Multiplying fractions using models worksheet - Free Printable

To solve the problems using the area models, we need to follow these steps:

1. Understand the fractions: Each fraction represents a part of the whole area.
2. Multiply the fractions: Multiply the numerators together and the denominators together.
3. Shade the area model: The shaded area in the resulting grid will represent the product of the two fractions.

Let's solve each problem step by step.

---

Example (Ex):

\[
\frac{1}{3} \times \frac{1}{2} =
\]
- The first fraction, \(\frac{1}{3}\), means we divide the grid into 3 equal columns and shade 1 column.
- The second fraction, \(\frac{1}{2}\), means we divide the grid into 2 equal rows and shade 1 row.
- The overlapping shaded area represents the product.

The result is:
\[
\frac{1}{3} \times \frac{1}{2} = \frac{1 \times 1}{3 \times 2} = \frac{1}{6}
\]

---

Problem 1:

\[
\frac{1}{2} \times \frac{3}{4} =
\]
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- Divide the grid into 4 columns and shade 3 columns for \(\frac{3}{4}\).
- The overlapping shaded area is 3 out of 8 parts.

The result is:
\[
\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}
\]

---

Problem 2:

\[
\frac{1}{5} \times \frac{2}{4} =
\]
- Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\).
- Divide the grid into 5 columns and shade 1 column for \(\frac{1}{5}\).
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- The overlapping shaded area is 1 out of 10 parts.

The result is:
\[
\frac{1}{5} \times \frac{1}{2} = \frac{1 \times 1}{5 \times 2} = \frac{1}{10}
\]

---

Problem 3:

\[
\frac{3}{4} \times \frac{2}{3} =
\]
- Divide the grid into 4 columns and shade 3 columns for \(\frac{3}{4}\).
- Divide the grid into 3 rows and shade 2 rows for \(\frac{2}{3}\).
- The overlapping shaded area is 6 out of 12 parts, which simplifies to \(\frac{1}{2}\).

The result is:
\[
\frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2}
\]

---

Problem 4:

\[
\frac{6}{8} \times \frac{1}{2} =
\]
- Simplify \(\frac{6}{8}\) to \(\frac{3}{4}\).
- Divide the grid into 4 columns and shade 3 columns for \(\frac{3}{4}\).
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- The overlapping shaded area is 3 out of 8 parts.

The result is:
\[
\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}
\]

---

Problem 5:

\[
\frac{1}{3} \times \frac{1}{7} =
\]
- Divide the grid into 3 columns and shade 1 column for \(\frac{1}{3}\).
- Divide the grid into 7 rows and shade 1 row for \(\frac{1}{7}\).
- The overlapping shaded area is 1 out of 21 parts.

The result is:
\[
\frac{1}{3} \times \frac{1}{7} = \frac{1 \times 1}{3 \times 7} = \frac{1}{21}
\]

---

Problem 6:

\[
\frac{2}{6} \times \frac{1}{2} =
\]
- Simplify \(\frac{2}{6}\) to \(\frac{1}{3}\).
- Divide the grid into 3 columns and shade 1 column for \(\frac{1}{3}\).
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- The overlapping shaded area is 1 out of 6 parts.

The result is:
\[
\frac{1}{3} \times \frac{1}{2} = \frac{1 \times 1}{3 \times 2} = \frac{1}{6}
\]

---

Problem 7:

\[
\frac{2}{9} \times \frac{1}{4} =
\]
- Divide the grid into 9 columns and shade 2 columns for \(\frac{2}{9}\).
- Divide the grid into 4 rows and shade 1 row for \(\frac{1}{4}\).
- The overlapping shaded area is 2 out of 36 parts, which simplifies to \(\frac{1}{18}\).

The result is:
\[
\frac{2}{9} \times \frac{1}{4} = \frac{2 \times 1}{9 \times 4} = \frac{2}{36} = \frac{1}{18}
\]

---

Problem 8:

\[
\frac{5}{7} \times \frac{1}{2} =
\]
- Divide the grid into 7 columns and shade 5 columns for \(\frac{5}{7}\).
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- The overlapping shaded area is 5 out of 14 parts.

The result is:
\[
\frac{5}{7} \times \frac{1}{2} = \frac{5 \times 1}{7 \times 2} = \frac{5}{14}
\]

---

Problem 9:

\[
\frac{1}{2} \times \frac{2}{5} =
\]
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- Divide the grid into 5 columns and shade 2 columns for \(\frac{2}{5}\).
- The overlapping shaded area is 2 out of 10 parts, which simplifies to \(\frac{1}{5}\).

The result is:
\[
\frac{1}{2} \times \frac{2}{5} = \frac{1 \times 2}{2 \times 5} = \frac{2}{10} = \frac{1}{5}
\]

---

Problem 10:

\[
\frac{5}{6} \times \frac{3}{6} =
\]
- Simplify \(\frac{3}{6}\) to \(\frac{1}{2}\).
- Divide the grid into 6 columns and shade 5 columns for \(\frac{5}{6}\).
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- The overlapping shaded area is 5 out of 12 parts.

The result is:
\[
\frac{5}{6} \times \frac{1}{2} = \frac{5 \times 1}{6 \times 2} = \frac{5}{12}
\]

---

Problem 11:

\[
\frac{1}{3} \times \frac{1}{2} =
\]
- Divide the grid into 3 columns and shade 1 column for \(\frac{1}{3}\).
- Divide the grid into 2 rows and shade 1 row for \(\frac{1}{2}\).
- The overlapping shaded area is 1 out of 6 parts.

The result is:
\[
\frac{1}{3} \times \frac{1}{2} = \frac{1 \times 1}{3 \times 2} = \frac{1}{6}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & \frac{3}{8} \\
2) & \frac{1}{10} \\
3) & \frac{1}{2} \\
4) & \frac{3}{8} \\
5) & \frac{1}{21} \\
6) & \frac{1}{6} \\
7) & \frac{1}{18} \\
8) & \frac{5}{14} \\
9) & \frac{1}{5} \\
10) & \frac{5}{12} \\
11) & \frac{1}{6} \\
\end{array}
}
\]