Types of Fractions Worksheets - Free Printable

Let's solve the problem step by step.

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A) State whether the following are proper fractions, improper fractions, or mixed numbers.

#### Definitions:
- Proper fraction: A fraction where the numerator is less than the denominator (e.g., $ \frac{2}{5} $).
- Improper fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., $ \frac{12}{11} $).
- Mixed number: A combination of a whole number and a proper fraction (e.g., $ 3\frac{5}{8} $).

Now let’s analyze each:

1) $ \frac{2}{5} $
- Numerator (2) < Denominator (5) → Proper fraction

2) $ \frac{12}{11} $
- Numerator (12) > Denominator (11) → Improper fraction

3) $ \frac{6}{4} $
- Numerator (6) > Denominator (4) → Improper fraction

4) $ 3\frac{5}{8} $
- This has a whole number and a fraction → Mixed number

5) $ 5\frac{8}{9} $
- Whole number + fraction → Mixed number

6) $ \frac{1}{7} $
- Numerator (1) < Denominator (7) → Proper fraction

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A) Answers:

1) Proper fraction
2) Improper fraction
3) Improper fraction
4) Mixed number
5) Mixed number
6) Proper fraction

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B) Identify each fraction and check "proper", "improper", or "mixed number" as appropriate.

We will fill in the table based on the definitions.

| S.No | Types of fractions | Proper | Improper | Mixed number |
|------|--------------------|--------|----------|---------------|
| 1) | $ \frac{3}{10} $ | ✔ | | |
| 2) | $ \frac{9}{2} $ | | ✔ | |
| 3) | $ 4\frac{1}{6} $ | | | ✔ |
| 4) | $ \frac{7}{3} $ | | ✔ | |

#### Explanation:
1) $ \frac{3}{10} $: 3 < 10 → Proper
2) $ \frac{9}{2} $: 9 > 2 → Improper
3) $ 4\frac{1}{6} $: Whole number + fraction → Mixed number
4) $ \frac{7}{3} $: 7 > 3 → Improper

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✔ Final Answer Table:

| S.No | Types of fractions | Proper | Improper | Mixed number |
|------|--------------------|--------|----------|---------------|
| 1) | $ \frac{3}{10} $ | ✔ | | |
| 2) | $ \frac{9}{2} $ | | ✔ | |
| 3) | $ 4\frac{1}{6} $ | | | ✔ |
| 4) | $ \frac{7}{3} $ | | ✔ | |

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✔ Summary:
- Proper fractions: Numerator < Denominator
- Improper fractions: Numerator ≥ Denominator
- Mixed numbers: Whole number + proper fraction

All answers are now correctly classified!