Multiply And Divide Positive And Negative Mixed Numbers Worksheet - Free Printable

It looks like you've uploaded an answer key for a worksheet titled *"Multiply and Divide Positive and Negative Fractions"*. This means the solutions to the problems are already provided. However, I can help you understand how to solve each problem step by step, so you can learn the process.

Let’s go through a few examples and explain the rules and methods used.

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🔷 Key Rules:

1. Multiplying fractions: Multiply numerators and denominators.
- Sign rule:
- (+) × (+) = (+)
- (−) × (−) = (+)
- (+) × (−) = (−)
- (−) × (+) = (−)

2. Dividing fractions: Multiply by the reciprocal of the divisor.
- Example: $ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} $
- Apply sign rules as above.

3. Simplify answers to lowest terms or mixed numbers if needed.

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Let’s walk through a few selected problems:

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✔ Problem 1:

$$
\frac{2}{3} \cdot \left(-\frac{1}{5}\right)
$$

- Multiply numerators: $ 2 \cdot (-1) = -2 $
- Multiply denominators: $ 3 \cdot 5 = 15 $
- Result: $ -\frac{2}{15} $

✔ Answer: $-\frac{2}{15}$ ✔️

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✔ Problem 2:

$$
\frac{2}{9} \div \frac{3}{4}
$$

- Change division to multiplication by reciprocal:
$$
\frac{2}{9} \cdot \frac{4}{3} = \frac{8}{27}
$$

✔ Answer: $\frac{8}{27}$ ✔️

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✔ Problem 4:

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

- Convert to multiplication:
$$
-\frac{5}{6} \cdot \frac{3}{1} = -\frac{15}{6} = -\frac{5}{2}
$$
- Simplify: $-\frac{5}{2} = -2\frac{1}{2}$

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

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✔ Problem 7:

$$
-\frac{5}{12} \div \left(-\frac{1}{10}\right)
$$

- Two negatives → positive result
- Multiply by reciprocal:
$$
\frac{5}{12} \cdot \frac{10}{1} = \frac{50}{12} = \frac{25}{6}
$$
- Simplify: $ \frac{25}{6} = 4\frac{1}{6} $

✔ Answer: $\frac{25}{6}$ or $4\frac{1}{6}$ ✔️

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✔ Problem 10:

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

- Multiply by reciprocal:
$$
\frac{6}{7} \cdot \left(-\frac{10}{3}\right) = -\frac{60}{21} = -\frac{20}{7}
$$
- Simplify: $-\frac{20}{7} = -2\frac{6}{7}$

✔ Answer: $-\frac{20}{7}$ or $-2\frac{6}{7}$ ✔️

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✔ Problem 14:

$$
-\frac{4}{9} \div \frac{1}{12}
$$

- Multiply by reciprocal:
$$
-\frac{4}{9} \cdot \frac{12}{1} = -\frac{48}{9} = -\frac{16}{3}
$$
- Simplify: $-\frac{16}{3} = -5\frac{1}{3}$

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

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✔ Problem 15:

$$
\frac{8}{15} \cdot \left(-\frac{5}{6}\right)
$$

- Multiply:
$$
\frac{8 \cdot (-5)}{15 \cdot 6} = \frac{-40}{90} = -\frac{4}{9}
$$
- Simplify: divide numerator and denominator by 10 → $-\frac{4}{9}$

✔ Answer: $-\frac{4}{9}$ ✔️

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📌 Summary of Steps:

1. Identify operation: multiply or divide.
2. Handle signs first.
3. For division: flip the second fraction (reciprocal).
4. Multiply across: numerator × numerator, denominator × denominator.
5. Simplify: reduce fraction and convert to mixed number if needed.

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