Mixed and Improper Fractions worksheet - Free Printable

Absolutely! Let’s solve this worksheet step by step. The goal is to convert between improper fractions and mixed numbers based on the pictures, without simplifying.

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📌 Key Concepts:

- Improper Fraction: A fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). It represents more than one whole.
- Mixed Number: A whole number + a proper fraction (e.g., 1 ½).
- To convert from a picture → improper fraction: Count total shaded parts over the number of parts in one whole.
- To convert to mixed number: Divide the numerator by the denominator. The quotient is the whole number, remainder becomes the numerator of the fraction, denominator stays the same.

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## ✔ Row 1: Circles divided into 8 parts

> Picture: One full yellow circle (8/8), and another circle with 3 yellow parts out of 8.

- Total shaded parts = 8 + 3 = 11
- Each whole = 8 parts → Denominator = 8
- Improper Fraction = 11/8
- Mixed Number: 11 ÷ 8 = 1 with remainder 3 → 1 3/8

✔ Answer:
- Improper Fraction: 11/8
- Mixed Number: 1 3/8

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## ✔ Row 2: Pentagons divided into 5 parts

> Picture: Three full orange pentagons (each = 5/5), and one pentagon with 4 shaded parts.

- Total shaded parts = 5+5+5+4 = 19
- Each whole = 5 parts → Denominator = 5
- Improper Fraction = 19/5
- Mixed Number: 19 ÷ 5 = 3 with remainder 4 → 3 4/5

✔ Answer:
- Improper Fraction: 19/5
- Mixed Number: 3 4/5

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## ✔ Row 3: Squares divided into 4 parts

> Picture: Two full blue squares (each = 4/4), and one square with 1 shaded part.

- Total shaded parts = 4 + 4 + 1 = 9
- Each whole = 4 parts → Denominator = 4
- Improper Fraction = 9/4
- Mixed Number: 9 ÷ 4 = 2 with remainder 1 → 2 1/4

✔ Answer:
- Improper Fraction: 9/4
- Mixed Number: 2 1/4

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## ✔ Row 4: Triangles divided into 2 parts

> Picture: Five full yellow triangles (each = 2/2), and one triangle with 1 shaded part.

- Total shaded parts = 2+2+2+2+2+1 = 11
- Each whole = 2 parts → Denominator = 2
- Improper Fraction = 11/2
- Mixed Number: 11 ÷ 2 = 5 with remainder 1 → 5 1/2

✔ Answer:
- Improper Fraction: 11/2
- Mixed Number: 5 1/2

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## ✔ Row 5: Pentagons divided into 5 parts

> Picture: Four full red pentagons (each = 5/5), and one pentagon with 4 shaded parts.

- Total shaded parts = 5+5+5+5+4 = 24
- Each whole = 5 parts → Denominator = 5
- Improper Fraction = 24/5
- Mixed Number: 24 ÷ 5 = 4 with remainder 4 → 4 4/5

✔ Answer:
- Improper Fraction: 24/5
- Mixed Number: 4 4/5

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## ✔ Row 6: Grids of 9 squares (3x3)

> Picture: Three full green grids (each = 9/9), and one grid with 4 shaded squares.

- Total shaded parts = 9+9+9+4 = 31
- Each whole = 9 parts → Denominator = 9
- Improper Fraction = 31/9
- Mixed Number: 31 ÷ 9 = 3 with remainder 4 → 3 4/9

✔ Answer:
- Improper Fraction: 31/9
- Mixed Number: 3 4/9

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## ✔ Row 7: Rectangles of 10 squares (1x10)

> Picture: Three full purple rectangles (each = 10/10), and one rectangle with 7 shaded squares.

- Total shaded parts = 10+10+10+7 = 37
- Each whole = 10 parts → Denominator = 10
- Improper Fraction = 37/10
- Mixed Number: 37 ÷ 10 = 3 with remainder 7 → 3 7/10

✔ Answer:
- Improper Fraction: 37/10
- Mixed Number: 3 7/10

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## 🎯 Final Answers Table:

| Picture | Improper Fractions | Mixed Numbers |
|---------|--------------------|---------------|
| Row 1 (Circles) | 11/8 | 1 3/8 |
| Row 2 (Pentagons) | 19/5 | 3 4/5 |
| Row 3 (Squares) | 9/4 | 2 1/4 |
| Row 4 (Triangles) | 11/2 | 5 1/2 |
| Row 5 (Pentagons) | 24/5 | 4 4/5 |
| Row 6 (Grids) | 31/9 | 3 4/9 |
| Row 7 (Rectangles) | 37/10 | 3 7/10 |

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✔ All answers are written as requested — not simplified, and match the visual representation.

Let me know if you’d like this turned into a printable answer key! 😊