To solve the problems involving the division of fractions, we use the rule:
\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
\]
This means we multiply the first fraction by the reciprocal of the second fraction. Let's solve each problem step by step.
---
Problem 1: $\frac{1}{3} \div \frac{7}{9}$
\[
\frac{1}{3} \div \frac{7}{9} = \frac{1}{3} \times \frac{9}{7} = \frac{1 \cdot 9}{3 \cdot 7} = \frac{9}{21} = \frac{3}{7}
\]
Answer: $\frac{3}{7}$
---
Problem 2: $\frac{1}{2} \div \frac{5}{6}$
\[
\frac{1}{2} \div \frac{5}{6} = \frac{1}{2} \times \frac{6}{5} = \frac{1 \cdot 6}{2 \cdot 5} = \frac{6}{10} = \frac{3}{5}
\]
Answer: $\frac{3}{5}$
---
Problem 3: $\frac{6}{9} \div \frac{1}{10}$
\[
\frac{6}{9} \div \frac{1}{10} = \frac{6}{9} \times \frac{10}{1} = \frac{6 \cdot 10}{9 \cdot 1} = \frac{60}{9} = \frac{20}{3}
\]
Answer: $\frac{20}{3}$
---
Problem 4: $\frac{1}{3} \div \frac{1}{2}$
\[
\frac{1}{3} \div \frac{1}{2} = \frac{1}{3} \times \frac{2}{1} = \frac{1 \cdot 2}{3 \cdot 1} = \frac{2}{3}
\]
Answer: $\frac{2}{3}$
---
Problem 5: $\frac{4}{10} \div \frac{1}{3}$
\[
\frac{4}{10} \div \frac{1}{3} = \frac{4}{10} \times \frac{3}{1} = \frac{4 \cdot 3}{10 \cdot 1} = \frac{12}{10} = \frac{6}{5}
\]
Answer: $\frac{6}{5}$
---
Problem 6: $\frac{3}{6} \div \frac{2}{3}$
\[
\frac{3}{6} \div \frac{2}{3} = \frac{3}{6} \times \frac{3}{2} = \frac{3 \cdot 3}{6 \cdot 2} = \frac{9}{12} = \frac{3}{4}
\]
Answer: $\frac{3}{4}$
---
Problem 7: $\frac{9}{10} \div \frac{2}{6}$
\[
\frac{9}{10} \div \frac{2}{6} = \frac{9}{10} \times \frac{6}{2} = \frac{9 \cdot 6}{10 \cdot 2} = \frac{54}{20} = \frac{27}{10}
\]
Answer: $\frac{27}{10}$
---
Problem 8: $\frac{7}{10} \div \frac{1}{3}$
\[
\frac{7}{10} \div \frac{1}{3} = \frac{7}{10} \times \frac{3}{1} = \frac{7 \cdot 3}{10 \cdot 1} = \frac{21}{10}
\]
Answer: $\frac{21}{10}$
---
Problem 9: $\frac{1}{4} \div \frac{4}{8}$
\[
\frac{1}{4} \div \frac{4}{8} = \frac{1}{4} \times \frac{8}{4} = \frac{1 \cdot 8}{4 \cdot 4} = \frac{8}{16} = \frac{1}{2}
\]
Answer: $\frac{1}{2}$
---
Problem 10: $\frac{1}{5} \div \frac{10}{11}$
\[
\frac{1}{5} \div \frac{10}{11} = \frac{1}{5} \times \frac{11}{10} = \frac{1 \cdot 11}{5 \cdot 10} = \frac{11}{50}
\]
Answer: $\frac{11}{50}$
---
Problem 11: $\frac{3}{4} \div \frac{2}{5}$
\[
\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{3 \cdot 5}{4 \cdot 2} = \frac{15}{8}
\]
Answer: $\frac{15}{8}$
---
Problem 12: $\frac{4}{5} \div \frac{3}{6}$
\[
\frac{4}{5} \div \frac{3}{6} = \frac{4}{5} \times \frac{6}{3} = \frac{4 \cdot 6}{5 \cdot 3} = \frac{24}{15} = \frac{8}{5}
\]
Answer: $\frac{8}{5}$
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
1. \frac{3}{7} & 7. \frac{27}{10} \\
2. \frac{3}{5} & 8. \frac{21}{10} \\
3. \frac{20}{3} & 9. \frac{1}{2} \\
4. \frac{2}{3} & 10. \frac{11}{50} \\
5. \frac{6}{5} & 11. \frac{15}{8} \\
6. \frac{3}{4} & 12. \frac{8}{5} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of dividing with fractions worksheet.
