Multiplying Fractions Worksheets with Answer Key - Free Printable

Problem: Multiplying Fractions

The task involves solving 18 multiplication problems involving fractions. Below, I will solve each problem step by step and provide the final answers.

---

#### Step-by-Step Solutions:

1. $\frac{7}{8} \times \frac{2}{15}$
- Multiply the numerators: $7 \times 2 = 14$
- Multiply the denominators: $8 \times 15 = 120$
- Simplify $\frac{14}{120}$ by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2:
$$
\frac{14 \div 2}{120 \div 2} = \frac{7}{60}
$$
- Answer: $\boxed{\frac{7}{60}}$

2. $\frac{2}{9} \times \frac{6}{18}$
- Multiply the numerators: $2 \times 6 = 12$
- Multiply the denominators: $9 \times 18 = 162$
- Simplify $\frac{12}{162}$ by dividing both numerator and denominator by their GCD, which is 6:
$$
\frac{12 \div 6}{162 \div 6} = \frac{2}{27}
$$
- Answer: $\boxed{\frac{2}{27}}$

3. $\frac{8}{15} \times \frac{5}{32}$
- Multiply the numerators: $8 \times 5 = 40$
- Multiply the denominators: $15 \times 32 = 480$
- Simplify $\frac{40}{480}$ by dividing both numerator and denominator by their GCD, which is 40:
$$
\frac{40 \div 40}{480 \div 40} = \frac{1}{12}
$$
- Answer: $\boxed{\frac{1}{12}}$

4. $\frac{11}{12} \times \frac{10}{22}$
- Multiply the numerators: $11 \times 10 = 110$
- Multiply the denominators: $12 \times 22 = 264$
- Simplify $\frac{110}{264}$ by dividing both numerator and denominator by their GCD, which is 22:
$$
\frac{110 \div 22}{264 \div 22} = \frac{5}{12}
$$
- Answer: $\boxed{\frac{5}{12}}$

5. $\frac{9}{10} \times \frac{2}{7}$
- Multiply the numerators: $9 \times 2 = 18$
- Multiply the denominators: $10 \times 7 = 70$
- Simplify $\frac{18}{70}$ by dividing both numerator and denominator by their GCD, which is 2:
$$
\frac{18 \div 2}{70 \div 2} = \frac{9}{35}
$$
- Answer: $\boxed{\frac{9}{35}}$

6. $\frac{5}{14} \times \frac{2}{5}$
- Multiply the numerators: $5 \times 2 = 10$
- Multiply the denominators: $14 \times 5 = 70$
- Simplify $\frac{10}{70}$ by dividing both numerator and denominator by their GCD, which is 10:
$$
\frac{10 \div 10}{70 \div 10} = \frac{1}{7}
$$
- Answer: $\boxed{\frac{1}{7}}$

7. $\frac{2}{3} \times \frac{7}{18}$
- Multiply the numerators: $2 \times 7 = 14$
- Multiply the denominators: $3 \times 18 = 54$
- Simplify $\frac{14}{54}$ by dividing both numerator and denominator by their GCD, which is 2:
$$
\frac{14 \div 2}{54 \div 2} = \frac{7}{27}
$$
- Answer: $\boxed{\frac{7}{27}}$

8. $\frac{5}{20} \times \frac{5}{8}$
- First, simplify $\frac{5}{20}$ to $\frac{1}{4}$ (since $5 \div 5 = 1$ and $20 \div 5 = 4$).
- Now multiply: $\frac{1}{4} \times \frac{5}{8}$
- Multiply the numerators: $1 \times 5 = 5$
- Multiply the denominators: $4 \times 8 = 32$
- The fraction $\frac{5}{32}$ is already in simplest form.
- Answer: $\boxed{\frac{5}{32}}$

9. $\frac{5}{6} \times \frac{3}{10}$
- Multiply the numerators: $5 \times 3 = 15$
- Multiply the denominators: $6 \times 10 = 60$
- Simplify $\frac{15}{60}$ by dividing both numerator and denominator by their GCD, which is 15:
$$
\frac{15 \div 15}{60 \div 15} = \frac{1}{4}
$$
- Answer: $\boxed{\frac{1}{4}}$

10. $\frac{1}{2} \times \frac{3}{24}$
- Multiply the numerators: $1 \times 3 = 3$
- Multiply the denominators: $2 \times 24 = 48$
- Simplify $\frac{3}{48}$ by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{3 \div 3}{48 \div 3} = \frac{1}{16}
$$
- Answer: $\boxed{\frac{1}{16}}$

11. $\frac{3}{10} \times \frac{5}{12}$
- Multiply the numerators: $3 \times 5 = 15$
- Multiply the denominators: $10 \times 12 = 120$
- Simplify $\frac{15}{120}$ by dividing both numerator and denominator by their GCD, which is 15:
$$
\frac{15 \div 15}{120 \div 15} = \frac{1}{8}
$$
- Answer: $\boxed{\frac{1}{8}}$

12. $\frac{3}{10} \times \frac{6}{15}$
- Multiply the numerators: $3 \times 6 = 18$
- Multiply the denominators: $10 \times 15 = 150$
- Simplify $\frac{18}{150}$ by dividing both numerator and denominator by their GCD, which is 6:
$$
\frac{18 \div 6}{150 \div 6} = \frac{3}{25}
$$
- Answer: $\boxed{\frac{3}{25}}$

13. $\frac{3}{15} \times \frac{5}{35}$
- First, simplify $\frac{3}{15}$ to $\frac{1}{5}$ (since $3 \div 3 = 1$ and $15 \div 3 = 5$).
- Then simplify $\frac{5}{35}$ to $\frac{1}{7}$ (since $5 \div 5 = 1$ and $35 \div 5 = 7$).
- Now multiply: $\frac{1}{5} \times \frac{1}{7}$
- Multiply the numerators: $1 \times 1 = 1$
- Multiply the denominators: $5 \times 7 = 35$
- The fraction $\frac{1}{35}$ is already in simplest form.
- Answer: $\boxed{\frac{1}{35}}$

14. $\frac{6}{4} \times \frac{5}{24}$
- First, simplify $\frac{6}{4}$ to $\frac{3}{2}$ (since $6 \div 2 = 3$ and $4 \div 2 = 2$).
- Now multiply: $\frac{3}{2} \times \frac{5}{24}$
- Multiply the numerators: $3 \times 5 = 15$
- Multiply the denominators: $2 \times 24 = 48$
- Simplify $\frac{15}{48}$ by dividing both numerator and denominator by their GCD, which is 3:
$$
\frac{15 \div 3}{48 \div 3} = \frac{5}{16}
$$
- Answer: $\boxed{\frac{5}{16}}$

15. $\frac{17}{18} \times \frac{12}{13}$
- Multiply the numerators: $17 \times 12 = 204$
- Multiply the denominators: $18 \times 13 = 234$
- Simplify $\frac{204}{234}$ by dividing both numerator and denominator by their GCD, which is 6:
$$
\frac{204 \div 6}{234 \div 6} = \frac{34}{39}
$$
- Answer: $\boxed{\frac{34}{39}}$

16. $\frac{2}{5} \times \frac{5}{14}$
- Multiply the numerators: $2 \times 5 = 10$
- Multiply the denominators: $5 \times 14 = 70$
- Simplify $\frac{10}{70}$ by dividing both numerator and denominator by their GCD, which is 10:
$$
\frac{10 \div 10}{70 \div 10} = \frac{1}{7}
$$
- Answer: $\boxed{\frac{1}{7}}$

17. $\frac{20}{21} \times \frac{6}{15}$
- First, simplify $\frac{6}{15}$ to $\frac{2}{5}$ (since $6 \div 3 = 2$ and $15 \div 3 = 5$).
- Now multiply: $\frac{20}{21} \times \frac{2}{5}$
- Multiply the numerators: $20 \times 2 = 40$
- Multiply the denominators: $21 \times 5 = 105$
- Simplify $\frac{40}{105}$ by dividing both numerator and denominator by their GCD, which is 5:
$$
\frac{40 \div 5}{105 \div 5} = \frac{8}{21}
$$
- Answer: $\boxed{\frac{8}{21}}$

18. $\frac{12}{15} \times \frac{3}{9}$
- First, simplify $\frac{12}{15}$ to $\frac{4}{5}$ (since $12 \div 3 = 4$ and $15 \div 3 = 5$).
- Then simplify $\frac{3}{9}$ to $\frac{1}{3}$ (since $3 \div 3 = 1$ and $9 \div 3 = 3$).
- Now multiply: $\frac{4}{5} \times \frac{1}{3}$
- Multiply the numerators: $4 \times 1 = 4$
- Multiply the denominators: $5 \times 3 = 15$
- The fraction $\frac{4}{15}$ is already in simplest form.
- Answer: $\boxed{\frac{4}{15}}$

---

Final Answers:

1. $\boxed{\frac{7}{60}}$
2. $\boxed{\frac{2}{27}}$
3. $\boxed{\frac{1}{12}}$
4. $\boxed{\frac{5}{12}}$
5. $\boxed{\frac{9}{35}}$
6. $\boxed{\frac{1}{7}}$
7. $\boxed{\frac{7}{27}}$
8. $\boxed{\frac{5}{32}}$
9. $\boxed{\frac{1}{4}}$
10. $\boxed{\frac{1}{16}}$
11. $\boxed{\frac{1}{8}}$
12. $\boxed{\frac{3}{25}}$
13. $\boxed{\frac{1}{35}}$
14. $\boxed{\frac{5}{16}}$
15. $\boxed{\frac{34}{39}}$
16. $\boxed{\frac{1}{7}}$
17. $\boxed{\frac{8}{21}}$
18. $\boxed{\frac{4}{15}}$

---

Final Answer Boxed:
$$
\boxed{
\begin{array}{ll}
1. & \frac{7}{60} \\
2. & \frac{2}{27} \\
3. & \frac{1}{12} \\
4. & \frac{5}{12} \\
5. & \frac{9}{35} \\
6. & \frac{1}{7} \\
7. & \frac{7}{27} \\
8. & \frac{5}{32} \\
9. & \frac{1}{4} \\
10. & \frac{1}{16} \\
11. & \frac{1}{8} \\
12. & \frac{3}{25} \\
13. & \frac{1}{35} \\
14. & \frac{5}{16} \\
15. & \frac{34}{39} \\
16. & \frac{1}{7} \\
17. & \frac{8}{21} \\
18. & \frac{4}{15} \\
\end{array}
}
$$