Dividing Fractions worksheet with 20 problems for practicing fraction division.
Worksheet titled "Dividing Fractions (A)" with 20 fraction division problems, including instructions to calculate each quotient and spaces for name, date, and score.
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Step-by-step solution for: Dividing Two Proper Fractions with No Simplification (Fillable) (A)
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Show Answer Key & Explanations
Step-by-step solution for: Dividing Two Proper Fractions with No Simplification (Fillable) (A)
Let's solve the problem step by step.
The task is to divide fractions. The rule for dividing fractions is:
> To divide two fractions, multiply the first fraction by the reciprocal (inverse) of the second fraction.
That is:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$
We'll go through each problem and apply this rule.
---
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{1}{4} \times \frac{3}{2} = \frac{3}{8}$
✔ Answer: $\frac{1}{4} \times \frac{3}{2} = \frac{3}{8}$
---
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{1}{8} \times \frac{3}{2} = \frac{3}{16}$
✔ Answer: $\frac{1}{8} \times \frac{3}{2} = \frac{3}{16}$
---
- Invert $\frac{4}{9}$ → $\frac{9}{4}$
- Multiply: $\frac{1}{5} \times \frac{9}{4} = \frac{9}{20}$
✔ Answer: $\frac{1}{5} \times \frac{9}{4} = \frac{9}{20}$
---
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{3}{8} \times \frac{3}{2} = \frac{9}{16}$
✔ Answer: $\frac{3}{8} \times \frac{3}{2} = \frac{9}{16}$
---
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{3}{7} \times \frac{3}{2} = \frac{9}{14}$
✔ Answer: $\frac{3}{7} \times \frac{3}{2} = \frac{9}{14}$
---
- Invert $\frac{8}{9}$ → $\frac{9}{8}$
- Multiply: $\frac{3}{4} \times \frac{9}{8} = \frac{27}{32}$
✔ Answer: $\frac{3}{4} \times \frac{9}{8} = \frac{27}{32}$
---
- Invert $\frac{1}{2}$ → $\frac{2}{1}$
- Multiply: $\frac{1}{3} \times \frac{2}{1} = \frac{2}{3}$
✔ Answer: $\frac{1}{3} \times \frac{2}{1} = \frac{2}{3}$
---
- Invert $\frac{3}{4}$ → $\frac{4}{3}$
- Multiply: $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$
✔ Answer: $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$
---
- Invert $\frac{5}{7}$ → $\frac{7}{5}$
- Multiply: $\frac{1}{3} \times \frac{7}{5} = \frac{7}{15}$
✔ Answer: $\frac{1}{3} \times \frac{7}{5} = \frac{7}{15}$
---
- Invert $\frac{1}{2}$ → $\frac{2}{1}$
- Multiply: $\frac{2}{9} \times \frac{2}{1} = \frac{4}{9}$
✔ Answer: $\frac{2}{9} \times \frac{2}{1} = \frac{4}{9}$
---
- Invert $\frac{6}{7}$ → $\frac{7}{6}$
- Multiply: $\frac{5}{6} \times \frac{7}{6} = \frac{35}{36}$
✔ Answer: $\frac{5}{6} \times \frac{7}{6} = \frac{35}{36}$
---
- Invert $\frac{4}{5}$ → $\frac{5}{4}$
- Multiply: $\frac{1}{4} \times \frac{5}{4} = \frac{5}{16}$
✔ Answer: $\frac{1}{4} \times \frac{5}{4} = \frac{5}{16}$
---
- Invert $\frac{2}{5}$ → $\frac{5}{2}$
- Multiply: $\frac{1}{8} \times \frac{5}{2} = \frac{5}{16}$
✔ Answer: $\frac{1}{8} \times \frac{5}{2} = \frac{5}{16}$
---
- Invert $\frac{5}{7}$ → $\frac{7}{5}$
- Multiply: $\frac{1}{2} \times \frac{7}{5} = \frac{7}{10}$
✔ Answer: $\frac{1}{2} \times \frac{7}{5} = \frac{7}{10}$
---
- Invert $\frac{1}{5}$ → $\frac{5}{1}$
- Multiply: $\frac{1}{7} \times \frac{5}{1} = \frac{5}{7}$
✔ Answer: $\frac{1}{7} \times \frac{5}{1} = \frac{5}{7}$
---
- Invert $\frac{3}{5}$ → $\frac{5}{3}$
- Multiply: $\frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$
✔ Answer: $\frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$
---
- Invert $\frac{2}{7}$ → $\frac{7}{2}$
- Multiply: $\frac{1}{4} \times \frac{7}{2} = \frac{7}{8}$
✔ Answer: $\frac{1}{4} \times \frac{7}{2} = \frac{7}{8}$
---
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{1}{5} \times \frac{3}{2} = \frac{3}{10}$
✔ Answer: $\frac{1}{5} \times \frac{3}{2} = \frac{3}{10}$
---
- Invert $\frac{7}{8}$ → $\frac{8}{7}$
- Multiply: $\frac{6}{7} \times \frac{8}{7} = \frac{48}{49}$
✔ Answer: $\frac{6}{7} \times \frac{8}{7} = \frac{48}{49}$
---
- Invert $\frac{1}{4}$ → $\frac{4}{1}$
- Multiply: $\frac{1}{5} \times \frac{4}{1} = \frac{4}{5}$
✔ Answer: $\frac{1}{5} \times \frac{4}{1} = \frac{4}{5}$
---
## ✔ Final Answers (Formatted):
| Problem | Inversion | Result |
|--------|-----------|--------|
| 1. $\frac{1}{4} \div \frac{2}{3}$ | $\frac{1}{4} \times \frac{3}{2}$ | $\frac{3}{8}$ |
| 2. $\frac{1}{8} \div \frac{2}{3}$ | $\frac{1}{8} \times \frac{3}{2}$ | $\frac{3}{16}$ |
| 3. $\frac{1}{5} \div \frac{4}{9}$ | $\frac{1}{5} \times \frac{9}{4}$ | $\frac{9}{20}$ |
| 4. $\frac{3}{8} \div \frac{2}{3}$ | $\frac{3}{8} \times \frac{3}{2}$ | $\frac{9}{16}$ |
| 5. $\frac{3}{7} \div \frac{2}{3}$ | $\frac{3}{7} \times \frac{3}{2}$ | $\frac{9}{14}$ |
| 6. $\frac{3}{4} \div \frac{8}{9}$ | $\frac{3}{4} \times \frac{9}{8}$ | $\frac{27}{32}$ |
| 7. $\frac{1}{3} \div \frac{1}{2}$ | $\frac{1}{3} \times \frac{2}{1}$ | $\frac{2}{3}$ |
| 8. $\frac{2}{3} \div \frac{3}{4}$ | $\frac{2}{3} \times \frac{4}{3}$ | $\frac{8}{9}$ |
| 9. $\frac{1}{3} \div \frac{5}{7}$ | $\frac{1}{3} \times \frac{7}{5}$ | $\frac{7}{15}$ |
| 10. $\frac{2}{9} \div \frac{1}{2}$ | $\frac{2}{9} \times \frac{2}{1}$ | $\frac{4}{9}$ |
| 11. $\frac{5}{6} \div \frac{6}{7}$ | $\frac{5}{6} \times \frac{7}{6}$ | $\frac{35}{36}$ |
| 12. $\frac{1}{4} \div \frac{4}{5}$ | $\frac{1}{4} \times \frac{5}{4}$ | $\frac{5}{16}$ |
| 13. $\frac{1}{8} \div \frac{2}{5}$ | $\frac{1}{8} \times \frac{5}{2}$ | $\frac{5}{16}$ |
| 14. $\frac{1}{2} \div \frac{5}{7}$ | $\frac{1}{2} \times \frac{7}{5}$ | $\frac{7}{10}$ |
| 15. $\frac{1}{7} \div \frac{1}{5}$ | $\frac{1}{7} \times \frac{5}{1}$ | $\frac{5}{7}$ |
| 16. $\frac{1}{2} \div \frac{3}{5}$ | $\frac{1}{2} \times \frac{5}{3}$ | $\frac{5}{6}$ |
| 17. $\frac{1}{4} \div \frac{2}{7}$ | $\frac{1}{4} \times \frac{7}{2}$ | $\frac{7}{8}$ |
| 18. $\frac{1}{5} \div \frac{2}{3}$ | $\frac{1}{5} \times \frac{3}{2}$ | $\frac{3}{10}$ |
| 19. $\frac{6}{7} \div \frac{7}{8}$ | $\frac{6}{7} \times \frac{8}{7}$ | $\frac{48}{49}$ |
| 20. $\frac{1}{5} \div \frac{1}{4}$ | $\frac{1}{5} \times \frac{4}{1}$ | $\frac{4}{5}$ |
---
To divide fractions:
1. Keep the first fraction.
2. Change the division to multiplication.
3. Flip (invert) the second fraction.
4. Multiply numerators and denominators.
5. Simplify if needed.
All answers are already in simplest form.
Let me know if you'd like a printable version or explanation with visuals!
The task is to divide fractions. The rule for dividing fractions is:
> To divide two fractions, multiply the first fraction by the reciprocal (inverse) of the second fraction.
That is:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$
We'll go through each problem and apply this rule.
---
1. $\frac{1}{4} \div \frac{2}{3}$
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{1}{4} \times \frac{3}{2} = \frac{3}{8}$
✔ Answer: $\frac{1}{4} \times \frac{3}{2} = \frac{3}{8}$
---
2. $\frac{1}{8} \div \frac{2}{3}$
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{1}{8} \times \frac{3}{2} = \frac{3}{16}$
✔ Answer: $\frac{1}{8} \times \frac{3}{2} = \frac{3}{16}$
---
3. $\frac{1}{5} \div \frac{4}{9}$
- Invert $\frac{4}{9}$ → $\frac{9}{4}$
- Multiply: $\frac{1}{5} \times \frac{9}{4} = \frac{9}{20}$
✔ Answer: $\frac{1}{5} \times \frac{9}{4} = \frac{9}{20}$
---
4. $\frac{3}{8} \div \frac{2}{3}$
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{3}{8} \times \frac{3}{2} = \frac{9}{16}$
✔ Answer: $\frac{3}{8} \times \frac{3}{2} = \frac{9}{16}$
---
5. $\frac{3}{7} \div \frac{2}{3}$
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{3}{7} \times \frac{3}{2} = \frac{9}{14}$
✔ Answer: $\frac{3}{7} \times \frac{3}{2} = \frac{9}{14}$
---
6. $\frac{3}{4} \div \frac{8}{9}$
- Invert $\frac{8}{9}$ → $\frac{9}{8}$
- Multiply: $\frac{3}{4} \times \frac{9}{8} = \frac{27}{32}$
✔ Answer: $\frac{3}{4} \times \frac{9}{8} = \frac{27}{32}$
---
7. $\frac{1}{3} \div \frac{1}{2}$
- Invert $\frac{1}{2}$ → $\frac{2}{1}$
- Multiply: $\frac{1}{3} \times \frac{2}{1} = \frac{2}{3}$
✔ Answer: $\frac{1}{3} \times \frac{2}{1} = \frac{2}{3}$
---
8. $\frac{2}{3} \div \frac{3}{4}$
- Invert $\frac{3}{4}$ → $\frac{4}{3}$
- Multiply: $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$
✔ Answer: $\frac{2}{3} \times \frac{4}{3} = \frac{8}{9}$
---
9. $\frac{1}{3} \div \frac{5}{7}$
- Invert $\frac{5}{7}$ → $\frac{7}{5}$
- Multiply: $\frac{1}{3} \times \frac{7}{5} = \frac{7}{15}$
✔ Answer: $\frac{1}{3} \times \frac{7}{5} = \frac{7}{15}$
---
10. $\frac{2}{9} \div \frac{1}{2}$
- Invert $\frac{1}{2}$ → $\frac{2}{1}$
- Multiply: $\frac{2}{9} \times \frac{2}{1} = \frac{4}{9}$
✔ Answer: $\frac{2}{9} \times \frac{2}{1} = \frac{4}{9}$
---
11. $\frac{5}{6} \div \frac{6}{7}$
- Invert $\frac{6}{7}$ → $\frac{7}{6}$
- Multiply: $\frac{5}{6} \times \frac{7}{6} = \frac{35}{36}$
✔ Answer: $\frac{5}{6} \times \frac{7}{6} = \frac{35}{36}$
---
12. $\frac{1}{4} \div \frac{4}{5}$
- Invert $\frac{4}{5}$ → $\frac{5}{4}$
- Multiply: $\frac{1}{4} \times \frac{5}{4} = \frac{5}{16}$
✔ Answer: $\frac{1}{4} \times \frac{5}{4} = \frac{5}{16}$
---
13. $\frac{1}{8} \div \frac{2}{5}$
- Invert $\frac{2}{5}$ → $\frac{5}{2}$
- Multiply: $\frac{1}{8} \times \frac{5}{2} = \frac{5}{16}$
✔ Answer: $\frac{1}{8} \times \frac{5}{2} = \frac{5}{16}$
---
14. $\frac{1}{2} \div \frac{5}{7}$
- Invert $\frac{5}{7}$ → $\frac{7}{5}$
- Multiply: $\frac{1}{2} \times \frac{7}{5} = \frac{7}{10}$
✔ Answer: $\frac{1}{2} \times \frac{7}{5} = \frac{7}{10}$
---
15. $\frac{1}{7} \div \frac{1}{5}$
- Invert $\frac{1}{5}$ → $\frac{5}{1}$
- Multiply: $\frac{1}{7} \times \frac{5}{1} = \frac{5}{7}$
✔ Answer: $\frac{1}{7} \times \frac{5}{1} = \frac{5}{7}$
---
16. $\frac{1}{2} \div \frac{3}{5}$
- Invert $\frac{3}{5}$ → $\frac{5}{3}$
- Multiply: $\frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$
✔ Answer: $\frac{1}{2} \times \frac{5}{3} = \frac{5}{6}$
---
17. $\frac{1}{4} \div \frac{2}{7}$
- Invert $\frac{2}{7}$ → $\frac{7}{2}$
- Multiply: $\frac{1}{4} \times \frac{7}{2} = \frac{7}{8}$
✔ Answer: $\frac{1}{4} \times \frac{7}{2} = \frac{7}{8}$
---
18. $\frac{1}{5} \div \frac{2}{3}$
- Invert $\frac{2}{3}$ → $\frac{3}{2}$
- Multiply: $\frac{1}{5} \times \frac{3}{2} = \frac{3}{10}$
✔ Answer: $\frac{1}{5} \times \frac{3}{2} = \frac{3}{10}$
---
19. $\frac{6}{7} \div \frac{7}{8}$
- Invert $\frac{7}{8}$ → $\frac{8}{7}$
- Multiply: $\frac{6}{7} \times \frac{8}{7} = \frac{48}{49}$
✔ Answer: $\frac{6}{7} \times \frac{8}{7} = \frac{48}{49}$
---
20. $\frac{1}{5} \div \frac{1}{4}$
- Invert $\frac{1}{4}$ → $\frac{4}{1}$
- Multiply: $\frac{1}{5} \times \frac{4}{1} = \frac{4}{5}$
✔ Answer: $\frac{1}{5} \times \frac{4}{1} = \frac{4}{5}$
---
## ✔ Final Answers (Formatted):
| Problem | Inversion | Result |
|--------|-----------|--------|
| 1. $\frac{1}{4} \div \frac{2}{3}$ | $\frac{1}{4} \times \frac{3}{2}$ | $\frac{3}{8}$ |
| 2. $\frac{1}{8} \div \frac{2}{3}$ | $\frac{1}{8} \times \frac{3}{2}$ | $\frac{3}{16}$ |
| 3. $\frac{1}{5} \div \frac{4}{9}$ | $\frac{1}{5} \times \frac{9}{4}$ | $\frac{9}{20}$ |
| 4. $\frac{3}{8} \div \frac{2}{3}$ | $\frac{3}{8} \times \frac{3}{2}$ | $\frac{9}{16}$ |
| 5. $\frac{3}{7} \div \frac{2}{3}$ | $\frac{3}{7} \times \frac{3}{2}$ | $\frac{9}{14}$ |
| 6. $\frac{3}{4} \div \frac{8}{9}$ | $\frac{3}{4} \times \frac{9}{8}$ | $\frac{27}{32}$ |
| 7. $\frac{1}{3} \div \frac{1}{2}$ | $\frac{1}{3} \times \frac{2}{1}$ | $\frac{2}{3}$ |
| 8. $\frac{2}{3} \div \frac{3}{4}$ | $\frac{2}{3} \times \frac{4}{3}$ | $\frac{8}{9}$ |
| 9. $\frac{1}{3} \div \frac{5}{7}$ | $\frac{1}{3} \times \frac{7}{5}$ | $\frac{7}{15}$ |
| 10. $\frac{2}{9} \div \frac{1}{2}$ | $\frac{2}{9} \times \frac{2}{1}$ | $\frac{4}{9}$ |
| 11. $\frac{5}{6} \div \frac{6}{7}$ | $\frac{5}{6} \times \frac{7}{6}$ | $\frac{35}{36}$ |
| 12. $\frac{1}{4} \div \frac{4}{5}$ | $\frac{1}{4} \times \frac{5}{4}$ | $\frac{5}{16}$ |
| 13. $\frac{1}{8} \div \frac{2}{5}$ | $\frac{1}{8} \times \frac{5}{2}$ | $\frac{5}{16}$ |
| 14. $\frac{1}{2} \div \frac{5}{7}$ | $\frac{1}{2} \times \frac{7}{5}$ | $\frac{7}{10}$ |
| 15. $\frac{1}{7} \div \frac{1}{5}$ | $\frac{1}{7} \times \frac{5}{1}$ | $\frac{5}{7}$ |
| 16. $\frac{1}{2} \div \frac{3}{5}$ | $\frac{1}{2} \times \frac{5}{3}$ | $\frac{5}{6}$ |
| 17. $\frac{1}{4} \div \frac{2}{7}$ | $\frac{1}{4} \times \frac{7}{2}$ | $\frac{7}{8}$ |
| 18. $\frac{1}{5} \div \frac{2}{3}$ | $\frac{1}{5} \times \frac{3}{2}$ | $\frac{3}{10}$ |
| 19. $\frac{6}{7} \div \frac{7}{8}$ | $\frac{6}{7} \times \frac{8}{7}$ | $\frac{48}{49}$ |
| 20. $\frac{1}{5} \div \frac{1}{4}$ | $\frac{1}{5} \times \frac{4}{1}$ | $\frac{4}{5}$ |
---
📝 Summary:
To divide fractions:
1. Keep the first fraction.
2. Change the division to multiplication.
3. Flip (invert) the second fraction.
4. Multiply numerators and denominators.
5. Simplify if needed.
All answers are already in simplest form.
Let me know if you'd like a printable version or explanation with visuals!
Parent Tip: Review the logic above to help your child master the concept of worksheet on dividing fractions.
