Math worksheet for multiplying and dividing fractions and mixed numbers.

Let's solve each of these problems step by step. The task is to multiply or divide fractions and mixed numbers.

We’ll go through each one carefully, converting mixed numbers to improper fractions when needed, simplifying, and applying the rules for multiplying and dividing fractions.

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1) $-\frac{5}{4} \cdot \frac{1}{3}$

Multiply numerators and denominators:

$$
-\frac{5 \cdot 1}{4 \cdot 3} = -\frac{5}{12}
$$

✔ Answer: $-\frac{5}{12}$

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2) $\frac{8}{7} \div \frac{7}{10}$

Dividing fractions: multiply by the reciprocal.

$$
\frac{8}{7} \cdot \frac{10}{7} = \frac{8 \cdot 10}{7 \cdot 7} = \frac{80}{49}
$$

Convert to mixed number:

$$
\frac{80}{49} = 1 \frac{31}{49}
$$

✔ Answer: $1 \frac{31}{49}$

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3) $\frac{4}{9} \div \frac{7}{4}$

Multiply by reciprocal:

$$
\frac{4}{9} \cdot \frac{4}{7} = \frac{16}{63}
$$

✔ Answer: $\frac{16}{63}$

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4) $-\frac{2}{3} \div \frac{5}{4}$

Multiply by reciprocal:

$$
-\frac{2}{3} \cdot \frac{4}{5} = -\frac{8}{15}
$$

✔ Answer: $-\frac{8}{15}$

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5) $-2 \cdot \frac{3}{7}$

Convert $-2$ to fraction: $-\frac{2}{1}$

$$
-\frac{2}{1} \cdot \frac{3}{7} = -\frac{6}{7}
$$

✔ Answer: $-\frac{6}{7}$

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6) $-2\frac{2}{3} \div 4\frac{1}{10}$

First, convert both to improper fractions:

- $-2\frac{2}{3} = -\frac{8}{3}$
- $4\frac{1}{10} = \frac{41}{10}$

Now divide:

$$
-\frac{8}{3} \div \frac{41}{10} = -\frac{8}{3} \cdot \frac{10}{41} = -\frac{80}{123}
$$

This cannot be simplified further.

✔ Answer: $-\frac{80}{123}$

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7) $-3\frac{1}{5} \div -1\frac{3}{4}$

Convert to improper fractions:

- $-3\frac{1}{5} = -\frac{16}{5}$
- $-1\frac{3}{4} = -\frac{7}{4}$

Now divide:

$$
-\frac{16}{5} \div -\frac{7}{4} = \frac{16}{5} \cdot \frac{4}{7} = \frac{64}{35}
$$

Convert to mixed number:

$$
\frac{64}{35} = 1 \frac{29}{35}
$$

✔ Answer: $1 \frac{29}{35}$

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8) $-1\frac{1}{4} \div 9$

Convert $-1\frac{1}{4} = -\frac{5}{4}$

Now divide:

$$
-\frac{5}{4} \div 9 = -\frac{5}{4} \cdot \frac{1}{9} = -\frac{5}{36}
$$

✔ Answer: $-\frac{5}{36}$

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9) $-1\frac{5}{7} \div -2\frac{1}{2}$

Convert to improper fractions:

- $-1\frac{5}{7} = -\frac{12}{7}$
- $-2\frac{1}{2} = -\frac{5}{2}$

Now divide:

$$
-\frac{12}{7} \div -\frac{5}{2} = \frac{12}{7} \cdot \frac{2}{5} = \frac{24}{35}
$$

✔ Answer: $\frac{24}{35}$

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10) $-2\frac{3}{8} \div 2\frac{1}{2}$

Convert to improper fractions:

- $-2\frac{3}{8} = -\frac{19}{8}$
- $2\frac{1}{2} = \frac{5}{2}$

Now divide:

$$
-\frac{19}{8} \div \frac{5}{2} = -\frac{19}{8} \cdot \frac{2}{5} = -\frac{38}{40} = -\frac{19}{20}
$$

(Simplified by dividing numerator and denominator by 2)

✔ Answer: $-\frac{19}{20}$

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✔ Final Answers:

1) $-\frac{5}{12}$
2) $1 \frac{31}{49}$
3) $\frac{16}{63}$
4) $-\frac{8}{15}$
5) $-\frac{6}{7}$
6) $-\frac{80}{123}$
7) $1 \frac{29}{35}$
8) $-\frac{5}{36}$
9) $\frac{24}{35}$
10) $-\frac{19}{20}$

Let me know if you'd like a printable version or step-by-step visuals!