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

You’re working on a worksheet titled “Multiplying Fractions With Area Models”. The goal is to visually represent each fraction in a multiplication problem using a grid (area model), shade the overlapping region to find the product, and write the answer.

Let’s solve each problem step by step.

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📌 Key Concept:

When multiplying two fractions using an area model:

1. Draw a rectangle.
2. Divide it into rows equal to the denominator of the first fraction → shade columns for the numerator.
3. Divide it into columns equal to the denominator of the second fraction → shade rows for the numerator.
4. The overlapping shaded area represents the product.
5. Count total small squares (denominator = row × column) and overlapping shaded squares (numerator).

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## ✔ Problem 1: Already Solved (Example)
> ½ × ¼ = ¹⁄₈

- Grid: 2 rows × 4 columns = 8 total squares.
- Shade 1 row (for ½) → horizontal shading.
- Shade 1 column (for ¼) → vertical shading.
- Overlap: 1 square → so answer is ¹⁄₈.

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## ✔ Problem 2: ⅔ × ¾ = ?

Step-by-step:

- Draw a 3×4 grid (since denominators are 3 and 4).
- Total squares = 3 × 4 = 12.
- Shade 2 out of 3 rows → that’s ⅔.
- Shade 3 out of 4 columns → that’s ¾.
- Overlapping shaded region: 2 rows × 3 columns = 6 squares.
- So, product = ⁶⁄₁₂ → simplify? Not required per instructions, but can reduce to ½ if needed.

✔ Answer: ⁶⁄₁₂

*(Note: You can leave as ⁶⁄₁₂ unless told to simplify.)*

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## ✔ Problem 3: ⅓ × ½ = ?

- Grid: 3 rows × 2 columns = 6 total squares.
- Shade 1 row (for ⅓).
- Shade 1 column (for ½).
- Overlap: 1 square.

✔ Answer: ¹⁄₆

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## ✔ Problem 4: ¾ × ½ = ?

- Grid: 4 rows × 2 columns = 8 total squares.
- Shade 3 rows (for ¾).
- Shade 1 column (for ½).
- Overlap: 3 squares.

✔ Answer: ³⁄₈

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## ✔ Problem 5: ¼ × ½ = ?

- Grid: 4 rows × 2 columns = 8 total squares.
- Shade 1 row (for ¼).
- Shade 1 column (for ½).
- Overlap: 1 square.

✔ Answer: ¹⁄₈

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## ✔ Problem 6: ⅔ × ½ = ?

- Grid: 3 rows × 2 columns = 6 total squares.
- Shade 2 rows (for ⅔).
- Shade 1 column (for ½).
- Overlap: 2 squares.

✔ Answer: ²⁄₆

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## ✔ Problem 7: ½ × ⅔ = ?

This is the same as Problem 6 — commutative property! But let’s draw it.

- Grid: 2 rows × 3 columns = 6 total squares.
- Shade 1 row (for ½).
- Shade 2 columns (for ⅔).
- Overlap: 2 squares.

✔ Answer: ²⁄₆

*(Same as above — order doesn’t matter in multiplication.)*

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## ✔ Problem 8: ¾ × ⅓ = ?

- Grid: 4 rows × 3 columns = 12 total squares.
- Shade 3 rows (for ¾).
- Shade 1 column (for ⅓).
- Overlap: 3 squares.

✔ Answer: ³⁄₁₂

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## ✔ Problem 9: ½ × ¼ = ?

- Grid: 2 rows × 4 columns = 8 total squares.
- Shade 1 row (for ½).
- Shade 1 column (for ¼).
- Overlap: 1 square.

✔ Answer: ¹⁄₈

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## ✔ Problem 10: ⅔ × ⅓ = ?

- Grid: 3 rows × 3 columns = 9 total squares.
- Shade 2 rows (for ⅔).
- Shade 1 column (for ⅓).
- Overlap: 2 squares.

✔ Answer: ²⁄₉

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## 🧾 Final Answers Summary:

| Problem | Equation | Answer |
|---------|----------------|--------|
| 1 | ½ × ¼ | ¹⁄₈ |
| 2 | ⅔ × ¾ | ⁶⁄₁₂ |
| 3 | ⅓ × ½ | ¹⁄₆ |
| 4 | ¾ × ½ | ³⁄₈ |
| 5 | ¼ × ½ | ¹⁄₈ |
| 6 | ⅔ × ½ | ²⁄₆ |
| 7 | ½ × ⅔ | ²⁄₆ |
| 8 | ¾ × ⅓ | ³⁄₁₂ |
| 9 | ½ × ¼ | ¹⁄₈ |
| 10 | ⅔ × ⅓ | ²⁄₉ |

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## 💡 Tips for Drawing Area Models:

- Always label your grid with rows/columns based on denominators.
- Use different shading directions (horizontal/vertical) to show each fraction.
- The overlapping region is your product!
- Don’t forget to count total squares for denominator and shaded overlap for numerator.

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✔ You’re all set! Just fill in the grids and answers as shown above. Let me know if you’d like printable templates or visual examples for any problem!