Which of the following is a vulgar fraction? `3/10` `13/10` `10/3` none of these

Options

A. `3/10`
B. `13/10`
C. `10/3`
D. none of these

Answer

To determine which of the given fractions is a vulgar fraction, we first need to understand what a vulgar fraction is.

### Step-by-step Solution:

1. **Definition of a Vulgar Fraction**:
A vulgar fraction is a fraction where the denominator is a whole number that is not 10, 100, 1000, etc. In simpler terms, it can be any whole number except for those specific values.

2. **Examine the Given Fractions**:
We have three fractions to consider:
- \( \frac{3}{10} \)
- \( \frac{13}{10} \)
- \( \frac{10}{3} \)

3. **Check Each Fraction**:
- **For \( \frac{3}{10} \)**: The denominator is 10. Since 10 is one of the numbers we are excluding, \( \frac{3}{10} \) is **not** a vulgar fraction.
- **For \( \frac{13}{10} \)**: The denominator is also 10. Therefore, \( \frac{13}{10} \) is **not** a vulgar fraction.
- **For \( \frac{10}{3} \)**: The denominator is 3, which is not one of the excluded numbers (10, 100, 1000). Thus, \( \frac{10}{3} \) **is** a vulgar fraction.

4. **Conclusion**:
From the analysis, the only vulgar fraction among the options provided is \( \frac{10}{3} \).

### Final Answer:
The vulgar fraction is \( \frac{10}{3} \).

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