Practice reducing fractions to their lowest terms by analyzing the shaded portions of these geometric shapes.

Let's solve each of the problems on the 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 shape one at a time.

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🔹 1. Octagon (8 sides)

- Total parts: 8
- Shaded parts: 3
- Fraction shaded: $ \frac{3}{8} $
- Is this simplifiable? No — 3 and 8 have no common factors.
- Simplest form: $ \frac{3}{8} $

✔ Answer:
- Fraction Shaded: $ \frac{3}{8} $
- Simplest Form: $ \frac{3}{8} $

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🔹 2. Star with 10 points

- Total parts: 10 (each point is a triangle)
- Shaded parts: 4
- Fraction shaded: $ \frac{4}{10} $
- Simplify: Divide numerator and denominator by 2 → $ \frac{2}{5} $
- Simplest form: $ \frac{2}{5} $

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

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🔹 3. Pentagon divided into triangles

- Total parts: 10 (5 large triangles, each split into 2 → 10 small ones)
- Shaded parts: 2 (one full triangle and half another? Wait — let’s count carefully)

Wait — actually, the pentagon is divided into 10 small triangles. Let's count:
- There are 5 outer triangles and 5 inner ones?
- But looking closely: it appears the pentagon is split into 10 equal small triangles.
- Shaded: 2 small triangles?

No — wait: the shading covers two full triangular sections, but each section is made of two small triangles?

Actually, the figure has 10 small triangles, and 4 are shaded.

Wait — look again: the orange shading covers 4 small triangles.

So:
- Total: 10
- Shaded: 4
- Fraction: $ \frac{4}{10} = \frac{2}{5} $

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

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🔹 4. Rectangle divided into 6 squares

- Total parts: 6
- Shaded parts: 4
- Fraction: $ \frac{4}{6} $
- Simplify: divide by 2 → $ \frac{2}{3} $

✔ Answer:
- Fraction Shaded: $ \frac{4}{6} $
- Simplest Form: $ \frac{2}{3} $

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🔹 5. Rectangle divided into 12 small rectangles

- Total parts: 12
- Shaded parts: 7
- Fraction: $ \frac{7}{12} $
- 7 and 12 have no common factors → already simplified

✔ Answer:
- Fraction Shaded: $ \frac{7}{12} $
- Simplest Form: $ \frac{7}{12} $

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🔹 6. Square grid: 3×4 = 12 squares

- Total: 12
- Shaded: 6
- Fraction: $ \frac{6}{12} = \frac{1}{2} $

✔ Answer:
- Fraction Shaded: $ \frac{6}{12} $
- Simplest Form: $ \frac{1}{2} $

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🔹 7. Grid of 12 rectangles (3 rows × 4 columns)

- Total: 12
- Shaded: 6 (bottom two rows fully shaded)
- Fraction: $ \frac{6}{12} = \frac{1}{2} $

✔ Answer:
- Fraction Shaded: $ \frac{6}{12} $
- Simplest Form: $ \frac{1}{2} $

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🔹 8. Rectangle with 10 squares (2×5)

- Total: 10
- Shaded: 6
- Fraction: $ \frac{6}{10} = \frac{3}{5} $

✔ Answer:
- Fraction Shaded: $ \frac{6}{10} $
- Simplest Form: $ \frac{3}{5} $

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🔹 9. Rectangle divided into 12 squares (3×4)

- Total: 12
- Shaded: 5 (diagonal line from top-left to bottom-right)
- Count: 5 shaded squares
- Fraction: $ \frac{5}{12} $
- Already simplified (5 and 12 have no common factors)

✔ Answer:
- Fraction Shaded: $ \frac{5}{12} $
- Simplest Form: $ \frac{5}{12} $

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🔹 10. Vertical rectangle: 10 squares high × 1 wide

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

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

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🔹 11. "T" shape made of squares

- Count total squares:
- Top: 4 squares (horizontal)
- Middle: 1 square
- Bottom: 3 squares (vertical)
- Total: 4 + 1 + 3 = 8 squares
- Shaded: 3 (the vertical column at the bottom)
- Fraction: $ \frac{3}{8} $
- Already simplified

✔ Answer:
- Fraction Shaded: $ \frac{3}{8} $
- Simplest Form: $ \frac{3}{8} $

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🔹 12. Parallelogram divided into 12 small rectangles

- Total: 12
- Shaded: 4 (bottom row)
- Fraction: $ \frac{4}{12} = \frac{1}{3} $

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

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## ✔ Final Answers Table

| Shape | Fraction Shaded | Simplest Form |
|------|------------------|---------------|
| 1. Octagon | $ \frac{3}{8} $ | $ \frac{3}{8} $ |
| 2. Star | $ \frac{4}{10} $ | $ \frac{2}{5} $ |
| 3. Pentagon | $ \frac{4}{10} $ | $ \frac{2}{5} $ |
| 4. 6-square rectangle | $ \frac{4}{6} $ | $ \frac{2}{3} $ |
| 5. 12-rectangle | $ \frac{7}{12} $ | $ \frac{7}{12} $ |
| 6. 3×4 grid | $ \frac{6}{12} $ | $ \frac{1}{2} $ |
| 7. 3×4 grid (shaded bottom) | $ \frac{6}{12} $ | $ \frac{1}{2} $ |
| 8. 2×5 grid | $ \frac{6}{10} $ | $ \frac{3}{5} $ |
| 9. 3×4 grid (diagonal) | $ \frac{5}{12} $ | $ \frac{5}{12} $ |
| 10. 10-square column | $ \frac{4}{10} $ | $ \frac{2}{5} $ |
| 11. "T" shape | $ \frac{3}{8} $ | $ \frac{3}{8} $ |
| 12. Parallelogram | $ \frac{4}{12} $ | $ \frac{1}{3} $ |

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📌 Summary Tips:

- To simplify fractions, find the greatest common divisor (GCD) of numerator and denominator.
- Divide both by the GCD.
- If no common factor (other than 1), the fraction is already in simplest form.

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