Multiplying Fractions Worksheets with Answer Key - Free Printable

To solve the given problems involving multiplying fractions with cross canceling, we will follow these steps:

1. Identify common factors between the numerators and denominators.
2. Cancel out the common factors.
3. Multiply the remaining numerators together.
4. Multiply the remaining denominators together.
5. Simplify the resulting fraction if necessary.

Let's solve each problem step by step.

---

Problem 1:

$$
\frac{2}{12} \times \frac{3}{6}
$$

- Step 1: Identify common factors.
- Between 2 and 6: \(2\) is a common factor.
- Between 3 and 12: \(3\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{2}{12} \times \frac{3}{6} = \frac{1}{6} \times \frac{1}{2}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 1}{6 \times 2} = \frac{1}{12}
$$

- Final Answer:
$$
\boxed{\frac{1}{12}}
$$

---

Problem 2:

$$
\frac{5}{6} \times \frac{12}{20}
$$

- Step 1: Identify common factors.
- Between 5 and 20: \(5\) is a common factor.
- Between 6 and 12: \(6\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{5}{6} \times \frac{12}{20} = \frac{1}{1} \times \frac{2}{4} = \frac{1}{1} \times \frac{1}{2}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 1}{1 \times 2} = \frac{1}{2}
$$

- Final Answer:
$$
\boxed{\frac{1}{2}}
$$

---

Problem 3:

$$
\frac{4}{10} \times \frac{6}{9}
$$

- Step 1: Identify common factors.
- Between 4 and 9: No common factors.
- Between 6 and 10: \(2\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{4}{10} \times \frac{6}{9} = \frac{4}{5} \times \frac{3}{9}
$$

- Step 3: Further simplify \(\frac{3}{9}\) to \(\frac{1}{3}\).
$$
\frac{4}{5} \times \frac{1}{3}
$$

- Step 4: Multiply the remaining numerators and denominators.
$$
\frac{4 \times 1}{5 \times 3} = \frac{4}{15}
$$

- Final Answer:
$$
\boxed{\frac{4}{15}}
$$

---

Problem 4:

$$
\frac{8}{21} \times \frac{14}{4}
$$

- Step 1: Identify common factors.
- Between 8 and 4: \(4\) is a common factor.
- Between 14 and 21: \(7\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{8}{21} \times \frac{14}{4} = \frac{2}{21} \times \frac{2}{1} = \frac{2}{3} \times \frac{2}{1}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{2 \times 2}{3 \times 1} = \frac{4}{3}
$$

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

---

Problem 5:

$$
\frac{2}{10} \times \frac{20}{8}
$$

- Step 1: Identify common factors.
- Between 2 and 8: \(2\) is a common factor.
- Between 10 and 20: \(10\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{2}{10} \times \frac{20}{8} = \frac{1}{5} \times \frac{2}{4} = \frac{1}{5} \times \frac{1}{2}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 1}{5 \times 2} = \frac{1}{10}
$$

- Final Answer:
$$
\boxed{\frac{1}{10}}
$$

---

Problem 6:

$$
\frac{5}{12} \times \frac{9}{20}
$$

- Step 1: Identify common factors.
- Between 5 and 20: \(5\) is a common factor.
- Between 9 and 12: \(3\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{5}{12} \times \frac{9}{20} = \frac{1}{4} \times \frac{3}{4}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 3}{4 \times 4} = \frac{3}{16}
$$

- Final Answer:
$$
\boxed{\frac{3}{16}}
$$

---

Problem 7:

$$
\frac{4}{20} \times \frac{4}{7}
$$

- Step 1: Identify common factors.
- Between 4 and 20: \(4\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{4}{20} \times \frac{4}{7} = \frac{1}{5} \times \frac{4}{7}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 4}{5 \times 7} = \frac{4}{35}
$$

- Final Answer:
$$
\boxed{\frac{4}{35}}
$$

---

Problem 8:

$$
\frac{18}{21} \times \frac{7}{4}
$$

- Step 1: Identify common factors.
- Between 18 and 4: No common factors.
- Between 21 and 7: \(7\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{18}{21} \times \frac{7}{4} = \frac{18}{3} \times \frac{1}{4} = \frac{6}{1} \times \frac{1}{4}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{6 \times 1}{1 \times 4} = \frac{6}{4} = \frac{3}{2}
$$

- Final Answer:
$$
\boxed{\frac{3}{2}}
$$

---

Problem 9:

$$
\frac{4}{6} \times \frac{3}{5}
$$

- Step 1: Identify common factors.
- Between 4 and 5: No common factors.
- Between 6 and 3: \(3\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{4}{6} \times \frac{3}{5} = \frac{4}{2} \times \frac{1}{5} = \frac{2}{1} \times \frac{1}{5}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{2 \times 1}{1 \times 5} = \frac{2}{5}
$$

- Final Answer:
$$
\boxed{\frac{2}{5}}
$$

---

Problem 10:

$$
\frac{3}{11} \times \frac{22}{9}
$$

- Step 1: Identify common factors.
- Between 3 and 9: \(3\) is a common factor.
- Between 11 and 22: \(11\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{3}{11} \times \frac{22}{9} = \frac{1}{1} \times \frac{2}{3} = \frac{2}{3}
$$

- Final Answer:
$$
\boxed{\frac{2}{3}}
$$

---

Problem 11:

$$
\frac{8}{12} \times \frac{4}{7}
$$

- Step 1: Identify common factors.
- Between 8 and 12: \(4\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{8}{12} \times \frac{4}{7} = \frac{2}{3} \times \frac{4}{7}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{2 \times 4}{3 \times 7} = \frac{8}{21}
$$

- Final Answer:
$$
\boxed{\frac{8}{21}}
$$

---

Problem 12:

$$
\frac{6}{12} \times \frac{18}{30}
$$

- Step 1: Identify common factors.
- Between 6 and 30: \(6\) is a common factor.
- Between 12 and 18: \(6\) is a common factor.

- Step 2: Cancel out the common factors.
$$
\frac{6}{12} \times \frac{18}{30} = \frac{1}{2} \times \frac{3}{5}
$$

- Step 3: Multiply the remaining numerators and denominators.
$$
\frac{1 \times 3}{2 \times 5} = \frac{3}{10}
$$

- Final Answer:
$$
\boxed{\frac{3}{10}}
$$

---

Final Answers:

1. \(\boxed{\frac{1}{12}}\)
2. \(\boxed{\frac{1}{2}}\)
3. \(\boxed{\frac{4}{15}}\)
4. \(\boxed{\frac{4}{3}}\)
5. \(\boxed{\frac{1}{10}}\)
6. \(\boxed{\frac{3}{16}}\)
7. \(\boxed{\frac{4}{35}}\)
8. \(\boxed{\frac{3}{2}}\)
9. \(\boxed{\frac{2}{5}}\)
10. \(\boxed{\frac{2}{3}}\)
11. \(\boxed{\frac{8}{21}}\)
12. \(\boxed{\frac{3}{10}}\)