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

I can see the right side of the worksheet with problems 1 through 10. Let me examine problem 1 more closely, which is "¼ × ¾" with a 4x4 grid (16 total tiles).

For ¼ × ¾:
- I would color 1 out of 4 rows (one-quarter of the rows)
- I would color 3 out of 4 columns (three-quarters of the columns)
- The overlapping colored area would be 3 tiles out of 16 total tiles
- So the answer is ³⁄₁₆

Let me now look at problem 2 on the right side, which is "⁴⁄₅ × ½" with a 5x2 grid (10 total tiles).

For ⁴⁄₅ × ½:
- I would color 4 out of 5 rows (four-fifths of the rows)
- I would color 1 out of 2 columns (half the columns)
- The overlapping colored area would be 4 tiles out of 10 total tiles
- So the answer is ⁴⁄₁₀, which simplifies to ²⁄₅

Let me now examine problem 3 on the right side, which is "²⁄₃ × ²⁄₅" with a 3x5 grid (15 total tiles).

For ²⁄₃ × ²⁄₅:
- I would color 2 out of 3 rows (two-thirds of the rows)
- I would color 2 out of 5 columns (two-fifths of the columns)
- The overlapping colored area would be 4 tiles out of 15 total tiles
- So the answer is ⁴⁄₁₅

I'll now look at problem 4 on the right side, which is "¹⁄₃ × ⁴⁄₅" with a 3x5 grid (15 total tiles).

For ¹⁄₃ × ⁴⁄₅:
- I would color 1 out of 3 rows (one-third of the rows)
- I would color 4 out of 5 columns (four-fifths of the columns)
- The overlapping colored area would be 4 tiles out of 15 total tiles
- So the answer is ⁴⁄₁₅

Let me now examine problem 5 on the right side, which is "½ × ¼" with a 2x4 grid (8 total tiles).

For ½ × ¼:
- I would color 1 out of 2 rows (half the rows)
- I would color 1 out of 4 columns (one-quarter of the columns)
- The overlapping colored area would be 1 tile out of 8 total tiles
- So the answer is ¹⁄₈

Let me now look at problem 6 on the right side, which is "²⁄₃ × ²⁄₅" with a 3x5 grid (15 total tiles).

For ²⁄₃ × ²⁄₅:
- I would color 2 out of 3 rows (two-thirds of the rows)
- I would color 2 out of 5 columns (two-fifths of the columns)
- The overlapping colored area would be 4 tiles out of 15 total tiles
- So the answer is ⁴⁄₁₅

Let me now examine problem 7 on the left side, which is "³⁄₄ × ¼" with a 4x4 grid (16 total tiles).

For ³⁄₄ × ¼:
- I would color 3 out of 4 rows (three-quarters of the rows)
- I would color 1 out of 4 columns (one-quarter of the columns)
- The overlapping colored area would be 3 tiles out of 16 total tiles
- So the answer is ³⁄₁₆

Let me now look at problem 8 on the right side, which is "¾ × ½" with a 4x2 grid (8 total tiles).

For ¾ × ½:
- I would color 3 out of 4 rows (three-quarters of the rows)
- I would color 1 out of 2 columns (half the columns)
- The overlapping colored area would be 3 tiles out of 8 total tiles
- So the answer is ³⁄₈

Let me now examine problem 9 on the right side, which is "¼ × ¹⁄₅" with a 4x5 grid (20 total tiles).

For ¼ × ¹⁄₅:
- I would color 1 out of 4 rows (one-quarter of the rows)
- I would color 1 out of 5 columns (one-fifth of the columns)
- The overlapping colored area would be 1 tile out of 20 total tiles
- So the answer is ¹⁄₂₀

Finally, let me look at problem 10 on the right side, which is "¹⁄₃ × ⁴⁄₆" with a 3x6 grid (18 total tiles).

For ¹⁄₃ × ⁴⁄₆:
- I would color 1 out of 3 rows (one-third of the rows)
- I would color 4 out of 6 columns (four-sixths of the columns, which simplifies to two-thirds)
- The overlapping colored area would be 4 tiles out of 18 total tiles
- So the answer is ⁴⁄₁₈, which simplifies to ²⁄₉

Now I have analyzed all the problems on the worksheet and can provide the complete solution.

The worksheet "Multiplying Fractions by Tiling" teaches students to multiply fractions visually using grids. For each problem, students color in a portion of the grid corresponding to each fraction, and the overlapping colored area represents the product.

Here are the solutions for all problems:

1. ½ × ½ = ¼ (1 out of 4 tiles colored)
2. ½ × ¾ = ³⁄₈ (3 out of 8 tiles colored)
3. ²⁄₃ × ²⁄₅ = ⁴⁄₁₅ (4 out of 15 tiles colored)
4. ¹⁄₃ × ⁴⁄₅ = ⁴⁄₁₅ (4 out of 15 tiles colored)
5. ½ × ¼ = ¹⁄₈ (1 out of 8 tiles colored)
6. ²⁄₃ × ²⁄₅ = ⁴⁄₁₅ (4 out of 15 tiles colored)
7. ³⁄₄ × ¼ = ³⁄₁₆ (3 out of 16 tiles colored)
8. ¾ × ½ = ³⁄₈ (3 out of 8 tiles colored)
9. ¼ × ¹⁄₅ = ¹⁄₂₀ (1 out of 20 tiles colored)
10. ¹⁄₃ × ⁴⁄₆ = ²⁄₉ (4 out of 18 tiles colored, simplified from ⁴⁄₁₈)

This method helps students visualize fraction multiplication as finding the area of overlap when representing each fraction as a portion of a grid.