Let's solve each of the fraction division problems step by step.
To divide fractions, we follow this rule:
>
Divide by multiplying by the reciprocal.
> That is:
> $$
> \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
> $$
We'll apply this rule to each problem.
---
1. $ \frac{4}{5} \div \frac{3}{4} $
$$
= \frac{4}{5} \times \frac{4}{3} = \frac{16}{15}
$$
✔ Answer: $ \frac{16}{15} $ or $ 1\frac{1}{15} $
---
2. $ \frac{5}{2} \div \frac{2}{3} $
$$
= \frac{5}{2} \times \frac{3}{2} = \frac{15}{4}
$$
✔ Answer: $ \frac{15}{4} $ or $ 3\frac{3}{4} $
---
3. $ \frac{6}{5} \div \frac{1}{2} $
$$
= \frac{6}{5} \times \frac{2}{1} = \frac{12}{5}
$$
✔ Answer: $ \frac{12}{5} $ or $ 2\frac{2}{5} $
---
4. $ \frac{3}{7} \div \frac{3}{5} $
$$
= \frac{3}{7} \times \frac{5}{3} = \frac{15}{21} = \frac{5}{7}
$$
✔ Answer: $ \frac{5}{7} $
---
5. $ \frac{3}{5} \div \frac{4}{7} $
$$
= \frac{3}{5} \times \frac{7}{4} = \frac{21}{20}
$$
✔ Answer: $ \frac{21}{20} $ or $ 1\frac{1}{20} $
---
6. $ \frac{1}{8} \div \frac{4}{5} $
$$
= \frac{1}{8} \times \frac{5}{4} = \frac{5}{32}
$$
✔ Answer: $ \frac{5}{32} $
---
7. $ \frac{1}{4} \div \frac{1}{5} $
$$
= \frac{1}{4} \times \frac{5}{1} = \frac{5}{4}
$$
✔ Answer: $ \frac{5}{4} $ or $ 1\frac{1}{4} $
---
8. $ \frac{7}{10} \div \frac{5}{7} $
$$
= \frac{7}{10} \times \frac{7}{5} = \frac{49}{50}
$$
✔ Answer: $ \frac{49}{50} $
---
9. $ \frac{2}{9} \div \frac{1}{6} $
$$
= \frac{2}{9} \times \frac{6}{1} = \frac{12}{9} = \frac{4}{3}
$$
✔ Answer: $ \frac{4}{3} $ or $ 1\frac{1}{3} $
---
10. $ \frac{3}{6} \div \frac{1}{3} $
First simplify $ \frac{3}{6} = \frac{1}{2} $
$$
= \frac{1}{2} \div \frac{1}{3} = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2}
$$
✔ Answer: $ \frac{3}{2} $ or $ 1\frac{1}{2} $
---
11. $ \frac{5}{6} \div \frac{2}{7} $
$$
= \frac{5}{6} \times \frac{7}{2} = \frac{35}{12}
$$
✔ Answer: $ \frac{35}{12} $ or $ 2\frac{11}{12} $
---
12. $ \frac{2}{9} \div \frac{1}{8} $
$$
= \frac{2}{9} \times \frac{8}{1} = \frac{16}{9}
$$
✔ Answer: $ \frac{16}{9} $ or $ 1\frac{7}{9} $
---
13. $ \frac{4}{7} \div \frac{1}{3} $
$$
= \frac{4}{7} \times \frac{3}{1} = \frac{12}{7}
$$
✔ Answer: $ \frac{12}{7} $ or $ 1\frac{5}{7} $
---
14. $ \frac{1}{2} \div \frac{4}{7} $
$$
= \frac{1}{2} \times \frac{7}{4} = \frac{7}{8}
$$
✔ Answer: $ \frac{7}{8} $
---
✔ Final Answers:
1. $ \frac{16}{15} $
2. $ \frac{15}{4} $
3. $ \frac{12}{5} $
4. $ \frac{5}{7} $
5. $ \frac{21}{20} $
6. $ \frac{5}{32} $
7. $ \frac{5}{4} $
8. $ \frac{49}{50} $
9. $ \frac{4}{3} $
10. $ \frac{3}{2} $
11. $ \frac{35}{12} $
12. $ \frac{16}{9} $
13. $ \frac{12}{7} $
14. $ \frac{7}{8} $
You can write them as
improper fractions or
mixed numbers, depending on preference.
Let me know if you'd like these in mixed number form!
Parent Tip: Review the logic above to help your child master the concept of multiplying fractions worksheet 7th grade.
