Dividing Fractions Worksheet - Free Printable

Problem: Solving the Multiplying and Dividing Fractions Worksheet

The worksheet asks us to solve problems involving multiplication and division of fractions. The instructions specify that the answers should be given as fractions and do not need to be simplified.

#### Key Rules:
1. Multiplying Fractions: Multiply the numerators together and the denominators together.
\[
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
\]

2. Dividing Fractions: Multiply the first fraction by the reciprocal of the second fraction.
\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}
\]

Let's solve each problem step by step.

---

Section 1: Multiplying Fractions

#### Problem 1: $\frac{3}{5} \times \frac{3}{4}$
\[
\frac{3}{5} \times \frac{3}{4} = \frac{3 \times 3}{5 \times 4} = \frac{9}{20}
\]

#### Problem 3: $\frac{3}{4} \times \frac{1}{5}$
\[
\frac{3}{4} \times \frac{1}{5} = \frac{3 \times 1}{4 \times 5} = \frac{3}{20}
\]

#### Problem 5: $\frac{3}{5} \times \frac{1}{4}$
\[
\frac{3}{5} \times \frac{1}{4} = \frac{3 \times 1}{5 \times 4} = \frac{3}{20}
\]

#### Problem 7: $\frac{3}{7} \times \frac{4}{5}$
\[
\frac{3}{7} \times \frac{4}{5} = \frac{3 \times 4}{7 \times 5} = \frac{12}{35}
\]

#### Problem 9: $\frac{5}{6} \times \frac{1}{2}$
\[
\frac{5}{6} \times \frac{1}{2} = \frac{5 \times 1}{6 \times 2} = \frac{5}{12}
\]

#### Problem 11: $\frac{4}{9} \times \frac{2}{5}$
\[
\frac{4}{9} \times \frac{2}{5} = \frac{4 \times 2}{9 \times 5} = \frac{8}{45}
\]

#### Problem 13: $\frac{1}{5} \times \frac{4}{5}$
\[
\frac{1}{5} \times \frac{4}{5} = \frac{1 \times 4}{5 \times 5} = \frac{4}{25}
\]

#### Problem 15: $\frac{2}{7} \times \frac{1}{3}$
\[
\frac{2}{7} \times \frac{1}{3} = \frac{2 \times 1}{7 \times 3} = \frac{2}{21}
\]

#### Problem 17: $\frac{2}{5} \times \frac{3}{7}$
\[
\frac{2}{5} \times \frac{3}{7} = \frac{2 \times 3}{5 \times 7} = \frac{6}{35}
\]

#### Problem 19: $\frac{1}{8} \times \frac{3}{5}$
\[
\frac{1}{8} \times \frac{3}{5} = \frac{1 \times 3}{8 \times 5} = \frac{3}{40}
\]

#### Problem 21: $\frac{3}{10} \times \frac{3}{5}$
\[
\frac{3}{10} \times \frac{3}{5} = \frac{3 \times 3}{10 \times 5} = \frac{9}{50}
\]

#### Problem 23: $\frac{7}{8} \times \frac{5}{6}$
\[
\frac{7}{8} \times \frac{5}{6} = \frac{7 \times 5}{8 \times 6} = \frac{35}{48}
\]

---

Section 2: Dividing Fractions

#### Problem 2: $\frac{2}{3} \div \frac{1}{2}$
\[
\frac{2}{3} \div \frac{1}{2} = \frac{2}{3} \times \frac{2}{1} = \frac{2 \times 2}{3 \times 1} = \frac{4}{3}
\]

#### Problem 4: $\frac{1}{3} \div \frac{2}{5}$
\[
\frac{1}{3} \div \frac{2}{5} = \frac{1}{3} \times \frac{5}{2} = \frac{1 \times 5}{3 \times 2} = \frac{5}{6}
\]

#### Problem 6: $\frac{5}{6} \div \frac{2}{5}$
\[
\frac{5}{6} \div \frac{2}{5} = \frac{5}{6} \times \frac{5}{2} = \frac{5 \times 5}{6 \times 2} = \frac{25}{12}
\]

#### Problem 8: $\frac{1}{8} \div \frac{2}{3}$
\[
\frac{1}{8} \div \frac{2}{3} = \frac{1}{8} \times \frac{3}{2} = \frac{1 \times 3}{8 \times 2} = \frac{3}{16}
\]

#### Problem 10: $\frac{4}{5} \div \frac{3}{8}$
\[
\frac{4}{5} \div \frac{3}{8} = \frac{4}{5} \times \frac{8}{3} = \frac{4 \times 8}{5 \times 3} = \frac{32}{15}
\]

#### Problem 12: $\frac{3}{8} \div \frac{2}{7}$
\[
\frac{3}{8} \div \frac{2}{7} = \frac{3}{8} \times \frac{7}{2} = \frac{3 \times 7}{8 \times 2} = \frac{21}{16}
\]

#### Problem 14: $\frac{3}{5} \div \frac{1}{2}$
\[
\frac{3}{5} \div \frac{1}{2} = \frac{3}{5} \times \frac{2}{1} = \frac{3 \times 2}{5 \times 1} = \frac{6}{5}
\]

#### Problem 16: $\frac{4}{7} \div \frac{1}{5}$
\[
\frac{4}{7} \div \frac{1}{5} = \frac{4}{7} \times \frac{5}{1} = \frac{4 \times 5}{7 \times 1} = \frac{20}{7}
\]

#### Problem 18: $\frac{2}{9} \div \frac{1}{4}$
\[
\frac{2}{9} \div \frac{1}{4} = \frac{2}{9} \times \frac{4}{1} = \frac{2 \times 4}{9 \times 1} = \frac{8}{9}
\]

#### Problem 20: $\frac{3}{7} \div \frac{1}{4}$
\[
\frac{3}{7} \div \frac{1}{4} = \frac{3}{7} \times \frac{4}{1} = \frac{3 \times 4}{7 \times 1} = \frac{12}{7}
\]

#### Problem 22: $\frac{2}{3} \div \frac{5}{8}$
\[
\frac{2}{3} \div \frac{5}{8} = \frac{2}{3} \times \frac{8}{5} = \frac{2 \times 8}{3 \times 5} = \frac{16}{15}
\]

#### Problem 24: $\frac{5}{9} \div \frac{4}{7}$
\[
\frac{5}{9} \div \frac{4}{7} = \frac{5}{9} \times \frac{7}{4} = \frac{5 \times 7}{9 \times 4} = \frac{35}{36}
\]

---

Final Answers

\[
\boxed{
\begin{array}{ll}
1. \frac{9}{20} & 2. \frac{4}{3} \\
3. \frac{3}{20} & 4. \frac{5}{6} \\
5. \frac{3}{20} & 6. \frac{25}{12} \\
7. \frac{12}{35} & 8. \frac{3}{16} \\
9. \frac{5}{12} & 10. \frac{32}{15} \\
11. \frac{8}{45} & 12. \frac{21}{16} \\
13. \frac{4}{25} & 14. \frac{6}{5} \\
15. \frac{2}{21} & 16. \frac{20}{7} \\
17. \frac{6}{35} & 18. \frac{8}{9} \\
19. \frac{3}{40} & 20. \frac{12}{7} \\
21. \frac{9}{50} & 22. \frac{16}{15} \\
23. \frac{35}{48} & 24. \frac{35}{36} \\
\end{array}
}
\]