Multiplying Fractions Worksheet - Free Printable

The image shows a worksheet titled "Multiplying Fractions Sheet 5," which contains several problems involving the multiplication of fractions. Below, I will solve each problem step by step and explain the process.

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Problem 1:

$$
\frac{2}{3} \times \frac{1}{4}
$$

Step 1: Multiply the numerators together.
$$
2 \times 1 = 2
$$

Step 2: Multiply the denominators together.
$$
3 \times 4 = 12
$$

Step 3: Write the resulting fraction.
$$
\frac{2}{12}
$$

Step 4: Simplify the fraction by finding the greatest common divisor (GCD) of 2 and 12, which is 2.
$$
\frac{2 \div 2}{12 \div 2} = \frac{1}{6}
$$

Final Answer:
$$
\boxed{\frac{1}{6}}
$$

---

Problem 2:

$$
\frac{3}{5} \times \frac{2}{7}
$$

Step 1: Multiply the numerators together.
$$
3 \times 2 = 6
$$

Step 2: Multiply the denominators together.
$$
5 \times 7 = 35
$$

Step 3: Write the resulting fraction.
$$
\frac{6}{35}
$$

Step 4: Check if the fraction can be simplified. Since 6 and 35 have no common factors other than 1, the fraction is already in its simplest form.

Final Answer:
$$
\boxed{\frac{6}{35}}
$$

---

Problem 3:

$$
\frac{5}{8} \times \frac{4}{9}
$$

Step 1: Multiply the numerators together.
$$
5 \times 4 = 20
$$

Step 2: Multiply the denominators together.
$$
8 \times 9 = 72
$$

Step 3: Write the resulting fraction.
$$
\frac{20}{72}
$$

Step 4: Simplify the fraction by finding the GCD of 20 and 72, which is 4.
$$
\frac{20 \div 4}{72 \div 4} = \frac{5}{18}
$$

Final Answer:
$$
\boxed{\frac{5}{18}}
$$

---

Problem 4:

$$
\frac{7}{10} \times \frac{5}{6}
$$

Step 1: Multiply the numerators together.
$$
7 \times 5 = 35
$$

Step 2: Multiply the denominators together.
$$
10 \times 6 = 60
$$

Step 3: Write the resulting fraction.
$$
\frac{35}{60}
$$

Step 4: Simplify the fraction by finding the GCD of 35 and 60, which is 5.
$$
\frac{35 \div 5}{60 \div 5} = \frac{7}{12}
$$

Final Answer:
$$
\boxed{\frac{7}{12}}
$$

---

Problem 5:

$$
\frac{3}{4} \times \frac{2}{3} \times \frac{1}{2}
$$

Step 1: Multiply the first two fractions.
$$
\frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12}
$$

Step 2: Simplify the intermediate result.
$$
\frac{6}{12} = \frac{1}{2}
$$

Step 3: Multiply the simplified result by the third fraction.
$$
\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}
$$

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

---

Problem 6:

$$
\frac{5}{6} \times \frac{3}{4} \times \frac{2}{5}
$$

Step 1: Multiply the first two fractions.
$$
\frac{5}{6} \times \frac{3}{4} = \frac{5 \times 3}{6 \times 4} = \frac{15}{24}
$$

Step 2: Simplify the intermediate result.
$$
\frac{15}{24} = \frac{5}{8}
$$

Step 3: Multiply the simplified result by the third fraction.
$$
\frac{5}{8} \times \frac{2}{5} = \frac{5 \times 2}{8 \times 5} = \frac{10}{40}
$$

Step 4: Simplify the final result.
$$
\frac{10}{40} = \frac{1}{4}
$$

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

---

Problem 7:

$$
\frac{4}{7} \times \frac{7}{8} \times \frac{2}{3}
$$

Step 1: Multiply the first two fractions.
$$
\frac{4}{7} \times \frac{7}{8} = \frac{4 \times 7}{7 \times 8} = \frac{28}{56}
$$

Step 2: Simplify the intermediate result.
$$
\frac{28}{56} = \frac{1}{2}
$$

Step 3: Multiply the simplified result by the third fraction.
$$
\frac{1}{2} \times \frac{2}{3} = \frac{1 \times 2}{2 \times 3} = \frac{2}{6}
$$

Step 4: Simplify the final result.
$$
\frac{2}{6} = \frac{1}{3}
$$

Final Answer:
$$
\boxed{\frac{1}{3}}
$$

---

Problem 8:

$$
\frac{3}{5} \times \frac{5}{6} \times \frac{2}{3}
$$

Step 1: Multiply the first two fractions.
$$
\frac{3}{5} \times \frac{5}{6} = \frac{3 \times 5}{5 \times 6} = \frac{15}{30}
$$

Step 2: Simplify the intermediate result.
$$
\frac{15}{30} = \frac{1}{2}
$$

Step 3: Multiply the simplified result by the third fraction.
$$
\frac{1}{2} \times \frac{2}{3} = \frac{1 \times 2}{2 \times 3} = \frac{2}{6}
$$

Step 4: Simplify the final result.
$$
\frac{2}{6} = \frac{1}{3}
$$

Final Answer:
$$
\boxed{\frac{1}{3}}
$$

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Final Answers:

1. $\boxed{\frac{1}{6}}$
2. $\boxed{\frac{6}{35}}$
3. $\boxed{\frac{5}{18}}$
4. $\boxed{\frac{7}{12}}$
5. $\boxed{\frac{1}{4}}$
6. $\boxed{\frac{1}{4}}$
7. $\boxed{\frac{1}{3}}$
8. $\boxed{\frac{1}{3}}$

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Thus, the complete set of answers is:
$$
\boxed{\frac{1}{6}, \frac{6}{35}, \frac{5}{18}, \frac{7}{12}, \frac{1}{4}, \frac{1}{4}, \frac{1}{3}, \frac{1}{3}}
$$