Mixed and Improper Fractions worksheet - Free Printable

Let's solve each row of the worksheet by analyzing the pictures and converting them into improper fractions and mixed numbers. We will not simplify the fractions, as instructed.

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🔹 Row 1: Circles (Divided into 8 parts)

- First circle: Fully shaded → 8/8
- Second circle: 3 out of 8 shaded → 3/8
- Total shaded = 8/8 + 3/8 = 11/8

✔ Improper Fraction: $ \frac{11}{8} $
✔ Mixed Number: $ 1 \frac{3}{8} $

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🔹 Row 2: Pentagons (Each divided into 5 parts)

- 3 full pentagons → 3 × 5 = 15 parts
- 4th pentagon: 4 out of 5 shaded → 4/5
- Total shaded = 15 + 4 = 19 parts → 19/5

✔ Improper Fraction: $ \frac{19}{5} $
✔ Mixed Number: $ 3 \frac{4}{5} $

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🔹 Row 3: Squares (Each divided into 4 parts)

- 2 full squares → 2 × 4 = 8 parts
- 3rd square: 1 out of 4 shaded → 1/4
- Total shaded = 8 + 1 = 9 parts → 9/4

✔ Improper Fraction: $ \frac{9}{4} $
✔ Mixed Number: $ 2 \frac{1}{4} $

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🔹 Row 4: Triangles (Each divided into 2 parts)

- 5 full triangles → 5 × 2 = 10 parts
- 6th triangle: 1 out of 2 shaded → 1/2
- Total shaded = 10 + 1 = 11 parts → 11/2

✔ Improper Fraction: $ \frac{11}{2} $
✔ Mixed Number: $ 5 \frac{1}{2} $

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🔹 Row 5: Pentagons (Each divided into 5 parts)

- 4 full pentagons → 4 × 5 = 20 parts
- 5th pentagon: 4 out of 5 shaded → 4/5
- Total shaded = 20 + 4 = 24 parts → 24/5

✔ Improper Fraction: $ \frac{24}{5} $
✔ Mixed Number: $ 4 \frac{4}{5} $

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🔹 Row 6: Rectangles (Each divided into 9 parts)

- 3 full rectangles → 3 × 9 = 27 parts
- 4th rectangle: 3 out of 9 shaded → 3/9
- Total shaded = 27 + 3 = 30 parts → 30/9

✔ Improper Fraction: $ \frac{30}{9} $
✔ Mixed Number: $ 3 \frac{3}{9} $

*(Note: Don't simplify — so leave as 3 3/9)*

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🔹 Row 7: Bars (Each bar has 10 parts)

- Count all shaded parts:
- First bar: 10 shaded → 10
- Second bar: 10 shaded → 10
- Third bar: 10 shaded → 10
- Fourth bar: 8 shaded → 8
- Total shaded = 10 + 10 + 10 + 8 = 38 parts

Each bar has 10 parts → total is in tenths → 38/10

✔ Improper Fraction: $ \frac{38}{10} $
✔ Mixed Number: $ 3 \frac{8}{10} $

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✔ Final Answer Table:

| Picture | Improper Fraction | Mixed Number |
|--------|-------------------|--------------|
| Two circles (8 parts) | $ \frac{11}{8} $ | $ 1 \frac{3}{8} $ |
| Four pentagons (5 parts) | $ \frac{19}{5} $ | $ 3 \frac{4}{5} $ |
| Three squares (4 parts) | $ \frac{9}{4} $ | $ 2 \frac{1}{4} $ |
| Six triangles (2 parts) | $ \frac{11}{2} $ | $ 5 \frac{1}{2} $ |
| Five pentagons (5 parts) | $ \frac{24}{5} $ | $ 4 \frac{4}{5} $ |
| Four rectangles (9 parts) | $ \frac{30}{9} $ | $ 3 \frac{3}{9} $ |
| Four bars (10 parts) | $ \frac{38}{10} $ | $ 3 \frac{8}{10} $ |

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📌 Explanation Summary:

To convert from a picture to a fraction:
1. Identify how many equal parts each shape has (denominator).
2. Count how many total shaded parts there are (numerator for improper).
3. For mixed number: count whole shapes and leftover parts.

We do not simplify, so even if fractions like $ \frac{30}{9} $ or $ \frac{38}{10} $ can be reduced, we leave them as-is.

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