Dividing Fractions by Fractions worksheet with 15 practice problems.

To solve the problems involving dividing fractions by 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.

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Problem 1: $\frac{4}{3} \div \frac{9}{5}$

\[
\frac{4}{3} \div \frac{9}{5} = \frac{4}{3} \times \frac{5}{9} = \frac{4 \times 5}{3 \times 9} = \frac{20}{27}
\]
Answer: $\boxed{\frac{20}{27}}$

---

Problem 2: $\frac{7}{2} \div \frac{17}{16}$

\[
\frac{7}{2} \div \frac{17}{16} = \frac{7}{2} \times \frac{16}{17} = \frac{7 \times 16}{2 \times 17} = \frac{112}{34} = \frac{56}{17}
\]
Answer: $\boxed{\frac{56}{17}}$

---

Problem 3: $\frac{20}{9} \div \frac{8}{24}$

\[
\frac{20}{9} \div \frac{8}{24} = \frac{20}{9} \times \frac{24}{8} = \frac{20 \times 24}{9 \times 8} = \frac{480}{72} = \frac{20}{3}
\]
Answer: $\boxed{\frac{20}{3}}$

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Problem 4: $\frac{1}{4} \div \frac{7}{9}$

\[
\frac{1}{4} \div \frac{7}{9} = \frac{1}{4} \times \frac{9}{7} = \frac{1 \times 9}{4 \times 7} = \frac{9}{28}
\]
Answer: $\boxed{\frac{9}{28}}$

---

Problem 5: $\frac{6}{5} \div \frac{3}{8}$

\[
\frac{6}{5} \div \frac{3}{8} = \frac{6}{5} \times \frac{8}{3} = \frac{6 \times 8}{5 \times 3} = \frac{48}{15} = \frac{16}{5}
\]
Answer: $\boxed{\frac{16}{5}}$

---

Problem 6: $\frac{1}{3} \div \frac{20}{9}$

\[
\frac{1}{3} \div \frac{20}{9} = \frac{1}{3} \times \frac{9}{20} = \frac{1 \times 9}{3 \times 20} = \frac{9}{60} = \frac{3}{20}
\]
Answer: $\boxed{\frac{3}{20}}$

---

Problem 7: $\frac{11}{10} \div \frac{2}{7}$

\[
\frac{11}{10} \div \frac{2}{7} = \frac{11}{10} \times \frac{7}{2} = \frac{11 \times 7}{10 \times 2} = \frac{77}{20}
\]
Answer: $\boxed{\frac{77}{20}}$

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Problem 8: $\frac{4}{15} \div \frac{11}{5}$

\[
\frac{4}{15} \div \frac{11}{5} = \frac{4}{15} \times \frac{5}{11} = \frac{4 \times 5}{15 \times 11} = \frac{20}{165} = \frac{4}{33}
\]
Answer: $\boxed{\frac{4}{33}}$

---

Problem 9: $\frac{18}{22} \div \frac{3}{7}$

\[
\frac{18}{22} \div \frac{3}{7} = \frac{18}{22} \times \frac{7}{3} = \frac{18 \times 7}{22 \times 3} = \frac{126}{66} = \frac{21}{11}
\]
Answer: $\boxed{\frac{21}{11}}$

---

Problem 10: $\frac{10}{6} \div \frac{9}{12}$

\[
\frac{10}{6} \div \frac{9}{12} = \frac{10}{6} \times \frac{12}{9} = \frac{10 \times 12}{6 \times 9} = \frac{120}{54} = \frac{20}{9}
\]
Answer: $\boxed{\frac{20}{9}}$

---

Problem 11: $\frac{2}{3} \div \frac{8}{20}$

\[
\frac{2}{3} \div \frac{8}{20} = \frac{2}{3} \times \frac{20}{8} = \frac{2 \times 20}{3 \times 8} = \frac{40}{24} = \frac{5}{3}
\]
Answer: $\boxed{\frac{5}{3}}$

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Problem 12: $\frac{5}{6} \div \frac{10}{12}$

\[
\frac{5}{6} \div \frac{10}{12} = \frac{5}{6} \times \frac{12}{10} = \frac{5 \times 12}{6 \times 10} = \frac{60}{60} = 1
\]
Answer: $\boxed{1}$

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Problem 13: $\frac{6}{10} \div \frac{3}{7}$

\[
\frac{6}{10} \div \frac{3}{7} = \frac{6}{10} \times \frac{7}{3} = \frac{6 \times 7}{10 \times 3} = \frac{42}{30} = \frac{7}{5}
\]
Answer: $\boxed{\frac{7}{5}}$

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Problem 14: $\frac{22}{5} \div \frac{8}{14}$

\[
\frac{22}{5} \div \frac{8}{14} = \frac{22}{5} \times \frac{14}{8} = \frac{22 \times 14}{5 \times 8} = \frac{308}{40} = \frac{77}{10}
\]
Answer: $\boxed{\frac{77}{10}}$

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Problem 15: $\frac{7}{5} \div \frac{21}{9}$

\[
\frac{7}{5} \div \frac{21}{9} = \frac{7}{5} \times \frac{9}{21} = \frac{7 \times 9}{5 \times 21} = \frac{63}{105} = \frac{3}{5}
\]
Answer: $\boxed{\frac{3}{5}}$

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Final Answers:

\[
\boxed{
\begin{array}{ccc}
1. & \frac{20}{27} & 2. & \frac{56}{17} & 3. & \frac{20}{3} \\
4. & \frac{9}{28} & 5. & \frac{16}{5} & 6. & \frac{3}{20} \\
7. & \frac{77}{20} & 8. & \frac{4}{33} & 9. & \frac{21}{11} \\
10. & \frac{20}{9} & 11. & \frac{5}{3} & 12. & 1 \\
13. & \frac{7}{5} & 14. & \frac{77}{10} & 15. & \frac{3}{5} \\
\end{array}
}
\]