Worksheet featuring 15 problems on dividing fractions, designed for math practice.
Worksheet titled "Dividing Fractions by Fractions" with 15 numbered problems involving division of fractions, presented by Math Monks.
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Step-by-step solution for: Dividing Fractions Worksheets with Answer Key
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Step-by-step solution for: Dividing Fractions Worksheets with Answer Key
To solve these problems, we use the rule for dividing fractions: keep the first fraction, flip the second fraction (take its reciprocal), and multiply.
Let’s go through each problem one by one.
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Problem 1:
$\frac{4}{3} \div \frac{9}{5}$
→ Flip $\frac{9}{5}$ → $\frac{5}{9}$
→ Multiply: $\frac{4}{3} \times \frac{5}{9} = \frac{20}{27}$
✔ Already simplified.
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Problem 2:
$\frac{7}{2} \div \frac{17}{16}$
→ Flip $\frac{17}{16}$ → $\frac{16}{17}$
→ Multiply: $\frac{7}{2} \times \frac{16}{17} = \frac{112}{34}$
Simplify: divide numerator and denominator by 2 → $\frac{56}{17}$
✔ Final answer: $\frac{56}{17}$ or $3\frac{5}{17}$
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Problem 3:
$\frac{20}{9} \div \frac{8}{24}$
First, simplify $\frac{8}{24}$ → $\frac{1}{3}$
Now: $\frac{20}{9} \div \frac{1}{3}$
→ Flip $\frac{1}{3}$ → $\frac{3}{1}$
→ Multiply: $\frac{20}{9} \times 3 = \frac{60}{9} = \frac{20}{3}$
✔ Final answer: $\frac{20}{3}$ or $6\frac{2}{3}$
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Problem 4:
$\frac{1}{4} \div \frac{7}{9}$
→ Flip $\frac{7}{9}$ → $\frac{9}{7}$
→ Multiply: $\frac{1}{4} \times \frac{9}{7} = \frac{9}{28}$
✔ Already simplified.
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Problem 5:
$\frac{6}{5} \div \frac{3}{8}$
→ Flip $\frac{3}{8}$ → $\frac{8}{3}$
→ Multiply: $\frac{6}{5} \times \frac{8}{3} = \frac{48}{15}$
Simplify: divide by 3 → $\frac{16}{5}$
✔ Final answer: $\frac{16}{5}$ or $3\frac{1}{5}$
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Problem 6:
$\frac{1}{3} \div \frac{20}{9}$
→ Flip $\frac{20}{9}$ → $\frac{9}{20}$
→ Multiply: $\frac{1}{3} \times \frac{9}{20} = \frac{9}{60} = \frac{3}{20}$
✔ Simplified.
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Problem 7:
$\frac{11}{10} \div \frac{2}{7}$
→ Flip $\frac{2}{7}$ → $\frac{7}{2}$
→ Multiply: $\frac{11}{10} \times \frac{7}{2} = \frac{77}{20}$
✔ Final answer: $\frac{77}{20}$ or $3\frac{17}{20}$
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Problem 8:
$\frac{4}{15} \div \frac{11}{5}$
→ Flip $\frac{11}{5}$ → $\frac{5}{11}$
→ Multiply: $\frac{4}{15} \times \frac{5}{11} = \frac{20}{165}$
Simplify: divide by 5 → $\frac{4}{33}$
✔ Done.
---
Problem 9:
$\frac{18}{22} \div \frac{3}{7}$
First, simplify $\frac{18}{22}$ → $\frac{9}{11}$
Now: $\frac{9}{11} \div \frac{3}{7}$
→ Flip $\frac{3}{7}$ → $\frac{7}{3}$
→ Multiply: $\frac{9}{11} \times \frac{7}{3} = \frac{63}{33}$
Simplify: divide by 3 → $\frac{21}{11}$
✔ Final answer: $\frac{21}{11}$ or $1\frac{10}{11}$
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Problem 10:
$\frac{10}{6} \div \frac{9}{12}$
Simplify both:
$\frac{10}{6} = \frac{5}{3}$, $\frac{9}{12} = \frac{3}{4}$
Now: $\frac{5}{3} \div \frac{3}{4}$
→ Flip $\frac{3}{4}$ → $\frac{4}{3}$
→ Multiply: $\frac{5}{3} \times \frac{4}{3} = \frac{20}{9}$
✔ Final answer: $\frac{20}{9}$ or $2\frac{2}{9}$
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Problem 11:
$\frac{2}{3} \div \frac{8}{20}$
Simplify $\frac{8}{20}$ → $\frac{2}{5}$
Now: $\frac{2}{3} \div \frac{2}{5}$
→ Flip $\frac{2}{5}$ → $\frac{5}{2}$
→ Multiply: $\frac{2}{3} \times \frac{5}{2} = \frac{10}{6} = \frac{5}{3}$
✔ Final answer: $\frac{5}{3}$ or $1\frac{2}{3}$
---
Problem 12:
$\frac{5}{6} \div \frac{10}{12}$
Simplify $\frac{10}{12}$ → $\frac{5}{6}$
Now: $\frac{5}{6} \div \frac{5}{6}$
→ Flip $\frac{5}{6}$ → $\frac{6}{5}$
→ Multiply: $\frac{5}{6} \times \frac{6}{5} = \frac{30}{30} = 1$
✔ Answer is 1.
---
Problem 13:
$\frac{6}{10} \div \frac{3}{7}$
Simplify $\frac{6}{10}$ → $\frac{3}{5}$
Now: $\frac{3}{5} \div \frac{3}{7}$
→ Flip $\frac{3}{7}$ → $\frac{7}{3}$
→ Multiply: $\frac{3}{5} \times \frac{7}{3} = \frac{21}{15} = \frac{7}{5}$
✔ Final answer: $\frac{7}{5}$ or $1\frac{2}{5}$
---
Problem 14:
$\frac{22}{5} \div \frac{8}{14}$
Simplify $\frac{8}{14}$ → $\frac{4}{7}$
Now: $\frac{22}{5} \div \frac{4}{7}$
→ Flip $\frac{4}{7}$ → $\frac{7}{4}$
→ Multiply: $\frac{22}{5} \times \frac{7}{4} = \frac{154}{20}$
Simplify: divide by 2 → $\frac{77}{10}$
✔ Final answer: $\frac{77}{10}$ or $7\frac{7}{10}$
---
Problem 15:
$\frac{7}{5} \div \frac{21}{9}$
Simplify $\frac{21}{9}$ → $\frac{7}{3}$
Now: $\frac{7}{5} \div \frac{7}{3}$
→ Flip $\frac{7}{3}$ → $\frac{3}{7}$
→ Multiply: $\frac{7}{5} \times \frac{3}{7} = \frac{21}{35} = \frac{3}{5}$
✔ Final answer: $\frac{3}{5}$
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Final Answer:
1. $\frac{20}{27}$
2. $\frac{56}{17}$
3. $\frac{20}{3}$
4. $\frac{9}{28}$
5. $\frac{16}{5}$
6. $\frac{3}{20}$
7. $\frac{77}{20}$
8. $\frac{4}{33}$
9. $\frac{21}{11}$
10. $\frac{20}{9}$
11. $\frac{5}{3}$
12. $1$
13. $\frac{7}{5}$
14. $\frac{77}{10}$
15. $\frac{3}{5}$
Let’s go through each problem one by one.
---
Problem 1:
$\frac{4}{3} \div \frac{9}{5}$
→ Flip $\frac{9}{5}$ → $\frac{5}{9}$
→ Multiply: $\frac{4}{3} \times \frac{5}{9} = \frac{20}{27}$
✔ Already simplified.
---
Problem 2:
$\frac{7}{2} \div \frac{17}{16}$
→ Flip $\frac{17}{16}$ → $\frac{16}{17}$
→ Multiply: $\frac{7}{2} \times \frac{16}{17} = \frac{112}{34}$
Simplify: divide numerator and denominator by 2 → $\frac{56}{17}$
✔ Final answer: $\frac{56}{17}$ or $3\frac{5}{17}$
---
Problem 3:
$\frac{20}{9} \div \frac{8}{24}$
First, simplify $\frac{8}{24}$ → $\frac{1}{3}$
Now: $\frac{20}{9} \div \frac{1}{3}$
→ Flip $\frac{1}{3}$ → $\frac{3}{1}$
→ Multiply: $\frac{20}{9} \times 3 = \frac{60}{9} = \frac{20}{3}$
✔ Final answer: $\frac{20}{3}$ or $6\frac{2}{3}$
---
Problem 4:
$\frac{1}{4} \div \frac{7}{9}$
→ Flip $\frac{7}{9}$ → $\frac{9}{7}$
→ Multiply: $\frac{1}{4} \times \frac{9}{7} = \frac{9}{28}$
✔ Already simplified.
---
Problem 5:
$\frac{6}{5} \div \frac{3}{8}$
→ Flip $\frac{3}{8}$ → $\frac{8}{3}$
→ Multiply: $\frac{6}{5} \times \frac{8}{3} = \frac{48}{15}$
Simplify: divide by 3 → $\frac{16}{5}$
✔ Final answer: $\frac{16}{5}$ or $3\frac{1}{5}$
---
Problem 6:
$\frac{1}{3} \div \frac{20}{9}$
→ Flip $\frac{20}{9}$ → $\frac{9}{20}$
→ Multiply: $\frac{1}{3} \times \frac{9}{20} = \frac{9}{60} = \frac{3}{20}$
✔ Simplified.
---
Problem 7:
$\frac{11}{10} \div \frac{2}{7}$
→ Flip $\frac{2}{7}$ → $\frac{7}{2}$
→ Multiply: $\frac{11}{10} \times \frac{7}{2} = \frac{77}{20}$
✔ Final answer: $\frac{77}{20}$ or $3\frac{17}{20}$
---
Problem 8:
$\frac{4}{15} \div \frac{11}{5}$
→ Flip $\frac{11}{5}$ → $\frac{5}{11}$
→ Multiply: $\frac{4}{15} \times \frac{5}{11} = \frac{20}{165}$
Simplify: divide by 5 → $\frac{4}{33}$
✔ Done.
---
Problem 9:
$\frac{18}{22} \div \frac{3}{7}$
First, simplify $\frac{18}{22}$ → $\frac{9}{11}$
Now: $\frac{9}{11} \div \frac{3}{7}$
→ Flip $\frac{3}{7}$ → $\frac{7}{3}$
→ Multiply: $\frac{9}{11} \times \frac{7}{3} = \frac{63}{33}$
Simplify: divide by 3 → $\frac{21}{11}$
✔ Final answer: $\frac{21}{11}$ or $1\frac{10}{11}$
---
Problem 10:
$\frac{10}{6} \div \frac{9}{12}$
Simplify both:
$\frac{10}{6} = \frac{5}{3}$, $\frac{9}{12} = \frac{3}{4}$
Now: $\frac{5}{3} \div \frac{3}{4}$
→ Flip $\frac{3}{4}$ → $\frac{4}{3}$
→ Multiply: $\frac{5}{3} \times \frac{4}{3} = \frac{20}{9}$
✔ Final answer: $\frac{20}{9}$ or $2\frac{2}{9}$
---
Problem 11:
$\frac{2}{3} \div \frac{8}{20}$
Simplify $\frac{8}{20}$ → $\frac{2}{5}$
Now: $\frac{2}{3} \div \frac{2}{5}$
→ Flip $\frac{2}{5}$ → $\frac{5}{2}$
→ Multiply: $\frac{2}{3} \times \frac{5}{2} = \frac{10}{6} = \frac{5}{3}$
✔ Final answer: $\frac{5}{3}$ or $1\frac{2}{3}$
---
Problem 12:
$\frac{5}{6} \div \frac{10}{12}$
Simplify $\frac{10}{12}$ → $\frac{5}{6}$
Now: $\frac{5}{6} \div \frac{5}{6}$
→ Flip $\frac{5}{6}$ → $\frac{6}{5}$
→ Multiply: $\frac{5}{6} \times \frac{6}{5} = \frac{30}{30} = 1$
✔ Answer is 1.
---
Problem 13:
$\frac{6}{10} \div \frac{3}{7}$
Simplify $\frac{6}{10}$ → $\frac{3}{5}$
Now: $\frac{3}{5} \div \frac{3}{7}$
→ Flip $\frac{3}{7}$ → $\frac{7}{3}$
→ Multiply: $\frac{3}{5} \times \frac{7}{3} = \frac{21}{15} = \frac{7}{5}$
✔ Final answer: $\frac{7}{5}$ or $1\frac{2}{5}$
---
Problem 14:
$\frac{22}{5} \div \frac{8}{14}$
Simplify $\frac{8}{14}$ → $\frac{4}{7}$
Now: $\frac{22}{5} \div \frac{4}{7}$
→ Flip $\frac{4}{7}$ → $\frac{7}{4}$
→ Multiply: $\frac{22}{5} \times \frac{7}{4} = \frac{154}{20}$
Simplify: divide by 2 → $\frac{77}{10}$
✔ Final answer: $\frac{77}{10}$ or $7\frac{7}{10}$
---
Problem 15:
$\frac{7}{5} \div \frac{21}{9}$
Simplify $\frac{21}{9}$ → $\frac{7}{3}$
Now: $\frac{7}{5} \div \frac{7}{3}$
→ Flip $\frac{7}{3}$ → $\frac{3}{7}$
→ Multiply: $\frac{7}{5} \times \frac{3}{7} = \frac{21}{35} = \frac{3}{5}$
✔ Final answer: $\frac{3}{5}$
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Final Answer:
1. $\frac{20}{27}$
2. $\frac{56}{17}$
3. $\frac{20}{3}$
4. $\frac{9}{28}$
5. $\frac{16}{5}$
6. $\frac{3}{20}$
7. $\frac{77}{20}$
8. $\frac{4}{33}$
9. $\frac{21}{11}$
10. $\frac{20}{9}$
11. $\frac{5}{3}$
12. $1$
13. $\frac{7}{5}$
14. $\frac{77}{10}$
15. $\frac{3}{5}$
Parent Tip: Review the logic above to help your child master the concept of division fractions worksheet 7th grade.
