301 Moved Permanently - Free Printable

Let's solve each problem on the "Multiplication of Rational Numbers" worksheet step by step. The key rules to remember:

1. Multiply numerators together and denominators together.
2. Sign rules:
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
3. Simplify fractions where possible.

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1) $\frac{11}{9} \times -\frac{1}{10}$

$$
= \frac{11 \times (-1)}{9 \times 10} = -\frac{11}{90}
$$

✔ Answer: $-\frac{11}{90}$

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2) $8 \times -\frac{2}{5}$

$$
= \frac{8}{1} \times -\frac{2}{5} = -\frac{16}{5}
$$

✔ Answer: $-\frac{16}{5}$ or $-3\frac{1}{5}$

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3) $0 \times -\frac{1}{2}$

Any number multiplied by zero is zero.

✔ Answer: $0$

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4) $-\frac{1}{10} \times \frac{5}{3}$

$$
= -\frac{1 \times 5}{10 \times 3} = -\frac{5}{30} = -\frac{1}{6}
$$

✔ Answer: $-\frac{1}{6}$

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5) $-2 \times \frac{12}{7}$

$$
= -\frac{2}{1} \times \frac{12}{7} = -\frac{24}{7}
$$

✔ Answer: $-\frac{24}{7}$ or $-3\frac{3}{7}$

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6) $-\frac{1}{2} \times \frac{8}{7}$

$$
= -\frac{1 \times 8}{2 \times 7} = -\frac{8}{14} = -\frac{4}{7}
$$

✔ Answer: $-\frac{4}{7}$

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7) $-\frac{3}{2} \times -\frac{17}{9}$

Negative × Negative = Positive

$$
= \frac{3 \times 17}{2 \times 9} = \frac{51}{18} = \frac{17}{6}
$$

✔ Answer: $\frac{17}{6}$ or $2\frac{5}{6}$

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8) $\frac{6}{5} \times -\frac{1}{3}$

$$
= -\frac{6 \times 1}{5 \times 3} = -\frac{6}{15} = -\frac{2}{5}
$$

✔ Answer: $-\frac{2}{5}$

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9) $-\frac{11}{6} \times -\frac{9}{8}$

Negative × Negative = Positive

$$
= \frac{11 \times 9}{6 \times 8} = \frac{99}{48}
$$

Simplify: Divide numerator and denominator by 3 → $\frac{33}{16}$

✔ Answer: $\frac{33}{16}$ or $2\frac{1}{16}$

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10) $\frac{1}{8} \times -\frac{1}{2}$

$$
= -\frac{1}{16}
$$

✔ Answer: $-\frac{1}{16}$

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11) $-\frac{1}{6} \times -\frac{5}{7} \times -\frac{5}{3}$

First, multiply signs:
(-) × (-) = (+), then (+) × (-) = (-)

So overall sign is negative

Now multiply numerators: $1 \times 5 \times 5 = 25$
Denominators: $6 \times 7 \times 3 = 126$

$$
= -\frac{25}{126}
$$

✔ Answer: $-\frac{25}{126}$

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12) $-2 \times \frac{4}{3} \times -\frac{1}{2}$

Signs: (-) × (+) = (-), then (-) × (-) = (+) → positive

Now compute:

$$
= \frac{-2 \times 4 \times -1}{1 \times 3 \times 2} = \frac{8}{6} = \frac{4}{3}
$$

✔ Answer: $\frac{4}{3}$ or $1\frac{1}{3}$

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13) $-\frac{11}{6} \times \frac{3}{4} \times \frac{1}{6}$

Sign: negative

Numerator: $11 \times 3 \times 1 = 33$
Denominator: $6 \times 4 \times 6 = 144$

$$
= -\frac{33}{144} = -\frac{11}{48}
$$

✔ Answer: $-\frac{11}{48}$

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14) $-\frac{5}{3} \times -\frac{1}{2} \times \frac{11}{6}$

Signs: (-) × (-) = (+), (+) × (+) = (+) → positive

Numerator: $5 \times 1 \times 11 = 55$
Denominator: $3 \times 2 \times 6 = 36$

$$
= \frac{55}{36}
$$

✔ Answer: $\frac{55}{36}$ or $1\frac{19}{36}$

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15) $2 \times 7 \times -\frac{6}{5}$

First: $2 \times 7 = 14$

Then: $14 \times -\frac{6}{5} = -\frac{84}{5}$

✔ Answer: $-\frac{84}{5}$ or $-16\frac{4}{5}$

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16) $-2 \times \frac{3}{2} \times -\frac{10}{9}$

Signs: (-) × (+) = (-), then (-) × (-) = (+) → positive

Compute:

$$
= \frac{-2 \times 3 \times -10}{1 \times 2 \times 9} = \frac{60}{18} = \frac{10}{3}
$$

✔ Answer: $\frac{10}{3}$ or $3\frac{1}{3}$

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17) $-\frac{5}{3} \times -\frac{2}{5} \times \frac{2}{3}$

Signs: (-) × (-) = (+), (+) × (+) = (+) → positive

Numerator: $5 \times 2 \times 2 = 20$
Denominator: $3 \times 5 \times 3 = 45$

$$
= \frac{20}{45} = \frac{4}{9}
$$

✔ Answer: $\frac{4}{9}$

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18) $2 \times -1 \times \frac{1}{7}$

$2 \times -1 = -2$, then $-2 \times \frac{1}{7} = -\frac{2}{7}$

✔ Answer: $-\frac{2}{7}$

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19) $-\frac{7}{4} \times -\frac{2}{5} \times \frac{5}{3}$

Signs: (-) × (-) = (+), (+) × (+) = (+) → positive

Numerator: $7 \times 2 \times 5 = 70$
Denominator: $4 \times 5 \times 3 = 60$

$$
= \frac{70}{60} = \frac{7}{6}
$$

✔ Answer: $\frac{7}{6}$ or $1\frac{1}{6}$

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20) $-10 \times -\frac{2}{7} \times -\frac{3}{2}$

Signs:
(-) × (-) = (+), then (+) × (-) = (-) → negative

Now compute:

$$
= \frac{-10 \times -2 \times -3}{1 \times 7 \times 2} = \frac{-60}{14} = -\frac{30}{7}
$$

✔ Answer: $-\frac{30}{7}$ or $-4\frac{2}{7}$

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1) | $-\frac{11}{90}$ |
| 2) | $-\frac{16}{5}$ |
| 3) | $0$ |
| 4) | $-\frac{1}{6}$ |
| 5) | $-\frac{24}{7}$ |
| 6) | $-\frac{4}{7}$ |
| 7) | $\frac{17}{6}$ |
| 8) | $-\frac{2}{5}$ |
| 9) | $\frac{33}{16}$ |
| 10) | $-\frac{1}{16}$ |
| 11) | $-\frac{25}{126}$ |
| 12) | $\frac{4}{3}$ |
| 13) | $-\frac{11}{48}$ |
| 14) | $\frac{55}{36}$ |
| 15) | $-\frac{84}{5}$ |
| 16) | $\frac{10}{3}$ |
| 17) | $\frac{4}{9}$ |
| 18) | $-\frac{2}{7}$ |
| 19) | $\frac{7}{6}$ |
| 20) | $-\frac{30}{7}$ |

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