frac{5}{14} \times \frac{11}{3} = \frac{55}{42}
$$

✔ Answer: $\boxed{\frac{55}{42}}$

---

17)

$$
\frac{6}{11} \div \frac{2}{9} = \frac{6}{11} \times \frac{9}{2} = \frac{54}{22}
$$

✔ Answer: $\boxed{\frac{54}{22}}$

---

18)

$$
\frac{5}{9} \div \frac{3}{14} = \frac{5}{9} \times \frac{14}{3} = \frac{70}{27}
$$

✔ Answer: $\boxed{\frac{70}{27}}$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1) | $\frac{8}{5}$ |
| 2) | $\frac{9}{14}$ |
| 3) | $\frac{16}{27}$ |
| 4) | $\frac{15}{8}$ |
| 5) | $\frac{36}{14}$ |
| 6) | $\frac{50}{18}$ |
| 7) | $\frac{12}{35}$ |
| 8) | $\frac{35}{12}$ |
| 9) | $\frac{32}{11}$ |
| 10) | $\frac{35}{30}$ |
| 11) | $\frac{45}{16}$ |
| 12) | $\frac{28}{33}$ |
| 13) | $\frac{35}{8}$ |
| 14) | $\frac{63}{40}$ |
| 15) | $\frac{16}{45}$ |
| 16) | $\frac{55}{42}$ |
| 17) | $\frac{54}{22}$ |
| 18) | $\frac{70}{27}$ |

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📌 Key Tip:

Always remember: "Keep, Change, Flip"
- Keep the first fraction,
- Change the division to multiplication,
- Flip (invert) the second fraction.

This method works every time!

Let me know if you'd like a printable version or explanation with visuals!