Dividing Fractions worksheet for students to practice simplifying answers.

To solve the problems involving dividing 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: $\frac{6}{1} \div \frac{3}{4}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{6}{1} \div \frac{3}{4} = \frac{6}{1} \times \frac{4}{3}
\]

2. Multiply the numerators and denominators:
\[
\frac{6 \times 4}{1 \times 3} = \frac{24}{3}
\]

3. Simplify the fraction:
\[
\frac{24}{3} = 8
\]

Answer: $\boxed{8}$

---

Problem 2: $\frac{2}{7} \div \frac{8}{12}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{2}{7} \div \frac{8}{12} = \frac{2}{7} \times \frac{12}{8}
\]

2. Simplify $\frac{12}{8}$ to $\frac{3}{2}$:
\[
\frac{2}{7} \times \frac{3}{2}
\]

3. Multiply the numerators and denominators:
\[
\frac{2 \times 3}{7 \times 2} = \frac{6}{14}
\]

4. Simplify the fraction:
\[
\frac{6}{14} = \frac{3}{7}
\]

Answer: $\boxed{\frac{3}{7}}$

---

Problem 3: $\frac{9}{10} \div \frac{12}{5}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{9}{10} \div \frac{12}{5} = \frac{9}{10} \times \frac{5}{12}
\]

2. Multiply the numerators and denominators:
\[
\frac{9 \times 5}{10 \times 12} = \frac{45}{120}
\]

3. Simplify the fraction:
\[
\frac{45}{120} = \frac{3}{8}
\]

Answer: $\boxed{\frac{3}{8}}$

---

Problem 4: $\frac{2}{4} \div \frac{12}{1}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{2}{4} \div \frac{12}{1} = \frac{2}{4} \times \frac{1}{12}
\]

2. Simplify $\frac{2}{4}$ to $\frac{1}{2}$:
\[
\frac{1}{2} \times \frac{1}{12}
\]

3. Multiply the numerators and denominators:
\[
\frac{1 \times 1}{2 \times 12} = \frac{1}{24}
\]

Answer: $\boxed{\frac{1}{24}}$

---

Problem 5: $\frac{3}{5} \div \frac{4}{10}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{3}{5} \div \frac{4}{10} = \frac{3}{5} \times \frac{10}{4}
\]

2. Simplify $\frac{10}{4}$ to $\frac{5}{2}$:
\[
\frac{3}{5} \times \frac{5}{2}
\]

3. Multiply the numerators and denominators:
\[
\frac{3 \times 5}{5 \times 2} = \frac{15}{10}
\]

4. Simplify the fraction:
\[
\frac{15}{10} = \frac{3}{2}
\]

Answer: $\boxed{\frac{3}{2}}$

---

Problem 6: $\frac{11}{2} \div \frac{11}{6}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{11}{2} \div \frac{11}{6} = \frac{11}{2} \times \frac{6}{11}
\]

2. Multiply the numerators and denominators:
\[
\frac{11 \times 6}{2 \times 11} = \frac{66}{22}
\]

3. Simplify the fraction:
\[
\frac{66}{22} = 3
\]

Answer: $\boxed{3}$

---

Problem 7: $\frac{12}{2} \div \frac{3}{8}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{12}{2} \div \frac{3}{8} = \frac{12}{2} \times \frac{8}{3}
\]

2. Simplify $\frac{12}{2}$ to $6$:
\[
6 \times \frac{8}{3}
\]

3. Multiply:
\[
6 \times \frac{8}{3} = \frac{6 \times 8}{3} = \frac{48}{3} = 16
\]

Answer: $\boxed{16}$

---

Problem 8: $\frac{4}{7} \div \frac{11}{2}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{4}{7} \div \frac{11}{2} = \frac{4}{7} \times \frac{2}{11}
\]

2. Multiply the numerators and denominators:
\[
\frac{4 \times 2}{7 \times 11} = \frac{8}{77}
\]

Answer: $\boxed{\frac{8}{77}}$

---

Problem 9: $\frac{2}{3} \div \frac{12}{9}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{2}{3} \div \frac{12}{9} = \frac{2}{3} \times \frac{9}{12}
\]

2. Simplify $\frac{9}{12}$ to $\frac{3}{4}$:
\[
\frac{2}{3} \times \frac{3}{4}
\]

3. Multiply the numerators and denominators:
\[
\frac{2 \times 3}{3 \times 4} = \frac{6}{12}
\]

4. Simplify the fraction:
\[
\frac{6}{12} = \frac{1}{2}
\]

Answer: $\boxed{\frac{1}{2}}$

---

Problem 10: $\frac{5}{3} \div \frac{6}{5}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{5}{3} \div \frac{6}{5} = \frac{5}{3} \times \frac{5}{6}
\]

2. Multiply the numerators and denominators:
\[
\frac{5 \times 5}{3 \times 6} = \frac{25}{18}
\]

Answer: $\boxed{\frac{25}{18}}$

---

Problem 11: $\frac{1}{8} \div \frac{16}{2}$

1. Rewrite the division as multiplication by the reciprocal:
\[
\frac{1}{8} \div \frac{16}{2} = \frac{1}{8} \times \frac{2}{16}
\]

2. Simplify $\frac{2}{16}$ to $\frac{1}{8}$:
\[
\frac{1}{8} \times \frac{1}{8}
\]

3. Multiply the numerators and denominators:
\[
\frac{1 \times 1}{8 \times 8} = \frac{1}{64}
\]

Answer: $\boxed{\frac{1}{64}}$

---

Final Answers:

\[
\boxed{8, \frac{3}{7}, \frac{3}{8}, \frac{1}{24}, \frac{3}{2}, 3, 16, \frac{8}{77}, \frac{1}{2}, \frac{25}{18}, \frac{1}{64}}
\]