Math worksheet for practicing multiplying and dividing fractions, featuring 12 problems with fractions and mixed numbers.

I'll solve each problem step by step, showing the work for multiplying and dividing fractions.

Problem 1: $\frac{1}{3} \times \frac{2}{4}$
- Multiply numerators: $1 \times 2 = 2$
- Multiply denominators: $3 \times 4 = 12$
- Result: $\frac{2}{12}$
- Simplify: $\frac{2}{12} = \frac{1}{6}$

Problem 2: $\frac{1}{4} \times \frac{2}{3}$
- Multiply numerators: $1 \times 2 = 2$
- Multiply denominators: $4 \times 3 = 12$
- Result: $\frac{2}{12}$
- Simplify: $\frac{2}{12} = \frac{1}{6}$

Problem 3: $2 \times \frac{1}{4}$
- Write 2 as a fraction: $\frac{2}{1}$
- Multiply: $\frac{2}{1} \times \frac{1}{4} = \frac{2}{4}$
- Simplify: $\frac{2}{4} = \frac{1}{2}$

Problem 4: $3 \times \frac{4}{5}$
- Write 3 as a fraction: $\frac{3}{1}$
- Multiply: $\frac{3}{1} \times \frac{4}{5} = \frac{12}{5}$
- Convert to mixed number: $2\frac{2}{5}$

Problem 5: $\frac{1}{3} \times 4$
- Write 4 as a fraction: $\frac{4}{1}$
- Multiply: $\frac{1}{3} \times \frac{4}{1} = \frac{4}{3}$
- Convert to mixed number: $1\frac{1}{3}$

Problem 6: $2\frac{1}{3} \times \frac{1}{4}$
- Convert mixed number to improper fraction: $2\frac{1}{3} = \frac{7}{3}$
- Multiply: $\frac{7}{3} \times \frac{1}{4} = \frac{7}{12}$

Problem 7: $1\frac{1}{3} \times 2\frac{1}{4}$
- Convert to improper fractions: $1\frac{1}{3} = \frac{4}{3}$ and $2\frac{1}{4} = \frac{9}{4}$
- Multiply: $\frac{4}{3} \times \frac{9}{4} = \frac{36}{12}$
- Simplify: $\frac{36}{12} = 3$

Problem 8: $1\frac{1}{2} \times 2\frac{1}{5}$
- Convert to improper fractions: $1\frac{1}{2} = \frac{3}{2}$ and $2\frac{1}{5} = \frac{11}{5}$
- Multiply: $\frac{3}{2} \times \frac{11}{5} = \frac{33}{10}$
- Convert to mixed number: $3\frac{3}{10}$

Problem 9: $\frac{2}{5} \div 5$
- Dividing by 5 is the same as multiplying by $\frac{1}{5}$
- $\frac{2}{5} \times \frac{1}{5} = \frac{2}{25}$

Problem 10: $\frac{3}{4} \div 3$
- Dividing by 3 is the same as multiplying by $\frac{1}{3}$
- $\frac{3}{4} \times \frac{1}{3} = \frac{3}{12}$
- Simplify: $\frac{3}{12} = \frac{1}{4}$

Problem 11: $5 \div \frac{4}{6}$
- To divide by a fraction, multiply by its reciprocal
- Reciprocal of $\frac{4}{6}$ is $\frac{6}{4}$
- $5 \times \frac{6}{4} = \frac{30}{4}$
- Simplify: $\frac{30}{4} = \frac{15}{2} = 7\frac{1}{2}$

Problem 12: $3 \div \frac{1}{4}$
- To divide by a fraction, multiply by its reciprocal
- Reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$ or just 4
- $3 \times 4 = 12$

Final Answer:
1. $\frac{1}{6}$
2. $\frac{1}{6}$
3. $\frac{1}{2}$
4. $2\frac{2}{5}$
5. $1\frac{1}{3}$
6. $\frac{7}{12}$
7. $3$
8. $3\frac{3}{10}$
9. $\frac{2}{25}$
10. $\frac{1}{4}$
11. $7\frac{1}{2}$
12. $12$