Simplifying Fractions (A) | Fun and Engaging 4th Grade PDF Worksheets - Free Printable

Let's solve each of the problems on this worksheet step by step. The goal is to:

1. Determine the fraction of each shape that is shaded (i.e., number of shaded parts ÷ total number of parts).
2. Simplify the fraction to its simplest form.

We’ll go through each image one at a time.

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🔹 Example (Already Done)

- Shape: Circle divided into 8 equal parts, 2 shaded.
- Fraction Shaded: $ \frac{2}{8} $
- Simplified: $ \frac{1}{4} $

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🔹 1. Octagon (8 sides)

- Total parts: 8
- Shaded parts: 2
- Fraction: $ \frac{2}{8} $
- Simplify: $ \frac{1}{4} $

✔ Answer:
- Fraction Shaded: $ \frac{2}{8} $
- Simplest Form: $ \frac{1}{4} $

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🔹 2. Star with 12 points

- Total parts: 12 (each point is a triangle)
- Shaded parts: 3
- Fraction: $ \frac{3}{12} $
- Simplify: Divide numerator and denominator by 3 → $ \frac{1}{4} $

✔ Answer:
- Fraction Shaded: $ \frac{3}{12} $
- Simplest Form: $ \frac{1}{4} $

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🔹 3. Pentagon divided into triangles

- Total parts: 10 (5 outer triangles + 5 inner ones? Wait — actually, it looks like a regular pentagon split into 10 equal triangles from center)
- Shaded parts: 2
- Fraction: $ \frac{2}{10} $
- Simplify: $ \frac{1}{5} $

✔ Answer:
- Fraction Shaded: $ \frac{2}{10} $
- Simplest Form: $ \frac{1}{5} $

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🔹 4. Rectangle divided into 6 squares

- Total parts: 6
- Shaded: 5
- Fraction: $ \frac{5}{6} $
- Already simplified.

✔ Answer:
- Fraction Shaded: $ \frac{5}{6} $
- Simplest Form: $ \frac{5}{6} $

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🔹 5. Rectangle divided into 10 vertical strips

- Total parts: 10
- Shaded: 4
- Fraction: $ \frac{4}{10} $
- Simplify: $ \frac{2}{5} $

✔ Answer:
- Fraction Shaded: $ \frac{4}{10} $
- Simplest Form: $ \frac{2}{5} $

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🔹 6. Grid of 4×4 = 16 squares

- Total parts: 16
- Shaded: 8
- Fraction: $ \frac{8}{16} $
- Simplify: $ \frac{1}{2} $

✔ Answer:
- Fraction Shaded: $ \frac{8}{16} $
- Simplest Form: $ \frac{1}{2} $

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🔹 7. Grid of 5×4 = 20 squares

- Total parts: 20
- Shaded: 10
- Fraction: $ \frac{10}{20} $
- Simplify: $ \frac{1}{2} $

✔ Answer:
- Fraction Shaded: $ \frac{10}{20} $
- Simplest Form: $ \frac{1}{2} $

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🔹 8. Grid of 5×5 = 25 squares

- Total parts: 25
- Shaded: 10
- Fraction: $ \frac{10}{25} $
- Simplify: Divide numerator and denominator by 5 → $ \frac{2}{5} $

✔ Answer:
- Fraction Shaded: $ \frac{10}{25} $
- Simplest Form: $ \frac{2}{5} $

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🔹 9. Rectangle with 10 squares (2 columns × 5 rows)

- Total parts: 10
- Shaded: 5
- Fraction: $ \frac{5}{10} $
- Simplify: $ \frac{1}{2} $

✔ Answer:
- Fraction Shaded: $ \frac{5}{10} $
- Simplest Form: $ \frac{1}{2} $

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🔹 10. Vertical bar of 10 squares

- Total parts: 10
- Shaded: 5
- Fraction: $ \frac{5}{10} $
- Simplify: $ \frac{1}{2} $

✔ Answer:
- Fraction Shaded: $ \frac{5}{10} $
- Simplest Form: $ \frac{1}{2} $

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🔹 11. T-shaped grid

- Total parts: Top rectangle is 4×4 = 16, stem is 4×3 = 12? Wait — let’s count carefully.

Looking at the figure:
- Top: 4×4 = 16 squares
- Stem: 3×4 = 12 squares
- But wait — the stem appears to be 4 squares tall and 1 wide → so 4 squares
- So total: 16 (top) + 4 (stem) = 20 squares

Shaded: Only the stem is shaded → 4 squares

Fraction: $ \frac{4}{20} $ → Simplify: $ \frac{1}{5} $

✔ Answer:
- Fraction Shaded: $ \frac{4}{20} $
- Simplest Form: $ \frac{1}{5} $

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🔹 12. Parallelogram divided into 20 small squares

- Total parts: 20 (arranged in a parallelogram)
- Shaded: 6
- Fraction: $ \frac{6}{20} $
- Simplify: Divide by 2 → $ \frac{3}{10} $

✔ Answer:
- Fraction Shaded: $ \frac{6}{20} $
- Simplest Form: $ \frac{3}{10} $

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## ✔ Final Answers Table:

| Image | Fraction Shaded | Simplest Form |
|------|------------------|---------------|
| 1 (Octagon) | $ \frac{2}{8} $ | $ \frac{1}{4} $ |
| 2 (Star) | $ \frac{3}{12} $ | $ \frac{1}{4} $ |
| 3 (Pentagon) | $ \frac{2}{10} $ | $ \frac{1}{5} $ |
| 4 (Rectangle 6 squares) | $ \frac{5}{6} $ | $ \frac{5}{6} $ |
| 5 (Striped rectangle) | $ \frac{4}{10} $ | $ \frac{2}{5} $ |
| 6 (4x4 grid) | $ \frac{8}{16} $ | $ \frac{1}{2} $ |
| 7 (5x4 grid) | $ \frac{10}{20} $ | $ \frac{1}{2} $ |
| 8 (5x5 grid) | $ \frac{10}{25} $ | $ \frac{2}{5} $ |
| 9 (Tilted 5x2) | $ \frac{5}{10} $ | $ \frac{1}{2} $ |
| 10 (Vertical bar) | $ \frac{5}{10} $ | $ \frac{1}{2} $ |
| 11 (T-shape) | $ \frac{4}{20} $ | $ \frac{1}{5} $ |
| 12 (Parallelogram) | $ \frac{6}{20} $ | $ \frac{3}{10} $ |

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📌 Tips for Simplifying Fractions:

To simplify a fraction:
1. Find the greatest common divisor (GCD) of numerator and denominator.
2. Divide both by the GCD.

For example:
- $ \frac{6}{20} $ → GCD of 6 and 20 is 2 → $ \frac{6÷2}{20÷2} = \frac{3}{10} $

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Let me know if you'd like this formatted as a printable answer key!