Convert between mixed and improper fractions using pictures.

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 any 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, denominator is 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

✔ 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

✔ 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

✔ 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

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

> Note: Do not simplify — so leave $ \frac{3}{9} $ as is.

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🔹 Row 7: Bars (Each bar has 10 parts)

- 3 full bars → 3 × 10 = 30 parts
- 4th bar: 7 out of 10 shaded → 7/10
- Total shaded = 30 + 7 = 37 parts

✔ Improper Fraction: $ \frac{37}{10} $
✔ Mixed Number: $ 3 \frac{7}{10} $

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## ✔ Final Answer Table:

| Picture | Improper Fraction | Mixed Number |
|--------|-------------------|--------------|
| 🟡🟡 (Circles) | $ \frac{11}{8} $ | $ 1 \frac{3}{8} $ |
| 🟧🟧🟧🟧 (Pentagons) | $ \frac{19}{5} $ | $ 3 \frac{4}{5} $ |
| 🔵🔵🔵 (Squares) | $ \frac{9}{4} $ | $ 2 \frac{1}{4} $ |
| 🟡🟡🟡🟡🟡🟡 (Triangles) | $ \frac{11}{2} $ | $ 5 \frac{1}{2} $ |
| 🔴🔴🔴🔴🔴 (Pentagons) | $ \frac{24}{5} $ | $ 4 \frac{4}{5} $ |
| 🟩🟩🟩🟩 (Rectangles) | $ \frac{30}{9} $ | $ 3 \frac{3}{9} $ |
| 💜💜💜💜 (Bars) | $ \frac{37}{10} $ | $ 3 \frac{7}{10} $ |

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✔ Summary of Steps:

- Count total number of equal parts in one shape.
- Count how many shaded parts there are.
- Use the total shaded parts as the numerator and the size of each part as the denominator for improper fraction.
- For mixed number: Whole shapes = whole number; remaining shaded parts = fractional part.

Let me know if you'd like this turned into a printable answer sheet!