Multiplying Fractions Worksheets with Answer Key - Free Printable

To solve the problem of multiplying fractions using the area model, we need to follow these steps:

1. Understand the Area Model: The area model represents fractions as parts of a whole rectangle. Each fraction is shown by shading a portion of the rectangle.
2. Identify the Fractions: Determine the two fractions being multiplied by observing the shaded areas in the rectangle.
3. Calculate the Product: Multiply the numerators together and the denominators together to find the product of the fractions.
4. Verify with the Shaded Area: Ensure that the shaded area in the resulting rectangle corresponds to the calculated product.

Let's solve each problem step by step:

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Problem ②:

- Fractions: $\frac{2}{5} \times \frac{3}{4}$
- Steps:
- The first fraction $\frac{2}{5}$ is represented by 2 out of 5 columns shaded.
- The second fraction $\frac{3}{4}$ is represented by 3 out of 4 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10}$.
- Answer: $\frac{3}{10}$

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Problem ③:

- Fractions: $\frac{2}{5} \times \frac{5}{8}$
- Steps:
- The first fraction $\frac{2}{5}$ is represented by 2 out of 5 columns shaded.
- The second fraction $\frac{5}{8}$ is represented by 5 out of 8 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{2}{5} \times \frac{5}{8} = \frac{2 \times 5}{5 \times 8} = \frac{10}{40} = \frac{1}{4}$.
- Answer: $\frac{1}{4}$

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Problem ④:

- Fractions: $\frac{4}{12} \times \frac{2}{3}$
- Steps:
- The first fraction $\frac{4}{12}$ is represented by 4 out of 12 columns shaded.
- The second fraction $\frac{2}{3}$ is represented by 2 out of 3 rows shaded.
- The overlapping shaded area represents the product.
- Simplify $\frac{4}{12}$ to $\frac{1}{3}$.
- Calculate: $\frac{1}{3} \times \frac{2}{3} = \frac{1 \times 2}{3 \times 3} = \frac{2}{9}$.
- Answer: $\frac{2}{9}$

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Problem ⑤:

- Fractions: $\frac{3}{6} \times \frac{2}{4}$
- Steps:
- The first fraction $\frac{3}{6}$ is represented by 3 out of 6 columns shaded.
- The second fraction $\frac{2}{4}$ is represented by 2 out of 4 rows shaded.
- The overlapping shaded area represents the product.
- Simplify $\frac{3}{6}$ to $\frac{1}{2}$ and $\frac{2}{4}$ to $\frac{1}{2}$.
- Calculate: $\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}$.
- Answer: $\frac{1}{4}$

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Problem ⑥:

- Fractions: $\frac{5}{6} \times \frac{5}{8}$
- Steps:
- The first fraction $\frac{5}{6}$ is represented by 5 out of 6 columns shaded.
- The second fraction $\frac{5}{8}$ is represented by 5 out of 8 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{5}{6} \times \frac{5}{8} = \frac{5 \times 5}{6 \times 8} = \frac{25}{48}$.
- Answer: $\frac{25}{48}$

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Problem ⑦:

- Fractions: $\frac{2}{7} \times \frac{2}{5}$
- Steps:
- The first fraction $\frac{2}{7}$ is represented by 2 out of 7 columns shaded.
- The second fraction $\frac{2}{5}$ is represented by 2 out of 5 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{2}{7} \times \frac{2}{5} = \frac{2 \times 2}{7 \times 5} = \frac{4}{35}$.
- Answer: $\frac{4}{35}$

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Problem ⑧:

- Fractions: $\frac{5}{9} \times \frac{3}{5}$
- Steps:
- The first fraction $\frac{5}{9}$ is represented by 5 out of 9 columns shaded.
- The second fraction $\frac{3}{5}$ is represented by 3 out of 5 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{5}{9} \times \frac{3}{5} = \frac{5 \times 3}{9 \times 5} = \frac{15}{45} = \frac{1}{3}$.
- Answer: $\frac{1}{3}$

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Problem ⑨:

- Fractions: $\frac{1}{2} \times \frac{3}{7}$
- Steps:
- The first fraction $\frac{1}{2}$ is represented by 1 out of 2 columns shaded.
- The second fraction $\frac{3}{7}$ is represented by 3 out of 7 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{1}{2} \times \frac{3}{7} = \frac{1 \times 3}{2 \times 7} = \frac{3}{14}$.
- Answer: $\frac{3}{14}$

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Problem ⑩:

- Fractions: $\frac{7}{8} \times \frac{1}{2}$
- Steps:
- The first fraction $\frac{7}{8}$ is represented by 7 out of 8 columns shaded.
- The second fraction $\frac{1}{2}$ is represented by 1 out of 2 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{7}{8} \times \frac{1}{2} = \frac{7 \times 1}{8 \times 2} = \frac{7}{16}$.
- Answer: $\frac{7}{16}$

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Problem ⑪:

- Fractions: $\frac{4}{5} \times \frac{7}{11}$
- Steps:
- The first fraction $\frac{4}{5}$ is represented by 4 out of 5 columns shaded.
- The second fraction $\frac{7}{11}$ is represented by 7 out of 11 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{4}{5} \times \frac{7}{11} = \frac{4 \times 7}{5 \times 11} = \frac{28}{55}$.
- Answer: $\frac{28}{55}$

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Problem ⑫:

- Fractions: $\frac{3}{4} \times \frac{3}{5}$
- Steps:
- The first fraction $\frac{3}{4}$ is represented by 3 out of 4 columns shaded.
- The second fraction $\frac{3}{5}$ is represented by 3 out of 5 rows shaded.
- The overlapping shaded area represents the product.
- Calculate: $\frac{3}{4} \times \frac{3}{5} = \frac{3 \times 3}{4 \times 5} = \frac{9}{20}$.
- Answer: $\frac{9}{20}$

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Final Answers:

\[
\boxed{
\begin{array}{ccc}
\text{②} & \frac{3}{10} & \\
\text{③} & \frac{1}{4} & \\
\text{④} & \frac{2}{9} & \\
\text{⑤} & \frac{1}{4} & \\
\text{⑥} & \frac{25}{48} & \\
\text{⑦} & \frac{4}{35} & \\
\text{⑧} & \frac{1}{3} & \\
\text{⑨} & \frac{3}{14} & \\
\text{⑩} & \frac{7}{16} & \\
\text{⑪} & \frac{28}{55} & \\
\text{⑫} & \frac{9}{20} &
\end{array}
}
\]