Multiplication and division of fractions activity worksheet | Live ... - Free Printable

Problem: Solve the multiplication and division of fractions problems and simplify each answer.

#### Step-by-Step Solutions:

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Section 1: Multiplication Problems (Questions 1–10)

#### 1. $\frac{2}{3} \times \frac{3}{8}$
- Multiply the numerators: $2 \times 3 = 6$
- Multiply the denominators: $3 \times 8 = 24$
- Simplify: $\frac{6}{24} = \frac{1}{4}$

Answer: $\boxed{\frac{1}{4}}$

#### 2. $\frac{6}{11} \times \frac{33}{4}$
- Multiply the numerators: $6 \times 33 = 198$
- Multiply the denominators: $11 \times 4 = 44$
- Simplify: $\frac{198}{44} = \frac{9}{2}$

Answer: $\boxed{\frac{9}{2}}$

#### 3. $\left(\frac{-4}{5}\right) \times \left(\frac{-5}{3}\right)$
- Multiply the numerators: $(-4) \times (-5) = 20$
- Multiply the denominators: $5 \times 3 = 15$
- Simplify: $\frac{20}{15} = \frac{4}{3}$

Answer: $\boxed{\frac{4}{3}}$

#### 4. $3 \times \frac{5}{12}$
- Write $3$ as a fraction: $\frac{3}{1}$
- Multiply the numerators: $3 \times 5 = 15$
- Multiply the denominators: $1 \times 12 = 12$
- Simplify: $\frac{15}{12} = \frac{5}{4}$

Answer: $\boxed{\frac{5}{4}}$

#### 5. $\frac{5}{6} \times 24$
- Write $24$ as a fraction: $\frac{24}{1}$
- Multiply the numerators: $5 \times 24 = 120$
- Multiply the denominators: $6 \times 1 = 6$
- Simplify: $\frac{120}{6} = 20$

Answer: $\boxed{20}$

#### 6. $\frac{3}{4} \times 2\frac{1}{2}$
- Convert $2\frac{1}{2}$ to an improper fraction: $2\frac{1}{2} = \frac{5}{2}$
- Multiply the numerators: $3 \times 5 = 15$
- Multiply the denominators: $4 \times 2 = 8$
- Simplify: $\frac{15}{8}$

Answer: $\boxed{\frac{15}{8}}$

#### 7. $-2\frac{1}{4} \times \frac{11}{6}$
- Convert $-2\frac{1}{4}$ to an improper fraction: $-2\frac{1}{4} = -\frac{9}{4}$
- Multiply the numerators: $(-9) \times 11 = -99$
- Multiply the denominators: $4 \times 6 = 24$
- Simplify: $\frac{-99}{24} = \frac{-33}{8}$

Answer: $\boxed{\frac{-33}{8}}$

#### 8. $1\frac{1}{4} \times 2\frac{2}{5}$
- Convert $1\frac{1}{4}$ to an improper fraction: $1\frac{1}{4} = \frac{5}{4}$
- Convert $2\frac{2}{5}$ to an improper fraction: $2\frac{2}{5} = \frac{12}{5}$
- Multiply the numerators: $5 \times 12 = 60$
- Multiply the denominators: $4 \times 5 = 20$
- Simplify: $\frac{60}{20} = 3$

Answer: $\boxed{3}$

#### 9. $-2\frac{2}{3} \times 1\frac{3}{4}$
- Convert $-2\frac{2}{3}$ to an improper fraction: $-2\frac{2}{3} = -\frac{8}{3}$
- Convert $1\frac{3}{4}$ to an improper fraction: $1\frac{3}{4} = \frac{7}{4}$
- Multiply the numerators: $(-8) \times 7 = -56$
- Multiply the denominators: $3 \times 4 = 12$
- Simplify: $\frac{-56}{12} = \frac{-14}{3}$

Answer: $\boxed{\frac{-14}{3}}$

#### 10. $\left(-3\frac{1}{3}\right) \times \left(-1\frac{1}{2}\right)$
- Convert $-3\frac{1}{3}$ to an improper fraction: $-3\frac{1}{3} = -\frac{10}{3}$
- Convert $-1\frac{1}{2}$ to an improper fraction: $-1\frac{1}{2} = -\frac{3}{2}$
- Multiply the numerators: $(-10) \times (-3) = 30$
- Multiply the denominators: $3 \times 2 = 6$
- Simplify: $\frac{30}{6} = 5$

Answer: $\boxed{5}$

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Section 2: Division Problems (Questions 11–20)

#### 11. $\frac{8}{9} \div \frac{2}{3}$
- Flip the second fraction and multiply: $\frac{8}{9} \times \frac{3}{2}$
- Multiply the numerators: $8 \times 3 = 24$
- Multiply the denominators: $9 \times 2 = 18$
- Simplify: $\frac{24}{18} = \frac{4}{3}$

Answer: $\boxed{\frac{4}{3}}$

#### 12. $\frac{6}{8} \div \frac{2}{6}$
- Flip the second fraction and multiply: $\frac{6}{8} \times \frac{6}{2}$
- Multiply the numerators: $6 \times 6 = 36$
- Multiply the denominators: $8 \times 2 = 16$
- Simplify: $\frac{36}{16} = \frac{9}{4}$

Answer: $\boxed{\frac{9}{4}}$

#### 13. $\frac{-5}{8} \div \frac{7}{9}$
- Flip the second fraction and multiply: $\frac{-5}{8} \times \frac{9}{7}$
- Multiply the numerators: $(-5) \times 9 = -45$
- Multiply the denominators: $8 \times 7 = 56$
- Simplify: $\frac{-45}{56}$

Answer: $\boxed{\frac{-45}{56}}$

#### 14. $2\frac{1}{5} \div 3\frac{2}{10}$
- Convert $2\frac{1}{5}$ to an improper fraction: $2\frac{1}{5} = \frac{11}{5}$
- Convert $3\frac{2}{10}$ to an improper fraction: $3\frac{2}{10} = \frac{32}{10} = \frac{16}{5}$
- Flip the second fraction and multiply: $\frac{11}{5} \times \frac{5}{16}$
- Multiply the numerators: $11 \times 5 = 55$
- Multiply the denominators: $5 \times 16 = 80$
- Simplify: $\frac{55}{80} = \frac{11}{16}$

Answer: $\boxed{\frac{11}{16}}$

#### 15. $3\frac{3}{4} \div 2\frac{2}{3}$
- Convert $3\frac{3}{4}$ to an improper fraction: $3\frac{3}{4} = \frac{15}{4}$
- Convert $2\frac{2}{3}$ to an improper fraction: $2\frac{2}{3} = \frac{8}{3}$
- Flip the second fraction and multiply: $\frac{15}{4} \times \frac{3}{8}$
- Multiply the numerators: $15 \times 3 = 45$
- Multiply the denominators: $4 \times 8 = 32$
- Simplify: $\frac{45}{32}$

Answer: $\boxed{\frac{45}{32}}$

#### 16. $\frac{-5}{8} \div (-25)$
- Write $-25$ as a fraction: $-25 = \frac{-25}{1}$
- Flip the second fraction and multiply: $\frac{-5}{8} \times \frac{1}{-25}$
- Multiply the numerators: $(-5) \times 1 = -5$
- Multiply the denominators: $8 \times (-25) = -200$
- Simplify: $\frac{-5}{-200} = \frac{1}{40}$

Answer: $\boxed{\frac{1}{40}}$

#### 17. $\frac{8}{3} \div 3\frac{2}{3}$
- Convert $3\frac{2}{3}$ to an improper fraction: $3\frac{2}{3} = \frac{11}{3}$
- Flip the second fraction and multiply: $\frac{8}{3} \times \frac{3}{11}$
- Multiply the numerators: $8 \times 3 = 24$
- Multiply the denominators: $3 \times 11 = 33$
- Simplify: $\frac{24}{33} = \frac{8}{11}$

Answer: $\boxed{\frac{8}{11}}$

#### 18. $(-4) \div 2\frac{2}{5}$
- Write $-4$ as a fraction: $-4 = \frac{-4}{1}$
- Convert $2\frac{2}{5}$ to an improper fraction: $2\frac{2}{5} = \frac{12}{5}$
- Flip the second fraction and multiply: $\frac{-4}{1} \times \frac{5}{12}$
- Multiply the numerators: $(-4) \times 5 = -20$
- Multiply the denominators: $1 \times 12 = 12$
- Simplify: $\frac{-20}{12} = \frac{-5}{3}$

Answer: $\boxed{\frac{-5}{3}}$

#### 19. $2\frac{1}{4} \div 2\frac{2}{6}$
- Convert $2\frac{1}{4}$ to an improper fraction: $2\frac{1}{4} = \frac{9}{4}$
- Convert $2\frac{2}{6}$ to an improper fraction: $2\frac{2}{6} = \frac{14}{6} = \frac{7}{3}$
- Flip the second fraction and multiply: $\frac{9}{4} \times \frac{3}{7}$
- Multiply the numerators: $9 \times 3 = 27$
- Multiply the denominators: $4 \times 7 = 28$
- Simplify: $\frac{27}{28}$

Answer: $\boxed{\frac{27}{28}}$

#### 20. $-7\frac{1}{5} \div 3\frac{3}{4}$
- Convert $-7\frac{1}{5}$ to an improper fraction: $-7\frac{1}{5} = -\frac{36}{5}$
- Convert $3\frac{3}{4}$ to an improper fraction: $3\frac{3}{4} = \frac{15}{4}$
- Flip the second fraction and multiply: $\frac{-36}{5} \times \frac{4}{15}$
- Multiply the numerators: $(-36) \times 4 = -144$
- Multiply the denominators: $5 \times 15 = 75$
- Simplify: $\frac{-144}{75} = \frac{-48}{25}$

Answer: $\boxed{\frac{-48}{25}}$

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Final Answers:

1. $\boxed{\frac{1}{4}}$
2. $\boxed{\frac{9}{2}}$
3. $\boxed{\frac{4}{3}}$
4. $\boxed{\frac{5}{4}}$
5. $\boxed{20}$
6. $\boxed{\frac{15}{8}}$
7. $\boxed{\frac{-33}{8}}$
8. $\boxed{3}$
9. $\boxed{\frac{-14}{3}}$
10. $\boxed{5}$
11. $\boxed{\frac{4}{3}}$
12. $\boxed{\frac{9}{4}}$
13. $\boxed{\frac{-45}{56}}$
14. $\boxed{\frac{11}{16}}$
15. $\boxed{\frac{45}{32}}$
16. $\boxed{\frac{1}{40}}$
17. $\boxed{\frac{8}{11}}$
18. $\boxed{\frac{-5}{3}}$
19. $\boxed{\frac{27}{28}}$
20. $\boxed{\frac{-48}{25}}$

Boxed Final Answer:
$$
\boxed{
\begin{array}{ll}
1. & \frac{1}{4} \\
2. & \frac{9}{2} \\
3. & \frac{4}{3} \\
4. & \frac{5}{4} \\
5. & 20 \\
6. & \frac{15}{8} \\
7. & \frac{-33}{8} \\
8. & 3 \\
9. & \frac{-14}{3} \\
10. & 5 \\
11. & \frac{4}{3} \\
12. & \frac{9}{4} \\
13. & \frac{-45}{56} \\
14. & \frac{11}{16} \\
15. & \frac{45}{32} \\
16. & \frac{1}{40} \\
17. & \frac{8}{11} \\
18. & \frac{-5}{3} \\
19. & \frac{27}{28} \\
20. & \frac{-48}{25} \\
\end{array}
}
$$