Multiplying Fractions by Tiling Activity for 3rd-5th Grade - Free Printable

I'll solve this worksheet on multiplying fractions using area models. Let me go through each problem step by step.

First, I need to understand the instructions: "Using the squares provided, create a visual representation of each fraction in the equation. One fraction should be represented horizontally, and the other should be represented vertically. Shade in both fractions and use the squares that overlap to determine the product."

Let me start with the first example which is already completed:
1. ½ × ¼ = ⅛
The model shows a square divided into 2 rows and 4 columns (or vice versa), creating 8 total parts. Half of the square is shaded one way (horizontally), and a quarter is shaded another way (vertically). The overlapping section (where both shadings intersect) represents 1 out of 8 parts, which is ⅛.

Now let me solve the remaining problems:

2. ⅔ × ½ = ?
- I need to represent ⅔ horizontally and ½ vertically (or vice versa)
- Divide the square into 3 columns and 2 rows, creating 6 total parts
- Shade 2 out of 3 columns for ⅔
- Shade 1 out of 2 rows for ½
- The overlapping area will be 2 out of 6 parts, which simplifies to ⅓

3. ¾ × ½ = ?
- Represent ¾ horizontally and ½ vertically
- Divide the square into 4 columns and 2 rows, creating 8 total parts
- Shade 3 out of 4 columns for ¾
- Shade 1 out of 2 rows for ½
- The overlapping area will be 3 out of 8 parts, which is ³⁄₈

4. ⅖ × ⅓ = ?
- Represent ⅖ horizontally and ⅓ vertically
- Divide the square into 5 columns and 3 rows, creating 15 total parts
- Shade 2 out of 5 columns for ⅖
- Shade 1 out of 3 rows for ⅓
- The overlapping area will be 2 out of 15 parts, which is ²⁄₁₅

5. ⅗ × ¼ = ?
- Represent ⅗ horizontally and ¼ vertically
- Divide the square into 5 columns and 4 rows, creating 20 total parts
- Shade 3 out of 5 columns for ⅗
- Shade 1 out of 4 rows for ¼
- The overlapping area will be 3 out of 20 parts, which is ³⁄₂₀

6. ½ × ⅔ = ?
- Represent ½ horizontally and ⅔ vertically
- Divide the square into 2 columns and 3 rows, creating 6 total parts
- Shade 1 out of 2 columns for ½
- Shade 2 out of 3 rows for ⅔
- The overlapping area will be 2 out of 6 parts, which simplifies to ⅓

7. ¾ × ⅓ = ?
- Represent ¾ horizontally and ⅓ vertically
- Divide the square into 4 columns and 3 rows, creating 12 total parts
- Shade 3 out of 4 columns for ¾
- Shade 1 out of 3 rows for ⅓
- The overlapping area will be 3 out of 12 parts, which simplifies to ¼

8. ⅘ × ½ = ?
- Represent ⅘ horizontally and ½ vertically
- Divide the square into 5 columns and 2 rows, creating 10 total parts
- Shade 4 out of 5 columns for ⅘
- Shade 1 out of 2 rows for ½
- The overlapping area will be 4 out of 10 parts, which simplifies to ⅖

9. ⅔ × ¾ = ?
- Represent ⅔ horizontally and ¾ vertically
- Divide the square into 3 columns and 4 rows, creating 12 total parts
- Shade 2 out of 3 columns for ⅔
- Shade 3 out of 4 rows for ¾
- The overlapping area will be 6 out of 12 parts, which simplifies to ½

10. ⅖ × ¾ = ?
- Represent ⅖ horizontally and ¾ vertically
- Divide the square into 5 columns and 4 rows, creating 20 total parts
- Shade 2 out of 5 columns for ⅖
- Shade 3 out of 4 rows for ¾
- The overlapping area will be 6 out of 20 parts, which simplifies to ³⁄₁₀

Here are the answers for each problem:
1. ½ × ¼ = ⅛ (given)
2. ⅔ × ½ = ⅓
3. ¾ × ½ = ³⁄₈
4. ⅖ × ⅓ = ²⁄₁₅
5. ⅗ × ¼ = ³⁄₂₀
6. ½ × ⅔ = ⅓
7. ¾ × ⅓ = ¼
8. ⅘ × ½ = ⅖
9. ⅔ × ¾ = ½
10. ⅖ × ¾ = ³⁄₁₀