Multiplying and Dividing Fractions worksheet with 12 problems, featuring a colorful lizard logo and Math-Salamanders.com branding.

Here's the complete solution to the worksheet “Multiplying and Dividing Fractions 3”, with step-by-step explanations for each problem. The instructions ask for answers as mixed fractions in simplest form where appropriate.

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Key Rules to Remember:

- Multiplying Fractions: Multiply numerators together, denominators together.
> \(\frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}\)

- Dividing Fractions: Multiply by the reciprocal (flip the second fraction).
> \(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}\)

- Simplify the result by reducing the fraction to lowest terms.
- Convert to a mixed number if the numerator is larger than the denominator.

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## ✔ Problem Solutions:

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1) \(\frac{4}{5} \times \frac{3}{4}\)

Multiply numerators: \(4 \times 3 = 12\)
Multiply denominators: \(5 \times 4 = 20\)
→ \(\frac{12}{20}\)

Simplify: divide numerator and denominator by 4 → \(\frac{3}{5}\)
✔ Answer: \(\frac{3}{5}\)

*(Not a mixed number since it’s less than 1)*

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2) \(\frac{4}{9} \div \frac{2}{5}\)

Flip the second fraction: \(\frac{4}{9} \times \frac{5}{2}\)
Multiply: \(\frac{4 \times 5}{9 \times 2} = \frac{20}{18}\)

Simplify: divide by 2 → \(\frac{10}{9}\)
Convert to mixed number: \(10 ÷ 9 = 1\) remainder 1 → \(1\frac{1}{9}\)

✔ Answer: \(1\frac{1}{9}\)

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3) \(\frac{6}{5} \times \frac{5}{6}\)

Multiply: \(\frac{6 \times 5}{5 \times 6} = \frac{30}{30} = 1\)

✔ Answer: \(1\)

*(Whole number — no mixed fraction needed)*

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4) \(\frac{5}{7} \div \frac{2}{9}\)

Flip: \(\frac{5}{7} \times \frac{9}{2} = \frac{45}{14}\)

Simplify? 45 and 14 have no common factors → already simplified.
Convert to mixed number: \(45 ÷ 14 = 3\) remainder 3 → \(3\frac{3}{14}\)

✔ Answer: \(3\frac{3}{14}\)

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5) \(\frac{3}{8} \times \frac{4}{9}\)

Multiply: \(\frac{3 \times 4}{8 \times 9} = \frac{12}{72}\)

Simplify: divide numerator and denominator by 12 → \(\frac{1}{6}\)

✔ Answer: \(\frac{1}{6}\)

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6) \(\frac{9}{10} \div \frac{3}{8}\)

Flip: \(\frac{9}{10} \times \frac{8}{3} = \frac{72}{30}\)

Simplify: divide by 6 → \(\frac{12}{5}\)
Convert to mixed number: \(12 ÷ 5 = 2\) remainder 2 → \(2\frac{2}{5}\)

✔ Answer: \(2\frac{2}{5}\)

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7) \(\frac{7}{8} \times \frac{4}{5}\)

Multiply: \(\frac{7 \times 4}{8 \times 5} = \frac{28}{40}\)

Simplify: divide by 4 → \(\frac{7}{10}\)

✔ Answer: \(\frac{7}{10}\)

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8) \(\frac{5}{3} \div \frac{7}{12}\)

Flip: \(\frac{5}{3} \times \frac{12}{7} = \frac{60}{21}\)

Simplify: divide by 3 → \(\frac{20}{7}\)
Convert to mixed number: \(20 ÷ 7 = 2\) remainder 6 → \(2\frac{6}{7}\)

✔ Answer: \(2\frac{6}{7}\)

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9) \(\frac{8}{3} \times \frac{5}{2}\)

Multiply: \(\frac{8 \times 5}{3 \times 2} = \frac{40}{6}\)

Simplify: divide by 2 → \(\frac{20}{3}\)
Convert to mixed number: \(20 ÷ 3 = 6\) remainder 2 → \(6\frac{2}{3}\)

✔ Answer: \(6\frac{2}{3}\)

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10) \(\frac{2}{9} \div \frac{5}{12}\)

Flip: \(\frac{2}{9} \times \frac{12}{5} = \frac{24}{45}\)

Simplify: divide by 3 → \(\frac{8}{15}\)

✔ Answer: \(\frac{8}{15}\)

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11) \(\frac{10}{7} \times \frac{9}{5}\)

Multiply: \(\frac{10 \times 9}{7 \times 5} = \frac{90}{35}\)

Simplify: divide by 5 → \(\frac{18}{7}\)
Convert to mixed number: \(18 ÷ 7 = 2\) remainder 4 → \(2\frac{4}{7}\)

✔ Answer: \(2\frac{4}{7}\)

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12) \(\frac{6}{5} \div \frac{4}{7}\)

Flip: \(\frac{6}{5} \times \frac{7}{4} = \frac{42}{20}\)

Simplify: divide by 2 → \(\frac{21}{10}\)
Convert to mixed number: \(21 ÷ 10 = 2\) remainder 1 → \(2\frac{1}{10}\)

✔ Answer: \(2\frac{1}{10}\)

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## 📝 Final Answers Summary:

1) \(\frac{3}{5}\)
2) \(1\frac{1}{9}\)
3) \(1\)
4) \(3\frac{3}{14}\)
5) \(\frac{1}{6}\)
6) \(2\frac{2}{5}\)
7) \(\frac{7}{10}\)
8) \(2\frac{6}{7}\)
9) \(6\frac{2}{3}\)
10) \(\frac{8}{15}\)
11) \(2\frac{4}{7}\)
12) \(2\frac{1}{10}\)

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