Shade the Models and Multiply Fractions — Printable Math Worksheet - Free Printable

Let's solve each of the fraction multiplication problems using area models, as shown in the worksheet. We'll go step by step for each problem.

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🔷 Problem 1:

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

#### Step 1: Understand the area model
We need to draw a rectangle divided into 4 rows (for the denominator of the first fraction, 4) and 3 columns (for the denominator of the second fraction, 3). This gives us a grid of $4 \times 3 = 12$ equal parts.

- Shade 1 out of 4 rows to represent $\frac{1}{4}$.
- Shade 2 out of 3 columns to represent $\frac{2}{3}$.
- The overlapping shaded region represents the product.

#### Step 2: Count the overlapping parts
- The overlapping area is where both shadings intersect.
- Since 1 row and 2 columns overlap, there are $1 \times 2 = 2$ small squares shaded twice.
- Total number of small squares: $12$

So,
$$
\frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \boxed{\frac{1}{6}}
$$

✔ Answer: $\frac{1}{6}$
✔ Shade: In the 4×3 grid, shade 1 entire row (top or bottom), then shade 2 columns (leftmost or any two), and the overlapping area will be 2 squares — that’s your answer.

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🔷 Problem 2:

$$
\frac{1}{3} \times \frac{3}{5} = ?
$$

#### Step 1: Draw the grid
- Divide the rectangle into 3 rows (for $\frac{1}{3}$)
- Divide it into 5 columns (for $\frac{3}{5}$)
- So, total $3 \times 5 = 15$ parts.

#### Step 2: Shade
- Shade 1 row (to represent $\frac{1}{3}$)
- Shade 3 columns (to represent $\frac{3}{5}$)
- Overlap = $1 \times 3 = 3$ squares

So,
$$
\frac{1}{3} \times \frac{3}{5} = \frac{3}{15} = \boxed{\frac{1}{5}}
$$

✔ Answer: $\frac{1}{5}$
✔ Shade: In the 3×5 grid, shade 1 row and 3 columns; the intersection is 3 squares.

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🔷 Problem 3:

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

#### Step 1: Grid setup
- 4 rows (for $\frac{3}{4}$)
- 4 columns (for $\frac{1}{4}$)
- Total: $4 \times 4 = 16$ parts

#### Step 2: Shade
- Shade 3 rows (for $\frac{3}{4}$)
- Shade 1 column (for $\frac{1}{4}$)
- Overlap = $3 \times 1 = 3$ squares

So,
$$
\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}
$$

✔ Answer: $\frac{3}{16}$
✔ Shade: In the 4×4 grid, shade 3 rows and 1 column; their intersection is 3 squares.

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| $\frac{1}{4} \times \frac{2}{3}$ | $\boxed{\frac{1}{6}}$ |
| $\frac{1}{3} \times \frac{3}{5}$ | $\boxed{\frac{1}{5}}$ |
| $\frac{3}{4} \times \frac{1}{4}$ | $\boxed{\frac{3}{16}}$ |

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🎯 How to Shade Each Grid:

1. First grid (4×3):
- Shade 1 full row (e.g., top row).
- Shade 2 full columns (e.g., leftmost two).
- The overlapping part (2 squares) should be doubly shaded (or highlighted).

2. Second grid (3×5):
- Shade 1 row.
- Shade 3 columns.
- Overlap = 3 squares → double-shaded.

3. Third grid (4×4):
- Shade 3 rows.
- Shade 1 column.
- Overlap = 3 squares → double-shaded.

> 💡 Tip: Use different colors or patterns to show the two fractions, and the overlapping area is the product.

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Let me know if you'd like a visual description or printable instructions!