Independent practice worksheet for multiplying fractions and mixed numbers.

Let's solve each of the multiplication problems step by step. We are asked to find the product of the given expressions.

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1. $ 2 \times (-\frac{1}{3}) $

Multiply the whole number by the fraction:

$$
2 \times \left(-\frac{1}{3}\right) = -\frac{2}{3}
$$

✔ Answer: $-\frac{2}{3}$

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2. $ (-\frac{1}{2}) \times (-\frac{1}{4}) $

Multiply the two negative fractions:

- Negative × Negative = Positive
- Multiply numerators: $1 \times 1 = 1$
- Multiply denominators: $2 \times 4 = 8$

$$
(-\frac{1}{2}) \times (-\frac{1}{4}) = \frac{1}{8}
$$

✔ Answer: $\frac{1}{8}$

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3. $ \frac{4}{11} \times \frac{5}{12} $

Multiply numerators and denominators:

- Numerator: $4 \times 5 = 20$
- Denominator: $11 \times 12 = 132$

$$
\frac{4}{11} \times \frac{5}{12} = \frac{20}{132}
$$

Now simplify: divide numerator and denominator by GCF (which is 4):

$$
\frac{20 \div 4}{132 \div 4} = \frac{5}{33}
$$

✔ Answer: $\frac{5}{33}$

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4. $ \frac{1}{9} \times \frac{3}{6} $

First, simplify $ \frac{3}{6} = \frac{1}{2} $

Now multiply:

$$
\frac{1}{9} \times \frac{1}{2} = \frac{1}{18}
$$

✔ Answer: $\frac{1}{18}$

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5. $ (-\frac{1}{2}) \times (\frac{1}{4}) $

Negative × Positive = Negative

$$
(-\frac{1}{2}) \times (\frac{1}{4}) = -\frac{1}{8}
$$

✔ Answer: $-\frac{1}{8}$

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6. $ (-\frac{2}{3}) \times (-9) $

Negative × Negative = Positive

Write $-9$ as a fraction: $-\frac{9}{1}$

$$
(-\frac{2}{3}) \times (-\frac{9}{1}) = \frac{2 \times 9}{3 \times 1} = \frac{18}{3} = 6
$$

✔ Answer: $6$

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7. $ \frac{8}{9} \times \frac{9}{11} $

Multiply:

- Numerator: $8 \times 9 = 72$
- Denominator: $9 \times 11 = 99$

$$
\frac{72}{99}
$$

Simplify: divide numerator and denominator by GCF (9):

$$
\frac{72 \div 9}{99 \div 9} = \frac{8}{11}
$$

✔ Answer: $\frac{8}{11}$

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8. $ \frac{1}{3} \times \frac{5}{12} $

Multiply:

- Numerator: $1 \times 5 = 5$
- Denominator: $3 \times 12 = 36$

$$
\frac{5}{36}
$$

This is already in simplest form.

✔ Answer: $\frac{5}{36}$

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✔ Final Answers:

1. $-\frac{2}{3}$
2. $\frac{1}{8}$
3. $\frac{5}{33}$
4. $\frac{1}{18}$
5. $-\frac{1}{8}$
6. $6$
7. $\frac{8}{11}$
8. $\frac{5}{36}$

Let me know if you'd like these written neatly or explained further!