Printable worksheet featuring 14 multiplication problems involving fractions for student practice.

Problem: Multiplying Fractions

The task involves multiplying pairs of fractions. The general rule for multiplying fractions is:

\[
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
\]

We will solve each problem step by step.

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#### 1. \( \frac{2}{3} \times \frac{4}{5} \)

\[
\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}
\]

#### 2. \( \frac{3}{7} \times \frac{5}{6} \)

\[
\frac{3}{7} \times \frac{5}{6} = \frac{3 \times 5}{7 \times 6} = \frac{15}{42}
\]

Simplify the fraction by finding the greatest common divisor (GCD) of 15 and 42, which is 3:

\[
\frac{15 \div 3}{42 \div 3} = \frac{5}{14}
\]

#### 3. \( \frac{5}{8} \times \frac{7}{9} \)

\[
\frac{5}{8} \times \frac{7}{9} = \frac{5 \times 7}{8 \times 9} = \frac{35}{72}
\]

#### 4. \( \frac{3}{4} \times \frac{12}{15} \)

\[
\frac{3}{4} \times \frac{12}{15} = \frac{3 \times 12}{4 \times 15} = \frac{36}{60}
\]

Simplify the fraction by finding the GCD of 36 and 60, which is 12:

\[
\frac{36 \div 12}{60 \div 12} = \frac{3}{5}
\]

#### 5. \( \frac{7}{9} \times \frac{3}{4} \)

\[
\frac{7}{9} \times \frac{3}{4} = \frac{7 \times 3}{9 \times 4} = \frac{21}{36}
\]

Simplify the fraction by finding the GCD of 21 and 36, which is 3:

\[
\frac{21 \div 3}{36 \div 3} = \frac{7}{12}
\]

#### 6. \( \frac{1}{2} \times \frac{1}{3} \)

\[
\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}
\]

#### 7. \( \frac{2}{5} \times \frac{3}{7} \)

\[
\frac{2}{5} \times \frac{3}{7} = \frac{2 \times 3}{5 \times 7} = \frac{6}{35}
\]

#### 8. \( \frac{4}{9} \times \frac{2}{3} \)

\[
\frac{4}{9} \times \frac{2}{3} = \frac{4 \times 2}{9 \times 3} = \frac{8}{27}
\]

#### 9. \( \frac{1}{3} \times \frac{2}{5} \)

\[
\frac{1}{3} \times \frac{2}{5} = \frac{1 \times 2}{3 \times 5} = \frac{2}{15}
\]

#### 10. \( \frac{7}{2} \times \frac{2}{9} \)

\[
\frac{7}{2} \times \frac{2}{9} = \frac{7 \times 2}{2 \times 9} = \frac{14}{18}
\]

Simplify the fraction by finding the GCD of 14 and 18, which is 2:

\[
\frac{14 \div 2}{18 \div 2} = \frac{7}{9}
\]

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Final Answers:

1. \( \frac{2}{3} \times \frac{4}{5} = \boxed{\frac{8}{15}} \)
2. \( \frac{3}{7} \times \frac{5}{6} = \boxed{\frac{5}{14}} \)
3. \( \frac{5}{8} \times \frac{7}{9} = \boxed{\frac{35}{72}} \)
4. \( \frac{3}{4} \times \frac{12}{15} = \boxed{\frac{3}{5}} \)
5. \( \frac{7}{9} \times \frac{3}{4} = \boxed{\frac{7}{12}} \)
6. \( \frac{1}{2} \times \frac{1}{3} = \boxed{\frac{1}{6}} \)
7. \( \frac{2}{5} \times \frac{3}{7} = \boxed{\frac{6}{35}} \)
8. \( \frac{4}{9} \times \frac{2}{3} = \boxed{\frac{8}{27}} \)
9. \( \frac{1}{3} \times \frac{2}{5} = \boxed{\frac{2}{15}} \)
10. \( \frac{7}{2} \times \frac{2}{9} = \boxed{\frac{7}{9}} \)

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Thus, the final boxed answers are:

\[
\boxed{\frac{8}{15}, \frac{5}{14}, \frac{35}{72}, \frac{3}{5}, \frac{7}{12}, \frac{1}{6}, \frac{6}{35}, \frac{8}{27}, \frac{2}{15}, \frac{7}{9}}
\]