Multiply and Divide Positive and Negative Fractions | Worksheet ... - Free Printable

Let's solve each of the 15 problems involving multiplication and division of positive and negative fractions. We'll follow the rules:

- Multiplying fractions: Multiply numerators and denominators, then simplify.
- Dividing fractions: Multiply by the reciprocal of the divisor.
- Sign rules:
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
- Same for division.

We’ll go step by step.

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1. $\frac{2}{3} \cdot \left(-\frac{1}{4}\right)$

Multiply:
$$
\frac{2 \cdot (-1)}{3 \cdot 4} = \frac{-2}{12} = -\frac{1}{6}
$$

✔ Answer: $-\frac{1}{6}$

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2. $\frac{2}{7} \div \frac{4}{9}$

Divide by multiplying by reciprocal:
$$
\frac{2}{7} \cdot \frac{9}{4} = \frac{18}{28} = \frac{9}{14}
$$

✔ Answer: $\frac{9}{14}$

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3. $-\frac{3}{8} \cdot \frac{2}{9}$

Multiply:
$$
\frac{-3 \cdot 2}{8 \cdot 9} = \frac{-6}{72} = -\frac{1}{12}
$$

✔ Answer: $-\frac{1}{12}$

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4. $-\frac{5}{6} \div \frac{1}{3}$

Multiply by reciprocal:
$$
-\frac{5}{6} \cdot \frac{3}{1} = -\frac{15}{6} = -\frac{5}{2}
$$

✔ Answer: $-\frac{5}{2}$ or $-2\frac{1}{2}$

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5. $-\frac{7}{9} \div \frac{4}{5}$

Multiply by reciprocal:
$$
-\frac{7}{9} \cdot \frac{5}{4} = -\frac{35}{36}
$$

✔ Answer: $-\frac{35}{36}$

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6. $-\frac{6}{7} \cdot \left(-\frac{1}{8}\right)$

Negative × Negative = Positive:
$$
\frac{6 \cdot 1}{7 \cdot 8} = \frac{6}{56} = \frac{3}{28}
$$

✔ Answer: $\frac{3}{28}$

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7. $-\frac{5}{8} \cdot \left(-\frac{3}{10}\right)$

Negative × Negative = Positive:
$$
\frac{5 \cdot 3}{8 \cdot 10} = \frac{15}{80} = \frac{3}{16}
$$

✔ Answer: $\frac{3}{16}$

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8. $\frac{6}{7} \cdot \left(-\frac{2}{3}\right)$

Positive × Negative = Negative:
$$
\frac{6 \cdot (-2)}{7 \cdot 3} = \frac{-12}{21} = -\frac{4}{7}
$$

✔ Answer: $-\frac{4}{7}$

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9. $-\frac{3}{4} \cdot \left(-\frac{5}{6}\right)$

Negative × Negative = Positive:
$$
\frac{3 \cdot 5}{4 \cdot 6} = \frac{15}{24} = \frac{5}{8}
$$

✔ Answer: $\frac{5}{8}$

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10. $\frac{6}{7} \cdot \left(-\frac{3}{10}\right)$

Positive × Negative = Negative:
$$
\frac{6 \cdot (-3)}{7 \cdot 10} = \frac{-18}{70} = -\frac{9}{35}
$$

✔ Answer: $-\frac{9}{35}$

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11. $-\frac{5}{8} \div \left(-\frac{1}{2}\right)$

Divide by multiplying by reciprocal:
$$
-\frac{5}{8} \cdot \left(-\frac{2}{1}\right) = \frac{10}{8} = \frac{5}{4}
$$

✔ Answer: $\frac{5}{4}$ or $1\frac{1}{4}$

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12. $-\frac{3}{10} \div \frac{5}{6}$

Multiply by reciprocal:
$$
-\frac{3}{10} \cdot \frac{6}{5} = -\frac{18}{50} = -\frac{9}{25}
$$

✔ Answer: $-\frac{9}{25}$

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13. $-\frac{3}{8} \div \frac{2}{9}$

Multiply by reciprocal:
$$
-\frac{3}{8} \cdot \frac{9}{2} = -\frac{27}{16}
$$

✔ Answer: $-\frac{27}{16}$ or $-1\frac{11}{16}$

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14. $-\frac{6}{9} \div \frac{1}{12}$

Simplify $-\frac{6}{9} = -\frac{2}{3}$

Now divide:
$$
-\frac{2}{3} \cdot \frac{12}{1} = -\frac{24}{3} = -8
$$

✔ Answer: $-8$

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15. $\frac{8}{15} \cdot \left(-\frac{2}{3}\right)$

Positive × Negative = Negative:
$$
\frac{8 \cdot (-2)}{15 \cdot 3} = \frac{-16}{45}
$$

✔ Answer: $-\frac{16}{45}$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $-\frac{1}{6}$ |
| 2 | $\frac{9}{14}$ |
| 3 | $-\frac{1}{12}$ |
| 4 | $-\frac{5}{2}$ |
| 5 | $-\frac{35}{36}$ |
| 6 | $\frac{3}{28}$ |
| 7 | $\frac{3}{16}$ |
| 8 | $-\frac{4}{7}$ |
| 9 | $\frac{5}{8}$ |
| 10 | $-\frac{9}{35}$ |
| 11 | $\frac{5}{4}$ |
| 12 | $-\frac{9}{25}$ |
| 13 | $-\frac{27}{16}$ |
| 14 | $-8$ |
| 15 | $-\frac{16}{45}$ |

Let me know if you'd like this in a printable format or with explanations for any specific problem!