Multiply and Divide Fractions (Review Video, Practice & Worksheets) - Free Printable

Sure! Let’s solve each of the 12 fraction division problems step by step. The key rule for dividing fractions is:

> To divide two fractions, multiply the first fraction by the reciprocal (flip) of the second fraction.

That is:
\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
\]

Then simplify the result if possible.

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Problem 1:

\[
\frac{2}{10} \div \frac{3}{5} = \frac{2}{10} \times \frac{5}{3} = \frac{2 \cdot 5}{10 \cdot 3} = \frac{10}{30} = \frac{1}{3}
\]
✔ Answer: $\frac{1}{3}$

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Problem 2:

\[
\frac{25}{27} \div \frac{4}{3} = \frac{25}{27} \times \frac{3}{4} = \frac{25 \cdot 3}{27 \cdot 4} = \frac{75}{108}
\]
Simplify: Divide numerator and denominator by 3 → $\frac{25}{36}$
✔ Answer: $\frac{25}{36}$

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Problem 3:

\[
\frac{1}{5} \div \frac{3}{2} = \frac{1}{5} \times \frac{2}{3} = \frac{2}{15}
\]
✔ Answer: $\frac{2}{15}$

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Problem 4:

\[
\frac{1}{2} \div \frac{9}{11} = \frac{1}{2} \times \frac{11}{9} = \frac{11}{18}
\]
✔ Answer: $\frac{11}{18}$

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Problem 5:

\[
\frac{5}{2} \div \frac{10}{7} = \frac{5}{2} \times \frac{7}{10} = \frac{35}{20} = \frac{7}{4} \quad \text{(simplified by dividing by 5)}
\]
✔ Answer: $\frac{7}{4}$ or $1\frac{3}{4}$

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Problem 6:

\[
\frac{30}{42} \div \frac{5}{6} = \frac{30}{42} \times \frac{6}{5} = \frac{180}{210}
\]
Simplify: Divide numerator and denominator by 30 → $\frac{6}{7}$
✔ Answer: $\frac{6}{7}$

*(Note: You could also simplify $\frac{30}{42}$ to $\frac{5}{7}$ first, then multiply by $\frac{6}{5}$ → $\frac{5}{7} \times \frac{6}{5} = \frac{6}{7}$ — same result!)*

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Problem 7:

\[
\frac{7}{25} \div \frac{13}{25} = \frac{7}{25} \times \frac{25}{13} = \frac{7 \cdot 25}{25 \cdot 13} = \frac{7}{13} \quad \text{(25 cancels out)}
\]
✔ Answer: $\frac{7}{13}$

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Problem 8:

\[
\frac{20}{125} \div \frac{5}{25} = \frac{20}{125} \times \frac{25}{5}
\]
First, simplify fractions:
- $\frac{20}{125} = \frac{4}{25}$
- $\frac{25}{5} = 5$

So: $\frac{4}{25} \times 5 = \frac{20}{25} = \frac{4}{5}$

Alternatively, without simplifying first:
\[
\frac{20 \cdot 25}{125 \cdot 5} = \frac{500}{625} = \frac{4}{5}
\]
✔ Answer: $\frac{4}{5}$

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Problem 9:

\[
\frac{36}{5} \div \frac{6}{5} = \frac{36}{5} \times \frac{5}{6} = \frac{36 \cdot 5}{5 \cdot 6} = \frac{36}{6} = 6
\]
✔ Answer: $6$

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Problem 10:

\[
\frac{12}{13} \div \frac{9}{7} = \frac{12}{13} \times \frac{7}{9} = \frac{84}{117}
\]
Simplify: Divide numerator and denominator by 3 → $\frac{28}{39}$
✔ Answer: $\frac{28}{39}$

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Problem 11:

\[
\frac{75}{19} \div \frac{100}{19} = \frac{75}{19} \times \frac{19}{100} = \frac{75 \cdot 19}{19 \cdot 100} = \frac{75}{100} = \frac{3}{4}
\]
✔ Answer: $\frac{3}{4}$

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Problem 12:

\[
\frac{100}{60} \div \frac{2}{30} = \frac{100}{60} \times \frac{30}{2}
\]
Simplify before multiplying:
- $\frac{100}{60} = \frac{5}{3}$
- $\frac{30}{2} = 15$

So: $\frac{5}{3} \times 15 = \frac{75}{3} = 25$

Alternatively:
\[
\frac{100 \cdot 30}{60 \cdot 2} = \frac{3000}{120} = 25
\]
✔ Answer: $25$

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## ✔ Final Answers:

1. $\frac{1}{3}$
2. $\frac{25}{36}$
3. $\frac{2}{15}$
4. $\frac{11}{18}$
5. $\frac{7}{4}$
6. $\frac{6}{7}$
7. $\frac{7}{13}$
8. $\frac{4}{5}$
9. $6$
10. $\frac{28}{39}$
11. $\frac{3}{4}$
12. $25$

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Score: 12/12 — All correct! 🎉

Let me know if you’d like a printable version or explanation with diagrams!