Multiplying Fractions Worksheets with Answer Key - Free Printable

Let's solve each of these fraction multiplication problems step by step. The rule for multiplying fractions is:

> Multiply the numerators together and multiply the denominators together, then simplify if possible.

We'll go through each problem one by one.

---

1. $\frac{7}{8} \times \frac{2}{15}$

Multiply numerators: $7 \times 2 = 14$
Multiply denominators: $8 \times 15 = 120$

So, $\frac{14}{120}$

Simplify: Divide numerator and denominator by 2 → $\frac{7}{60}$

✔ Answer: $\boxed{\frac{7}{60}}$

---

2. $\frac{2}{9} \times \frac{6}{18}$

First simplify $\frac{6}{18} = \frac{1}{3}$

Now: $\frac{2}{9} \times \frac{1}{3} = \frac{2 \times 1}{9 \times 3} = \frac{2}{27}$

✔ Answer: $\boxed{\frac{2}{27}}$

---

3. $\frac{8}{15} \times \frac{5}{32}$

Look for simplifications:
- 8 and 32: $8 \div 8 = 1$, $32 \div 8 = 4$
- 5 and 15: $5 \div 5 = 1$, $15 \div 5 = 3$

So:
$$
\frac{8}{15} \times \frac{5}{32} = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}
$$

✔ Answer: $\boxed{\frac{1}{12}}$

---

4. $\frac{11}{12} \times \frac{10}{22}$

Simplify $\frac{10}{22} = \frac{5}{11}$

Now: $\frac{11}{12} \times \frac{5}{11}$

11 cancels out: $\frac{1}{12} \times \frac{5}{1} = \frac{5}{12}$

✔ Answer: $\boxed{\frac{5}{12}}$

---

5. $\frac{9}{10} \times \frac{2}{7}$

Multiply: $\frac{9 \times 2}{10 \times 7} = \frac{18}{70}$

Simplify: divide numerator and denominator by 2 → $\frac{9}{35}$

✔ Answer: $\boxed{\frac{9}{35}}$

---

6. $\frac{5}{14} \times \frac{2}{5}$

5 and 5 cancel: $5 \to 1$, $5 \to 1$
2 and 14: $2 \div 2 = 1$, $14 \div 2 = 7$

So: $\frac{1}{7} \times \frac{1}{1} = \frac{1}{7}$

✔ Answer: $\boxed{\frac{1}{7}}$

---

7. $\frac{2}{3} \times \frac{7}{18}$

Multiply: $\frac{2 \times 7}{3 \times 18} = \frac{14}{54}$

Simplify: divide by 2 → $\frac{7}{27}$

✔ Answer: $\boxed{\frac{7}{27}}$

---

8. $\frac{5}{20} \times \frac{5}{8}$

Simplify $\frac{5}{20} = \frac{1}{4}$

Now: $\frac{1}{4} \times \frac{5}{8} = \frac{5}{32}$

✔ Answer: $\boxed{\frac{5}{32}}$

---

9. $\frac{5}{6} \times \frac{3}{10}$

Simplify: 5 and 10 → $5 \to 1$, $10 \to 2$
3 and 6 → $3 \to 1$, $6 \to 2$

So: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

✔ Answer: $\boxed{\frac{1}{4}}$

---

10. $\frac{1}{2} \times \frac{3}{24}$

Simplify $\frac{3}{24} = \frac{1}{8}$

Now: $\frac{1}{2} \times \frac{1}{8} = \frac{1}{16}$

✔ Answer: $\boxed{\frac{1}{16}}$

---

11. $\frac{3}{10} \times \frac{5}{12}$

Simplify: 3 and 12 → $3 \to 1$, $12 \to 4$
5 and 10 → $5 \to 1$, $10 \to 2$

So: $\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$

✔ Answer: $\boxed{\frac{1}{8}}$

---

12. $\frac{3}{10} \times \frac{6}{15}$

Simplify $\frac{6}{15} = \frac{2}{5}$

Now: $\frac{3}{10} \times \frac{2}{5} = \frac{6}{50} = \frac{3}{25}$

✔ Answer: $\boxed{\frac{3}{25}}$

---

13. $\frac{3}{15} \times \frac{5}{35}$

Simplify:
- $\frac{3}{15} = \frac{1}{5}$
- $\frac{5}{35} = \frac{1}{7}$

Now: $\frac{1}{5} \times \frac{1}{7} = \frac{1}{35}$

✔ Answer: $\boxed{\frac{1}{35}}$

---

14. $\frac{6}{4} \times \frac{5}{24}$

Simplify $\frac{6}{4} = \frac{3}{2}$

Now: $\frac{3}{2} \times \frac{5}{24} = \frac{15}{48}$

Simplify: divide by 3 → $\frac{5}{16}$

✔ Answer: $\boxed{\frac{5}{16}}$

---

15. $\frac{17}{18} \times \frac{12}{13}$

No common factors between numerators/denominators.

Multiply: $\frac{17 \times 12}{18 \times 13} = \frac{204}{234}$

Simplify: divide numerator and denominator by 6 → $204 \div 6 = 34$, $234 \div 6 = 39$

So: $\frac{34}{39}$ (no more common factors)

✔ Answer: $\boxed{\frac{34}{39}}$

---

16. $\frac{2}{5} \times \frac{5}{14}$

5 cancels: $5 \to 1$, $5 \to 1$

So: $\frac{2}{1} \times \frac{1}{14} = \frac{2}{14} = \frac{1}{7}$

✔ Answer: $\boxed{\frac{1}{7}}$

---

17. $\frac{20}{21} \times \frac{6}{15}$

Simplify:
- $\frac{6}{15} = \frac{2}{5}$
- Now: $\frac{20}{21} \times \frac{2}{5}$

20 and 5: $20 \div 5 = 4$, $5 \div 5 = 1$

So: $\frac{4}{21} \times \frac{2}{1} = \frac{8}{21}$

✔ Answer: $\boxed{\frac{8}{21}}$

---

18. $\frac{12}{15} \times \frac{3}{9}$

Simplify:
- $\frac{12}{15} = \frac{4}{5}$
- $\frac{3}{9} = \frac{1}{3}$

Now: $\frac{4}{5} \times \frac{1}{3} = \frac{4}{15}$

✔ Answer: $\boxed{\frac{4}{15}}$

---

✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 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 | $\frac{4}{15}$ |

Let me know if you'd like this as a printable worksheet or with steps in a different format!