Let's solve each of these fraction division problems step by step. The rule for dividing fractions is:
>
To divide by a fraction, multiply by its reciprocal.
That is:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$
---
1. $\frac{1}{3} \div \frac{7}{9}$
$$
= \frac{1}{3} \times \frac{9}{7} = \frac{9}{21} = \frac{3}{7}
$$
✔ Answer: $\boxed{\frac{3}{7}}$
---
2. $\frac{1}{2} \div \frac{5}{6}$
$$
= \frac{1}{2} \times \frac{6}{5} = \frac{6}{10} = \frac{3}{5}
$$
✔ Answer: $\boxed{\frac{3}{5}}$
---
3. $\frac{6}{9} \div \frac{1}{10}$
First simplify $\frac{6}{9} = \frac{2}{3}$
$$
= \frac{2}{3} \div \frac{1}{10} = \frac{2}{3} \times \frac{10}{1} = \frac{20}{3} = 6\frac{2}{3}
$$
✔ Answer: $\boxed{\frac{20}{3}}$ or $6\frac{2}{3}$
---
4. $\frac{1}{3} \div \frac{1}{2}$
$$
= \frac{1}{3} \times \frac{2}{1} = \frac{2}{3}
$$
✔ Answer: $\boxed{\frac{2}{3}}$
---
5. $\frac{4}{10} \div \frac{1}{3}$
Simplify $\frac{4}{10} = \frac{2}{5}$
$$
= \frac{2}{5} \times \frac{3}{1} = \frac{6}{5} = 1\frac{1}{5}
$$
✔ Answer: $\boxed{\frac{6}{5}}$ or $1\frac{1}{5}$
---
6. $\frac{3}{6} \div \frac{2}{3}$
Simplify $\frac{3}{6} = \frac{1}{2}$
$$
= \frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}
$$
✔ Answer: $\boxed{\frac{3}{4}}$
---
7. $\frac{9}{10} \div \frac{2}{6}$
Simplify $\frac{2}{6} = \frac{1}{3}$
$$
= \frac{9}{10} \div \frac{1}{3} = \frac{9}{10} \times \frac{3}{1} = \frac{27}{10} = 2\frac{7}{10}
$$
✔ Answer: $\boxed{\frac{27}{10}}$ or $2\frac{7}{10}$
---
8. $\frac{7}{10} \div \frac{1}{3}$
$$
= \frac{7}{10} \times \frac{3}{1} = \frac{21}{10} = 2\frac{1}{10}
$$
✔ Answer: $\boxed{\frac{21}{10}}$ or $2\frac{1}{10}$
---
9. $\frac{1}{4} \div \frac{4}{8}$
Simplify $\frac{4}{8} = \frac{1}{2}$
$$
= \frac{1}{4} \div \frac{1}{2} = \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2}
$$
✔ Answer: $\boxed{\frac{1}{2}}$
---
10. $\frac{1}{5} \div \frac{10}{11}$
$$
= \frac{1}{5} \times \frac{11}{10} = \frac{11}{50}
$$
✔ Answer: $\boxed{\frac{11}{50}}$
---
11. $\frac{3}{4} \div \frac{2}{5}$
$$
= \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}
$$
✔ Answer: $\boxed{\frac{15}{8}}$ or $1\frac{7}{8}$
---
12. $\frac{4}{5} \div \frac{3}{6}$
Simplify $\frac{3}{6} = \frac{1}{2}$
$$
= \frac{4}{5} \div \frac{1}{2} = \frac{4}{5} \times \frac{2}{1} = \frac{8}{5} = 1\frac{3}{5}
$$
✔ Answer: $\boxed{\frac{8}{5}}$ or $1\frac{3}{5}$
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✔ Final Answers:
1. $\frac{3}{7}$
2. $\frac{3}{5}$
3. $\frac{20}{3}$ (or $6\frac{2}{3}$)
4. $\frac{2}{3}$
5. $\frac{6}{5}$ (or $1\frac{1}{5}$)
6. $\frac{3}{4}$
7. $\frac{27}{10}$ (or $2\frac{7}{10}$)
8. $\frac{21}{10}$ (or $2\frac{1}{10}$)
9. $\frac{1}{2}$
10. $\frac{11}{50}$
11. $\frac{15}{8}$ (or $1\frac{7}{8}$)
12. $\frac{8}{5}$ (or $1\frac{3}{5}$)
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of division of fractions worksheet 6th grade.
