Multiplying Fractions Worksheets - Free Printable

Problem: Multiplying Fractions

The task involves interpreting illustrations and writing multiplication problems for fractions, then solving them. Below is a detailed explanation of each part:

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#### Part (a)
Illustration:
- The first row shows 3 groups of 2 shaded rectangles out of 5 total rectangles.
- The second row shows 1 group of 3 shaded rectangles out of 4 total rectangles.

Interpretation:
- The first fraction is \( \frac{2}{5} \) because there are 2 shaded parts out of 5 total parts in each group.
- The second fraction is \( \frac{3}{4} \) because there are 3 shaded parts out of 4 total parts in the second row.
- The problem is to multiply these two fractions: \( \frac{2}{5} \times \frac{3}{4} \).

Solution:
\[
\frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20}
\]
Simplify \( \frac{6}{20} \) by dividing the numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{6 \div 2}{20 \div 2} = \frac{3}{10}
\]

Answer:
\[
\boxed{\frac{3}{10}}
\]

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#### Part (b)
Illustration:
- The first row shows 1 group of 8 shaded squares out of 10 total squares.
- The second row shows 1 group of 5 shaded squares out of 8 total squares.

Interpretation:
- The first fraction is \( \frac{8}{10} \).
- The second fraction is \( \frac{5}{8} \).
- The problem is to multiply these two fractions: \( \frac{8}{10} \times \frac{5}{8} \).

Solution:
\[
\frac{8}{10} \times \frac{5}{8} = \frac{8 \times 5}{10 \times 8} = \frac{40}{80}
\]
Simplify \( \frac{40}{80} \) by dividing the numerator and denominator by their GCD, which is 40:
\[
\frac{40 \div 40}{80 \div 40} = \frac{1}{2}
\]

Answer:
\[
\boxed{\frac{1}{2}}
\]

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#### Part (c)
Illustration:
- The first row shows 1 group of 3 shaded squares out of 4 total squares.
- The second row shows 1 group of 2 shaded squares out of 3 total squares.

Interpretation:
- The first fraction is \( \frac{3}{4} \).
- The second fraction is \( \frac{2}{3} \).
- The problem is to multiply these two fractions: \( \frac{3}{4} \times \frac{2}{3} \).

Solution:
\[
\frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12}
\]
Simplify \( \frac{6}{12} \) by dividing the numerator and denominator by their GCD, which is 6:
\[
\frac{6 \div 6}{12 \div 6} = \frac{1}{2}
\]

Answer:
\[
\boxed{\frac{1}{2}}
\]

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#### Part (d)
Illustration:
- There are 3 circles, each divided into 4 equal parts.
- In the first circle, 2 parts are shaded.
- In the second circle, 1 part is shaded.
- In the third circle, 3 parts are shaded.

Interpretation:
- The first fraction is \( \frac{2}{4} \).
- The second fraction is \( \frac{1}{4} \).
- The third fraction is \( \frac{3}{4} \).
- The problem is to multiply these three fractions: \( \frac{2}{4} \times \frac{1}{4} \times \frac{3}{4} \).

Solution:
\[
\frac{2}{4} \times \frac{1}{4} \times \frac{3}{4} = \frac{2 \times 1 \times 3}{4 \times 4 \times 4} = \frac{6}{64}
\]
Simplify \( \frac{6}{64} \) by dividing the numerator and denominator by their GCD, which is 2:
\[
\frac{6 \div 2}{64 \div 2} = \frac{3}{32}
\]

Answer:
\[
\boxed{\frac{3}{32}}
\]

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#### Part (e)
Illustration:
- There are 5 rectangles, each divided into 6 equal parts.
- In the first rectangle, 4 parts are shaded.
- In the second rectangle, 3 parts are shaded.
- In the third rectangle, 2 parts are shaded.
- In the fourth rectangle, 1 part is shaded.
- In the fifth rectangle, 5 parts are shaded.

Interpretation:
- The first fraction is \( \frac{4}{6} \).
- The second fraction is \( \frac{3}{6} \).
- The third fraction is \( \frac{2}{6} \).
- The fourth fraction is \( \frac{1}{6} \).
- The fifth fraction is \( \frac{5}{6} \).
- The problem is to multiply these five fractions: \( \frac{4}{6} \times \frac{3}{6} \times \frac{2}{6} \times \frac{1}{6} \times \frac{5}{6} \).

Solution:
\[
\frac{4}{6} \times \frac{3}{6} \times \frac{2}{6} \times \frac{1}{6} \times \frac{5}{6} = \frac{4 \times 3 \times 2 \times 1 \times 5}{6 \times 6 \times 6 \times 6 \times 6} = \frac{120}{7776}
\]
Simplify \( \frac{120}{7776} \) by dividing the numerator and denominator by their GCD, which is 24:
\[
\frac{120 \div 24}{7776 \div 24} = \frac{5}{324}
\]

Answer:
\[
\boxed{\frac{5}{324}}
\]

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Final Answers:

\[
\boxed{\frac{3}{10}, \frac{1}{2}, \frac{1}{2}, \frac{3}{32}, \frac{5}{324}}
\]