Dividing Fractions worksheet with 20 practice problems for students to solve.
A worksheet titled "Dividing Fractions" with 20 problems requiring the division of fractions, presented by Math Monks.
JPG
742×1050
75 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #740204
⭐
Show Answer Key & Explanations
Step-by-step solution for: Dividing Fractions Worksheets with Answer Key
▼
Show Answer Key & Explanations
Step-by-step solution for: Dividing Fractions Worksheets with Answer Key
Let's solve each of these fraction division problems step by step.
To divide fractions, we use the rule:
> $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
That is, multiply by the reciprocal of the second fraction.
---
$$
= \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}
$$
---
First simplify $\frac{9}{6} = \frac{3}{2}$
$$
= \frac{2}{3} \div \frac{3}{2} = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9}
$$
---
Simplify $\frac{6}{4} = \frac{3}{2}$
$$
= \frac{5}{8} \div \frac{3}{2} = \frac{5}{8} \times \frac{2}{3} = \frac{10}{24} = \frac{5}{12}
$$
---
Simplify $\frac{9}{12} = \frac{3}{4}$
$$
= \frac{3}{4} \div \frac{7}{3} = \frac{3}{4} \times \frac{3}{7} = \frac{9}{28}
$$
---
$$
= \frac{5}{9} \times \frac{4}{3} = \frac{20}{27}
$$
---
$$
= \frac{6}{5} \times \frac{10}{7} = \frac{60}{35} = \frac{12}{7} = 1\frac{5}{7}
$$
---
Simplify $\frac{4}{6} = \frac{2}{3}$
$$
= \frac{7}{9} \div \frac{2}{3} = \frac{7}{9} \times \frac{3}{2} = \frac{21}{18} = \frac{7}{6} = 1\frac{1}{6}
$$
---
$$
= \frac{14}{9} \times \frac{6}{7} = \frac{84}{63} = \frac{4}{3} = 1\frac{1}{3}
$$
---
$$
= \frac{3}{4} \times \frac{4}{1} = \frac{12}{4} = 3
$$
---
$$
= \frac{15}{4} \times \frac{4}{3} = \frac{60}{12} = 5
$$
---
$$
= \frac{16}{7} \times \frac{7}{4} = \frac{112}{28} = 4
$$
---
$$
= \frac{3}{2} \times \frac{9}{2} = \frac{27}{4} = 6\frac{3}{4}
$$
---
Simplify $\frac{6}{8} = \frac{3}{4}$
$$
= \frac{1}{9} \div \frac{3}{4} = \frac{1}{9} \times \frac{4}{3} = \frac{4}{27}
$$
---
$$
= \frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3}
$$
---
$$
= \frac{2}{3} \times \frac{5}{1} = \frac{10}{3} = 3\frac{1}{3}
$$
---
Simplify $\frac{4}{2} = 2$
$$
= 2 \div \frac{10}{3} = 2 \times \frac{3}{10} = \frac{6}{10} = \frac{3}{5}
$$
---
$$
= \frac{5}{12} \times \frac{4}{1} = \frac{20}{12} = \frac{5}{3} = 1\frac{2}{3}
$$
---
$$
= \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}
$$
---
$$
= \frac{5}{2} \times \frac{7}{2} = \frac{35}{4} = 8\frac{3}{4}
$$
---
$$
= \frac{7}{8} \times \frac{3}{7} = \frac{21}{56} = \frac{3}{8}
$$
---
1. $\frac{2}{3}$
2. $\frac{4}{9}$
3. $\frac{5}{12}$
4. $\frac{9}{28}$
5. $\frac{20}{27}$
6. $\frac{12}{7}$ or $1\frac{5}{7}$
7. $\frac{7}{6}$ or $1\frac{1}{6}$
8. $\frac{4}{3}$ or $1\frac{1}{3}$
9. $3$
10. $5$
11. $4$
12. $\frac{27}{4}$ or $6\frac{3}{4}$
13. $\frac{4}{27}$
14. $\frac{2}{3}$
15. $\frac{10}{3}$ or $3\frac{1}{3}$
16. $\frac{3}{5}$
17. $\frac{5}{3}$ or $1\frac{2}{3}$
18. $\frac{6}{5}$ or $1\frac{1}{5}$
19. $\frac{35}{4}$ or $8\frac{3}{4}$
20. $\frac{3}{8}$
Let me know if you'd like this in a printable format or with steps shown differently!
To divide fractions, we use the rule:
> $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
That is, multiply by the reciprocal of the second fraction.
---
1. $\frac{1}{2} \div \frac{3}{4}$
$$
= \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}
$$
---
2. $\frac{2}{3} \div \frac{9}{6}$
First simplify $\frac{9}{6} = \frac{3}{2}$
$$
= \frac{2}{3} \div \frac{3}{2} = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9}
$$
---
3. $\frac{5}{8} \div \frac{6}{4}$
Simplify $\frac{6}{4} = \frac{3}{2}$
$$
= \frac{5}{8} \div \frac{3}{2} = \frac{5}{8} \times \frac{2}{3} = \frac{10}{24} = \frac{5}{12}
$$
---
4. $\frac{9}{12} \div \frac{7}{3}$
Simplify $\frac{9}{12} = \frac{3}{4}$
$$
= \frac{3}{4} \div \frac{7}{3} = \frac{3}{4} \times \frac{3}{7} = \frac{9}{28}
$$
---
5. $\frac{5}{9} \div \frac{3}{4}$
$$
= \frac{5}{9} \times \frac{4}{3} = \frac{20}{27}
$$
---
6. $\frac{6}{5} \div \frac{7}{10}$
$$
= \frac{6}{5} \times \frac{10}{7} = \frac{60}{35} = \frac{12}{7} = 1\frac{5}{7}
$$
---
7. $\frac{7}{9} \div \frac{4}{6}$
Simplify $\frac{4}{6} = \frac{2}{3}$
$$
= \frac{7}{9} \div \frac{2}{3} = \frac{7}{9} \times \frac{3}{2} = \frac{21}{18} = \frac{7}{6} = 1\frac{1}{6}
$$
---
8. $\frac{14}{9} \div \frac{7}{6}$
$$
= \frac{14}{9} \times \frac{6}{7} = \frac{84}{63} = \frac{4}{3} = 1\frac{1}{3}
$$
---
9. $\frac{3}{4} \div \frac{1}{4}$
$$
= \frac{3}{4} \times \frac{4}{1} = \frac{12}{4} = 3
$$
---
10. $\frac{15}{4} \div \frac{3}{4}$
$$
= \frac{15}{4} \times \frac{4}{3} = \frac{60}{12} = 5
$$
---
11. $\frac{16}{7} \div \frac{4}{7}$
$$
= \frac{16}{7} \times \frac{7}{4} = \frac{112}{28} = 4
$$
---
12. $\frac{3}{2} \div \frac{2}{9}$
$$
= \frac{3}{2} \times \frac{9}{2} = \frac{27}{4} = 6\frac{3}{4}
$$
---
13. $\frac{1}{9} \div \frac{6}{8}$
Simplify $\frac{6}{8} = \frac{3}{4}$
$$
= \frac{1}{9} \div \frac{3}{4} = \frac{1}{9} \times \frac{4}{3} = \frac{4}{27}
$$
---
14. $\frac{3}{5} \div \frac{9}{10}$
$$
= \frac{3}{5} \times \frac{10}{9} = \frac{30}{45} = \frac{2}{3}
$$
---
15. $\frac{2}{3} \div \frac{1}{5}$
$$
= \frac{2}{3} \times \frac{5}{1} = \frac{10}{3} = 3\frac{1}{3}
$$
---
16. $\frac{4}{2} \div \frac{10}{3}$
Simplify $\frac{4}{2} = 2$
$$
= 2 \div \frac{10}{3} = 2 \times \frac{3}{10} = \frac{6}{10} = \frac{3}{5}
$$
---
17. $\frac{5}{12} \div \frac{1}{4}$
$$
= \frac{5}{12} \times \frac{4}{1} = \frac{20}{12} = \frac{5}{3} = 1\frac{2}{3}
$$
---
18. $\frac{4}{5} \div \frac{2}{3}$
$$
= \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}
$$
---
19. $\frac{5}{2} \div \frac{2}{7}$
$$
= \frac{5}{2} \times \frac{7}{2} = \frac{35}{4} = 8\frac{3}{4}
$$
---
20. $\frac{7}{8} \div \frac{7}{3}$
$$
= \frac{7}{8} \times \frac{3}{7} = \frac{21}{56} = \frac{3}{8}
$$
---
✔ Final Answers:
1. $\frac{2}{3}$
2. $\frac{4}{9}$
3. $\frac{5}{12}$
4. $\frac{9}{28}$
5. $\frac{20}{27}$
6. $\frac{12}{7}$ or $1\frac{5}{7}$
7. $\frac{7}{6}$ or $1\frac{1}{6}$
8. $\frac{4}{3}$ or $1\frac{1}{3}$
9. $3$
10. $5$
11. $4$
12. $\frac{27}{4}$ or $6\frac{3}{4}$
13. $\frac{4}{27}$
14. $\frac{2}{3}$
15. $\frac{10}{3}$ or $3\frac{1}{3}$
16. $\frac{3}{5}$
17. $\frac{5}{3}$ or $1\frac{2}{3}$
18. $\frac{6}{5}$ or $1\frac{1}{5}$
19. $\frac{35}{4}$ or $8\frac{3}{4}$
20. $\frac{3}{8}$
Let me know if you'd like this in a printable format or with steps shown differently!
Parent Tip: Review the logic above to help your child master the concept of divide fraction worksheet.
