Multiplying Fractions Worksheets - 15 Worksheets Library - Free Printable

Let's solve each of the fraction multiplication problems using the area model shown in the image. The area model visually represents multiplying two fractions by dividing a rectangle into parts and shading the overlapping region.

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Problem 1:

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

- The rectangle is divided into 4 columns (for $\frac{3}{4}$) and 2 rows (for $\frac{1}{2}$).
- Total parts: $4 \times 2 = 8$ small squares.
- Shade $\frac{3}{4}$ of the width (3 out of 4 columns).
- Shade $\frac{1}{2}$ of the height (1 out of 2 rows).
- The overlapping shaded area is $3 \times 1 = 3$ squares.
- So, the product is:
$$
\frac{3}{8}
$$

✔ Answer: $\boxed{\frac{3}{8}}$

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Problem 2:

$$
\frac{1}{2} \times \frac{1}{3} = ?
$$

- Rectangle divided into 2 columns (for $\frac{1}{2}$) and 3 rows (for $\frac{1}{3}$).
- Total parts: $2 \times 3 = 6$ squares.
- Shade 1 out of 2 columns and 1 out of 3 rows.
- Overlapping area: $1 \times 1 = 1$ square.
- So:
$$
\frac{1}{6}
$$

✔ Answer: $\boxed{\frac{1}{6}}$

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Problem 3:

$$
\frac{4}{5} \times \frac{1}{2} = ?
$$

- Rectangle divided into 5 columns (for $\frac{4}{5}$) and 2 rows (for $\frac{1}{2}$).
- Total parts: $5 \times 2 = 10$ squares.
- Shade 4 out of 5 columns and 1 out of 2 rows.
- Overlapping area: $4 \times 1 = 4$ squares.
- So:
$$
\frac{4}{10} = \frac{2}{5}
$$

✔ Answer: $\boxed{\frac{2}{5}}$

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Problem 4:

$$
\frac{6}{7} \times \frac{2}{3} = ?
$$

- Rectangle divided into 7 columns (for $\frac{6}{7}$) and 3 rows (for $\frac{2}{3}$).
- Total parts: $7 \times 3 = 21$ squares.
- Shade 6 out of 7 columns and 2 out of 3 rows.
- Overlapping area: $6 \times 2 = 12$ squares.
- So:
$$
\frac{12}{21} = \frac{4}{7}
$$

✔ Answer: $\boxed{\frac{4}{7}}$

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Problem 5:

$$
\frac{3}{4} \times \frac{2}{3} = ?
$$

- Rectangle divided into 4 columns (for $\frac{3}{4}$) and 3 rows (for $\frac{2}{3}$).
- Total parts: $4 \times 3 = 12$ squares.
- Shade 3 out of 4 columns and 2 out of 3 rows.
- Overlapping area: $3 \times 2 = 6$ squares.
- So:
$$
\frac{6}{12} = \frac{1}{2}
$$

✔ Answer: $\boxed{\frac{1}{2}}$

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Problem 6:

$$
\frac{2}{3} \times \frac{3}{4} = ?
$$

- Rectangle divided into 3 columns (for $\frac{2}{3}$) and 4 rows (for $\frac{3}{4}$).
- Total parts: $3 \times 4 = 12$ squares.
- Shade 2 out of 3 columns and 3 out of 4 rows.
- Overlapping area: $2 \times 3 = 6$ squares.
- So:
$$
\frac{6}{12} = \frac{1}{2}
$$

✔ Answer: $\boxed{\frac{1}{2}}$

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✔ Final Answers:

1) $\frac{3}{8}$
2) $\frac{1}{6}$
3) $\frac{2}{5}$
4) $\frac{4}{7}$
5) $\frac{1}{2}$
6) $\frac{1}{2}$

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🔍 Explanation Summary:

In the area model, you:
1. Draw a rectangle.
2. Divide it vertically into parts based on the denominator of the first fraction.
3. Divide it horizontally based on the denominator of the second fraction.
4. Shade the appropriate number of parts for each fraction.
5. The overlapping shaded region represents the product.
6. Count the shaded unit squares and divide by total squares to get the answer.
7. Simplify if possible.

This visual method helps understand why multiplying fractions results in smaller values — because you're taking a part of a part.

Let me know if you'd like this explained with diagrams or step-by-step drawings! 😊