Math worksheet for practicing division of fractions with 15 problems.

To solve the given problems, we need to divide fractions. The general rule for dividing fractions is:

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

This means we take the reciprocal of the divisor (the second fraction) and then multiply the two fractions.

Let's solve each problem step by step.

---

Problem 1:

\[
\frac{3}{4} \div \frac{1}{2}
\]

1. Take the reciprocal of \(\frac{1}{2}\), which is \(\frac{2}{1}\).
2. Multiply:
\[
\frac{3}{4} \times \frac{2}{1} = \frac{3 \cdot 2}{4 \cdot 1} = \frac{6}{4}
\]
3. Simplify \(\frac{6}{4}\):
\[
\frac{6}{4} = \frac{3}{2}
\]

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

---

Problem 2:

\[
\frac{2}{3} \div \frac{3}{9}
\]

1. Take the reciprocal of \(\frac{3}{9}\), which is \(\frac{9}{3}\).
2. Multiply:
\[
\frac{2}{3} \times \frac{9}{3} = \frac{2 \cdot 9}{3 \cdot 3} = \frac{18}{9}
\]
3. Simplify \(\frac{18}{9}\):
\[
\frac{18}{9} = 2
\]

Answer: \(\boxed{2}\)

---

Problem 3:

\[
\frac{2}{5} \div \frac{7}{9}
\]

1. Take the reciprocal of \(\frac{7}{9}\), which is \(\frac{9}{7}\).
2. Multiply:
\[
\frac{2}{5} \times \frac{9}{7} = \frac{2 \cdot 9}{5 \cdot 7} = \frac{18}{35}
\]

Answer: \(\boxed{\frac{18}{35}}\)

---

Problem 4:

\[
\frac{2}{3} \div \frac{1}{2}
\]

1. Take the reciprocal of \(\frac{1}{2}\), which is \(\frac{2}{1}\).
2. Multiply:
\[
\frac{2}{3} \times \frac{2}{1} = \frac{2 \cdot 2}{3 \cdot 1} = \frac{4}{3}
\]

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

---

Problem 5:

\[
\frac{2}{9} \div \frac{2}{3}
\]

1. Take the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\).
2. Multiply:
\[
\frac{2}{9} \times \frac{3}{2} = \frac{2 \cdot 3}{9 \cdot 2} = \frac{6}{18}
\]
3. Simplify \(\frac{6}{18}\):
\[
\frac{6}{18} = \frac{1}{3}
\]

Answer: \(\boxed{\frac{1}{3}}\)

---

Problem 6:

\[
\frac{1}{3} \div \frac{2}{3}
\]

1. Take the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\).
2. Multiply:
\[
\frac{1}{3} \times \frac{3}{2} = \frac{1 \cdot 3}{3 \cdot 2} = \frac{3}{6}
\]
3. Simplify \(\frac{3}{6}\):
\[
\frac{3}{6} = \frac{1}{2}
\]

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

---

Problem 7:

\[
\frac{2}{4} \div \frac{5}{9}
\]

1. Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\).
2. Take the reciprocal of \(\frac{5}{9}\), which is \(\frac{9}{5}\).
3. Multiply:
\[
\frac{1}{2} \times \frac{9}{5} = \frac{1 \cdot 9}{2 \cdot 5} = \frac{9}{10}
\]

Answer: \(\boxed{\frac{9}{10}}\)

---

Problem 8:

\[
\frac{1}{2} \div \frac{1}{2}
\]

1. Take the reciprocal of \(\frac{1}{2}\), which is \(\frac{2}{1}\).
2. Multiply:
\[
\frac{1}{2} \times \frac{2}{1} = \frac{1 \cdot 2}{2 \cdot 1} = \frac{2}{2}
\]
3. Simplify \(\frac{2}{2}\):
\[
\frac{2}{2} = 1
\]

Answer: \(\boxed{1}\)

---

Problem 9:

\[
\frac{1}{2} \div \frac{3}{4}
\]

1. Take the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\).
2. Multiply:
\[
\frac{1}{2} \times \frac{4}{3} = \frac{1 \cdot 4}{2 \cdot 3} = \frac{4}{6}
\]
3. Simplify \(\frac{4}{6}\):
\[
\frac{4}{6} = \frac{2}{3}
\]

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

---

Problem 10:

\[
\frac{1}{2} \div \frac{3}{8}
\]

1. Take the reciprocal of \(\frac{3}{8}\), which is \(\frac{8}{3}\).
2. Multiply:
\[
\frac{1}{2} \times \frac{8}{3} = \frac{1 \cdot 8}{2 \cdot 3} = \frac{8}{6}
\]
3. Simplify \(\frac{8}{6}\):
\[
\frac{8}{6} = \frac{4}{3}
\]

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

---

Problem 11:

\[
\frac{5}{9} \div \frac{3}{4}
\]

1. Take the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\).
2. Multiply:
\[
\frac{5}{9} \times \frac{4}{3} = \frac{5 \cdot 4}{9 \cdot 3} = \frac{20}{27}
\]

Answer: \(\boxed{\frac{20}{27}}\)

---

Problem 12:

\[
\frac{3}{4} \div \frac{1}{4}
\]

1. Take the reciprocal of \(\frac{1}{4}\), which is \(\frac{4}{1}\).
2. Multiply:
\[
\frac{3}{4} \times \frac{4}{1} = \frac{3 \cdot 4}{4 \cdot 1} = \frac{12}{4}
\]
3. Simplify \(\frac{12}{4}\):
\[
\frac{12}{4} = 3
\]

Answer: \(\boxed{3}\)

---

Problem 13:

\[
\frac{1}{9} \div \frac{6}{8}
\]

1. Simplify \(\frac{6}{8}\) to \(\frac{3}{4}\).
2. Take the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\).
3. Multiply:
\[
\frac{1}{9} \times \frac{4}{3} = \frac{1 \cdot 4}{9 \cdot 3} = \frac{4}{27}
\]

Answer: \(\boxed{\frac{4}{27}}\)

---

Problem 14:

\[
\frac{5}{6} \div \frac{5}{6}
\]

1. Take the reciprocal of \(\frac{5}{6}\), which is \(\frac{6}{5}\).
2. Multiply:
\[
\frac{5}{6} \times \frac{6}{5} = \frac{5 \cdot 6}{6 \cdot 5} = \frac{30}{30}
\]
3. Simplify \(\frac{30}{30}\):
\[
\frac{30}{30} = 1
\]

Answer: \(\boxed{1}\)

---

Problem 15:

\[
\frac{1}{3} \div \frac{5}{9}
\]

1. Take the reciprocal of \(\frac{5}{9}\), which is \(\frac{9}{5}\).
2. Multiply:
\[
\frac{1}{3} \times \frac{9}{5} = \frac{1 \cdot 9}{3 \cdot 5} = \frac{9}{15}
\]
3. Simplify \(\frac{9}{15}\):
\[
\frac{9}{15} = \frac{3}{5}
\]

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

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ \frac{3}{2} \\
2. & \ 2 \\
3. & \ \frac{18}{35} \\
4. & \ \frac{4}{3} \\
5. & \ \frac{1}{3} \\
6. & \ \frac{1}{2} \\
7. & \ \frac{9}{10} \\
8. & \ 1 \\
9. & \ \frac{2}{3} \\
10. & \ \frac{4}{3} \\
11. & \ \frac{20}{27} \\
12. & \ 3 \\
13. & \ \frac{4}{27} \\
14. & \ 1 \\
15. & \ \frac{3}{5}
\end{aligned}
}
\]