Grade 6 Equivalent Fractions Worksheets | Math Worksheets - Free Printable

Let’s solve each problem step by step. Remember: when dividing fractions, you flip the second fraction (that’s called finding its reciprocal) and then multiply.

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Problem 1:

$\frac{1}{3} \div \frac{7}{9}$
→ Flip $\frac{7}{9}$ to get $\frac{9}{7}$
→ Multiply: $\frac{1}{3} \times \frac{9}{7} = \frac{9}{21}$
→ Simplify: divide numerator and denominator by 3 → $\frac{3}{7}$

✔ Answer: $\frac{3}{7}$

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Problem 2:

$\frac{1}{5} \div \frac{5}{8}$
→ Flip $\frac{5}{8}$ to get $\frac{8}{5}$
→ Multiply: $\frac{1}{5} \times \frac{8}{5} = \frac{8}{25}$
→ Already simplified.

✔ Answer: $\frac{8}{25}$

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Problem 3:

$\frac{10}{11} \div \frac{20}{22}$
→ Flip $\frac{20}{22}$ to get $\frac{22}{20}$
→ Multiply: $\frac{10}{11} \times \frac{22}{20}$
→ Notice: 10 and 20 cancel → 1/2; 11 and 22 cancel → 2/1
→ So: $\frac{1}{1} \times \frac{2}{2} = \frac{2}{2} = 1$
Wait — let’s do it carefully:

$\frac{10 \times 22}{11 \times 20} = \frac{220}{220} = 1$

✔ Answer: $1$

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Problem 4:

$\frac{2}{3} \div \frac{18}{15}$
→ Flip $\frac{18}{15}$ to get $\frac{15}{18}$
→ Multiply: $\frac{2}{3} \times \frac{15}{18}$
→ Simplify before multiplying:
- 2 and 18 → divide by 2 → 1 and 9
- 3 and 15 → divide by 3 → 1 and 5
→ Now: $\frac{1}{1} \times \frac{5}{9} = \frac{5}{9}$

✔ Answer: $\frac{5}{9}$

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Problem 5:

$\frac{1}{9} \div \frac{3}{10}$
→ Flip $\frac{3}{10}$ to get $\frac{10}{3}$
→ Multiply: $\frac{1}{9} \times \frac{10}{3} = \frac{10}{27}$
→ Already simplified.

✔ Answer: $\frac{10}{27}$

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Problem 6:

$\frac{7}{16} \div \frac{9}{8}$
→ Flip $\frac{9}{8}$ to get $\frac{8}{9}$
→ Multiply: $\frac{7}{16} \times \frac{8}{9}$
→ Simplify: 8 and 16 → divide by 8 → 1 and 2
→ Now: $\frac{7}{2} \times \frac{1}{9} = \frac{7}{18}$

✔ Answer: $\frac{7}{18}$

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Problem 7:

$\frac{4}{5} \div \frac{1}{10}$
→ Flip $\frac{1}{10}$ to get $\frac{10}{1}$
→ Multiply: $\frac{4}{5} \times \frac{10}{1} = \frac{40}{5} = 8$

✔ Answer: $8$

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Problem 8:

$\frac{1}{11} \div \frac{4}{44}$
→ First, simplify $\frac{4}{44}$ → divide top and bottom by 4 → $\frac{1}{11}$
→ So now: $\frac{1}{11} \div \frac{1}{11}$
→ Flip $\frac{1}{11}$ → $\frac{11}{1}$
→ Multiply: $\frac{1}{11} \times \frac{11}{1} = \frac{11}{11} = 1$

✔ Answer: $1$

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Problem 9:

$\frac{3}{13} \div \frac{2}{3}$
→ Flip $\frac{2}{3}$ to get $\frac{3}{2}$
→ Multiply: $\frac{3}{13} \times \frac{3}{2} = \frac{9}{26}$
→ Already simplified.

✔ Answer: $\frac{9}{26}$

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Problem 10:

$\frac{8}{25} \div \frac{16}{32}$
→ First, simplify $\frac{16}{32}$ → divide by 16 → $\frac{1}{2}$
→ Now: $\frac{8}{25} \div \frac{1}{2}$
→ Flip $\frac{1}{2}$ → $\frac{2}{1}$
→ Multiply: $\frac{8}{25} \times \frac{2}{1} = \frac{16}{25}$

✔ Answer: $\frac{16}{25}$

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Problem 11:

$\frac{1}{7} \div \frac{3}{42}$
→ Simplify $\frac{3}{42}$ → divide by 3 → $\frac{1}{14}$
→ Now: $\frac{1}{7} \div \frac{1}{14}$
→ Flip $\frac{1}{14}$ → $\frac{14}{1}$
→ Multiply: $\frac{1}{7} \times \frac{14}{1} = \frac{14}{7} = 2$

✔ Answer: $2$

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Problem 12:

$\frac{8}{9} \div \frac{32}{45}$
→ Flip $\frac{32}{45}$ to get $\frac{45}{32}$
→ Multiply: $\frac{8}{9} \times \frac{45}{32}$
→ Simplify:
- 8 and 32 → divide by 8 → 1 and 4
- 9 and 45 → divide by 9 → 1 and 5
→ Now: $\frac{1}{1} \times \frac{5}{4} = \frac{5}{4}$
→ Or as mixed number: $1\frac{1}{4}$, but we’ll leave as improper unless asked.

✔ Answer: $\frac{5}{4}$

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Final Answer:
1. $\frac{3}{7}$
2. $\frac{8}{25}$
3. $1$
4. $\frac{5}{9}$
5. $\frac{10}{27}$
6. $\frac{7}{18}$
7. $8$
8. $1$
9. $\frac{9}{26}$
10. $\frac{16}{25}$
11. $2$
12. $\frac{5}{4}$