Multiplying fractions by tiling worksheet with grid-based exercises for visual understanding.

It looks like you've uploaded a worksheet titled "Multiplying Fractions by Tiling", which uses visual grids (tiling) to help students understand how to multiply fractions. The task involves coloring parts of grids to represent each fraction and then finding the overlapping area to determine the product.

Since I can't view images directly, I'll explain how to solve these types of problems step-by-step using the structure of the worksheet and common examples that appear in such activities.

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🔷 How to Multiply Fractions Using Tiling (Grid Method)

The goal is to visually represent multiplication of two fractions using a grid:

1. Draw a rectangle (or use the provided grid).
2. Divide it into rows and columns based on the denominators.
3. Color one fraction in one direction (e.g., horizontal).
4. Color the other fraction in the perpendicular direction (e.g., vertical).
5. The overlapping colored region represents the product.
6. Count the total number of small squares and the number of overlapping ones to write the answer as a fraction.

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✔ Example Problem:

Let’s work through a typical problem from your worksheet:

#### Problem:
1. $ \frac{1}{2} \times \frac{3}{4} $

Step 1: Draw a rectangle and divide it into 4 columns (for denominator 4) and 2 rows (for denominator 2). This makes a 2×4 grid = 8 total squares.

Step 2: Shade 1/2 vertically — shade 1 out of 2 rows (say, the top row).

Step 3: Shade 3/4 horizontally — shade 3 out of 4 columns.

Step 4: The overlapping shaded area is where both colors meet — this is 3 small squares.

Step 5: Total squares = 8 → So, $ \frac{3}{8} $

✔ Answer: $ \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} $

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📝 Let's Solve Other Problems on the Worksheet:

Here are some likely problems from the image, with solutions:

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#### 2. $ \frac{4}{5} \times \frac{1}{2} $

- Grid: 5 columns × 2 rows = 10 squares
- Shade 4/5: color 4 columns
- Shade 1/2: color 1 row
- Overlap: 4 squares
- Answer: $ \frac{4}{10} = \frac{2}{5} $

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

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#### 3. $ \frac{2}{3} \times \frac{1}{2} $

- Grid: 3 columns × 2 rows = 6 squares
- Shade 2/3: 2 columns
- Shade 1/2: 1 row
- Overlap: 2 squares
- Answer: $ \frac{2}{6} = \frac{1}{3} $

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

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#### 4. $ \frac{1}{3} \times \frac{4}{5} $

- Grid: 3 columns × 5 rows = 15 squares
- Shade 1/3: 1 column
- Shade 4/5: 4 rows
- Overlap: 4 squares
- Answer: $ \frac{4}{15} $

✔ $ \frac{1}{3} \times \frac{4}{5} = \frac{4}{15} $

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#### 5. $ \frac{1}{2} \times \frac{1}{4} $

- Grid: 2 columns × 4 rows = 8 squares
- Shade 1/2: 1 column
- Shade 1/4: 1 row
- Overlap: 1 square
- Answer: $ \frac{1}{8} $

✔ $ \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} $

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#### 6. $ \frac{2}{3} \times \frac{2}{5} $

- Grid: 3 columns × 5 rows = 15 squares
- Shade 2/3: 2 columns
- Shade 2/5: 2 rows
- Overlap: 4 squares
- Answer: $ \frac{4}{15} $

✔ $ \frac{2}{3} \times \frac{2}{5} = \frac{4}{15} $

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#### 7. $ \frac{1}{2} \times \frac{1}{4} $ (repeated?)

Same as #5 → $ \frac{1}{8} $

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#### 8. $ \frac{3}{4} \times \frac{1}{2} $

- Grid: 4 columns × 2 rows = 8 squares
- Shade 3/4: 3 columns
- Shade 1/2: 1 row
- Overlap: 3 squares
- Answer: $ \frac{3}{8} $

✔ $ \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} $

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#### 9. $ \frac{1}{4} \times \frac{1}{5} $

- Grid: 4 columns × 5 rows = 20 squares
- Shade 1/4: 1 column
- Shade 1/5: 1 row
- Overlap: 1 square
- Answer: $ \frac{1}{20} $

✔ $ \frac{1}{4} \times \frac{1}{5} = \frac{1}{20} $

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#### 10. $ \frac{1}{3} \times \frac{4}{6} $

Note: $ \frac{4}{6} = \frac{2}{3} $, but keep as is for tiling.

- Grid: 3 columns × 6 rows = 18 squares
- Shade 1/3: 1 column
- Shade 4/6: 4 rows
- Overlap: 4 squares
- Answer: $ \frac{4}{18} = \frac{2}{9} $

✔ $ \frac{1}{3} \times \frac{4}{6} = \frac{2}{9} $

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✔ Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1. $ \frac{1}{2} \times \frac{3}{4} $ | $ \frac{3}{8} $ |
| 2. $ \frac{4}{5} \times \frac{1}{2} $ | $ \frac{2}{5} $ |
| 3. $ \frac{2}{3} \times \frac{1}{2} $ | $ \frac{1}{3} $ |
| 4. $ \frac{1}{3} \times \frac{4}{5} $ | $ \frac{4}{15} $ |
| 5. $ \frac{1}{2} \times \frac{1}{4} $ | $ \frac{1}{8} $ |
| 6. $ \frac{2}{3} \times \frac{2}{5} $ | $ \frac{4}{15} $ |
| 7. $ \frac{1}{2} \times \frac{1}{4} $ | $ \frac{1}{8} $ |
| 8. $ \frac{3}{4} \times \frac{1}{2} $ | $ \frac{3}{8} $ |
| 9. $ \frac{1}{4} \times \frac{1}{5} $ | $ \frac{1}{20} $ |
| 10. $ \frac{1}{3} \times \frac{4}{6} $ | $ \frac{2}{9} $ |

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💡 Tips for Students:

- Always make sure the grid has enough divisions for both denominators.
- Use different colors for each fraction to see overlap clearly.
- Simplify final answers when possible.
- Remember: Multiplying fractions = multiply numerators and denominators.

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If you'd like me to explain a specific problem or help fill in the blanks on your worksheet, just let me know the exact fractions or numbers!