Multiplying Fractions Worksheets with Answer Key - Free Printable

Let's solve each problem step by step. We'll be multiplying fractions and mixed numbers. The general approach is:

1. Convert all mixed numbers to improper fractions.
2. Simplify if possible (cross-cancel).
3. Multiply the numerators and denominators.
4. Simplify the result and convert back to a mixed number if needed.

---

Problem 1:

$$
\frac{10}{35} \times 4\frac{3}{4}
$$

Step 1: Simplify $\frac{10}{35}$:
$$
\frac{10}{35} = \frac{2}{7}
$$

Step 2: Convert $4\frac{3}{4}$ to improper fraction:
$$
4\frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}
$$

Step 3: Multiply:
$$
\frac{2}{7} \times \frac{19}{4} = \frac{2 \times 19}{7 \times 4} = \frac{38}{28}
$$

Step 4: Simplify:
$$
\frac{38}{28} = \frac{19}{14} = 1\frac{5}{14}
$$

✔ Answer: $1\frac{5}{14}$

---

Problem 2:

$$
2\frac{2}{5} \times 2\frac{11}{12}
$$

Step 1: Convert both to improper fractions:

- $2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$
- $2\frac{11}{12} = \frac{2 \times 12 + 11}{12} = \frac{35}{12}$

Step 2: Multiply:
$$
\frac{12}{5} \times \frac{35}{12} = \frac{12 \times 35}{5 \times 12}
$$

Cancel common factors:
- 12 in numerator and denominator cancel → $1$
- 35 and 5: $35 \div 5 = 7$

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

✔ Answer: $7$

---

Problem 3:

$$
\frac{8}{15} \times 6\frac{1}{4}
$$

Step 1: Convert $6\frac{1}{4}$ to improper fraction:
$$
6\frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{25}{4}
$$

Step 2: Multiply:
$$
\frac{8}{15} \times \frac{25}{4} = \frac{8 \times 25}{15 \times 4} = \frac{200}{60}
$$

Step 3: Simplify:
- Divide numerator and denominator by 20:
$\frac{200 \div 20}{60 \div 20} = \frac{10}{3} = 3\frac{1}{3}$

✔ Answer: $3\frac{1}{3}$

---

Problem 4:

$$
\frac{20}{21} \times 2\frac{3}{4}
$$

Step 1: Convert $2\frac{3}{4}$:
$$
2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}
$$

Step 2: Multiply:
$$
\frac{20}{21} \times \frac{11}{4} = \frac{20 \times 11}{21 \times 4} = \frac{220}{84}
$$

Step 3: Simplify:
- Find GCF of 220 and 84: GCF = 4
- $\frac{220 \div 4}{84 \div 4} = \frac{55}{21} = 2\frac{13}{21}$

✔ Answer: $2\frac{13}{21}$

---

Problem 5:

$$
3\frac{3}{4} \times 4\frac{2}{9}
$$

Step 1: Convert both:

- $3\frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4}$
- $4\frac{2}{9} = \frac{4 \times 9 + 2}{9} = \frac{38}{9}$

Step 2: Multiply:
$$
\frac{15}{4} \times \frac{38}{9} = \frac{15 \times 38}{4 \times 9} = \frac{570}{36}
$$

Step 3: Simplify:
- GCF of 570 and 36: Let's divide both by 6:
- $570 \div 6 = 95$, $36 \div 6 = 6$ → $\frac{95}{6}$
- $\frac{95}{6} = 15\frac{5}{6}$

✔ Answer: $15\frac{5}{6}$

---

Problem 6:

$$
\frac{6}{15} \times 2\frac{8}{10}
$$

Step 1: Simplify $\frac{6}{15} = \frac{2}{5}$

Step 2: Simplify $2\frac{8}{10}$:
- $8/10 = 4/5$, so $2\frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{14}{5}$

Step 3: Multiply:
$$
\frac{2}{5} \times \frac{14}{5} = \frac{28}{25} = 1\frac{3}{25}
$$

✔ Answer: $1\frac{3}{25}$

---

Problem 7:

$$
\frac{12}{14} \times 7\frac{5}{8}
$$

Step 1: Simplify $\frac{12}{14} = \frac{6}{7}$

Step 2: Convert $7\frac{5}{8}$:
$$
7\frac{5}{8} = \frac{7 \times 8 + 5}{8} = \frac{61}{8}
$$

Step 3: Multiply:
$$
\frac{6}{7} \times \frac{61}{8} = \frac{6 \times 61}{7 \times 8} = \frac{366}{56}
$$

Step 4: Simplify:
- GCF of 366 and 56: Try dividing by 2 → $\frac{183}{28}$
- $183 \div 28 = 6$ remainder $15$ → $6\frac{15}{28}$

✔ Answer: $6\frac{15}{28}$

---

Problem 8:

$$
3\frac{6}{7} \times 3\frac{1}{6}
$$

Step 1: Convert both:

- $3\frac{6}{7} = \frac{3 \times 7 + 6}{7} = \frac{27}{7}$
- $3\frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6}$

Step 2: Multiply:
$$
\frac{27}{7} \times \frac{19}{6} = \frac{27 \times 19}{7 \times 6} = \frac{513}{42}
$$

Step 3: Simplify:
- GCF of 513 and 42: Try dividing by 3 → $513 \div 3 = 171$, $42 \div 3 = 14$ → $\frac{171}{14}$
- $171 \div 14 = 12$ remainder $3$ → $12\frac{3}{14}$

✔ Answer: $12\frac{3}{14}$

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✔ Final Answers:

1. $1\frac{5}{14}$
2. $7$
3. $3\frac{1}{3}$
4. $2\frac{13}{21}$
5. $15\frac{5}{6}$
6. $1\frac{3}{25}$
7. $6\frac{15}{28}$
8. $12\frac{3}{14}$

Let me know if you'd like these shown in a printable format!