Which of the following is a proper fraction?

Options

A. `(8)/(8)`
B. `1(7)/(8)`
C. `(8)/(7)`
D. none of these

Answer

To determine which of the following is a proper fraction, we need to understand the definition of a proper fraction. A proper fraction is one where the numerator (the top number) is less than the denominator (the bottom number).

Let's analyze the given options step by step:

1. **Identify the fractions**: The options provided are:
- \( \frac{7}{8} \)
- \( 1 \times \frac{7}{8} \) (which is equivalent to \( \frac{7}{8} \))
- \( \frac{8}{7} \)
- None of these

2. **Check each fraction**:
- **For \( \frac{7}{8} \)**:
- The numerator is 7 and the denominator is 8.
- Since 7 is less than 8, \( \frac{7}{8} \) is a proper fraction.
- **For \( 1 \times \frac{7}{8} \)**:
- This is still \( \frac{7}{8} \), which we already established is a proper fraction.
- **For \( \frac{8}{7} \)**:
- The numerator is 8 and the denominator is 7.
- Since 8 is greater than 7, \( \frac{8}{7} \) is not a proper fraction.

3. **Conclusion**:
- The proper fractions from the options are \( \frac{7}{8} \) and \( 1 \times \frac{7}{8} \).
- The fraction \( \frac{8}{7} \) is not a proper fraction.

Therefore, the answer is that \( \frac{7}{8} \) and \( 1 \times \frac{7}{8} \) are proper fractions.