Math worksheet for practicing division of fractions.

Problem Overview:

The task involves dividing fractions and finding the quotient for each problem. The general rule for dividing fractions is:

\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \cdot d}{b \cdot c}
\]

We will solve each problem step by step using this rule.

---

Solution:

#### Problem 1:
\[
\frac{2}{4} \div \frac{3}{4}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{2}{4} \times \frac{4}{3} = \frac{2 \cdot 4}{4 \cdot 3} = \frac{8}{12}
\]
- Simplify the fraction:
\[
\frac{8}{12} = \frac{2}{3}
\]

Answer: \(\boxed{\frac{2}{3}}\)

---

#### Problem 2:
\[
\frac{3}{9} \div \frac{1}{3}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{3}{9} \times \frac{3}{1} = \frac{3 \cdot 3}{9 \cdot 1} = \frac{9}{9}
\]
- Simplify the fraction:
\[
\frac{9}{9} = 1
\]

Answer: \(\boxed{1}\)

---

#### Problem 3:
\[
\frac{2}{3} \div \frac{6}{8}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{2}{3} \times \frac{8}{6} = \frac{2 \cdot 8}{3 \cdot 6} = \frac{16}{18}
\]
- Simplify the fraction:
\[
\frac{16}{18} = \frac{8}{9}
\]

Answer: \(\boxed{\frac{8}{9}}\)

---

#### Problem 4:
\[
\frac{7}{8} \div \frac{1}{6}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{7}{8} \times \frac{6}{1} = \frac{7 \cdot 6}{8 \cdot 1} = \frac{42}{8}
\]
- Simplify the fraction:
\[
\frac{42}{8} = \frac{21}{4}
\]

Answer: \(\boxed{\frac{21}{4}}\)

---

#### Problem 5:
\[
\frac{3}{8} \div \frac{1}{3}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{3}{8} \times \frac{3}{1} = \frac{3 \cdot 3}{8 \cdot 1} = \frac{9}{8}
\]

Answer: \(\boxed{\frac{9}{8}}\)

---

#### Problem 6:
\[
\frac{1}{4} \div \frac{1}{2}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{1}{4} \times \frac{2}{1} = \frac{1 \cdot 2}{4 \cdot 1} = \frac{2}{4}
\]
- Simplify the fraction:
\[
\frac{2}{4} = \frac{1}{2}
\]

Answer: \(\boxed{\frac{1}{2}}\)

---

#### Problem 7:
\[
\frac{1}{5} \div \frac{1}{3}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{1}{5} \times \frac{3}{1} = \frac{1 \cdot 3}{5 \cdot 1} = \frac{3}{5}
\]

Answer: \(\boxed{\frac{3}{5}}\)

---

#### Problem 8:
\[
\frac{1}{2} \div \frac{5}{8}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{1}{2} \times \frac{8}{5} = \frac{1 \cdot 8}{2 \cdot 5} = \frac{8}{10}
\]
- Simplify the fraction:
\[
\frac{8}{10} = \frac{4}{5}
\]

Answer: \(\boxed{\frac{4}{5}}\)

---

#### Problem 9:
\[
\frac{1}{2} \div \frac{6}{9}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{1}{2} \times \frac{9}{6} = \frac{1 \cdot 9}{2 \cdot 6} = \frac{9}{12}
\]
- Simplify the fraction:
\[
\frac{9}{12} = \frac{3}{4}
\]

Answer: \(\boxed{\frac{3}{4}}\)

---

#### Problem 10:
\[
\frac{4}{6} \div \frac{7}{8}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{4}{6} \times \frac{8}{7} = \frac{4 \cdot 8}{6 \cdot 7} = \frac{32}{42}
\]
- Simplify the fraction:
\[
\frac{32}{42} = \frac{16}{21}
\]

Answer: \(\boxed{\frac{16}{21}}\)

---

#### Problem 11:
\[
\frac{2}{9} \div \frac{1}{3}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{2}{9} \times \frac{3}{1} = \frac{2 \cdot 3}{9 \cdot 1} = \frac{6}{9}
\]
- Simplify the fraction:
\[
\frac{6}{9} = \frac{2}{3}
\]

Answer: \(\boxed{\frac{2}{3}}\)

---

#### Problem 12:
\[
\frac{3}{6} \div \frac{2}{3}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{3}{6} \times \frac{3}{2} = \frac{3 \cdot 3}{6 \cdot 2} = \frac{9}{12}
\]
- Simplify the fraction:
\[
\frac{9}{12} = \frac{3}{4}
\]

Answer: \(\boxed{\frac{3}{4}}\)

---

#### Problem 13:
\[
\frac{7}{8} \div \frac{2}{4}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{7}{8} \times \frac{4}{2} = \frac{7 \cdot 4}{8 \cdot 2} = \frac{28}{16}
\]
- Simplify the fraction:
\[
\frac{28}{16} = \frac{7}{4}
\]

Answer: \(\boxed{\frac{7}{4}}\)

---

#### Problem 14:
\[
\frac{8}{9} \div \frac{1}{9}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{8}{9} \times \frac{9}{1} = \frac{8 \cdot 9}{9 \cdot 1} = \frac{72}{9}
\]
- Simplify the fraction:
\[
\frac{72}{9} = 8
\]

Answer: \(\boxed{8}\)

---

#### Problem 15:
\[
\frac{2}{6} \div \frac{5}{8}
\]
- Rewrite as multiplication by the reciprocal:
\[
\frac{2}{6} \times \frac{8}{5} = \frac{2 \cdot 8}{6 \cdot 5} = \frac{16}{30}
\]
- Simplify the fraction:
\[
\frac{16}{30} = \frac{8}{15}
\]

Answer: \(\boxed{\frac{8}{15}}\)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ \frac{2}{3} \\
2. & \ 1 \\
3. & \ \frac{8}{9} \\
4. & \ \frac{21}{4} \\
5. & \ \frac{9}{8} \\
6. & \ \frac{1}{2} \\
7. & \ \frac{3}{5} \\
8. & \ \frac{4}{5} \\
9. & \ \frac{3}{4} \\
10. & \ \frac{16}{21} \\
11. & \ \frac{2}{3} \\
12. & \ \frac{3}{4} \\
13. & \ \frac{7}{4} \\
14. & \ 8 \\
15. & \ \frac{8}{15}
\end{aligned}
}
\]