Which of the following numbers is in standard form?

Options

A. `(-12)/(26)`
B. `(-49)/(70)`
C. `(-9)/(16)`
D. `(28)/(-105)`

Answer

To determine which of the given numbers is in standard form, we need to check if each fraction can be simplified further. A fraction is in standard form if the numerator and denominator have no common factors other than 1.

### Step-by-Step Solution:

1. **Check Option 1: \(-\frac{12}{26}\)**
- Find the greatest common divisor (GCD) of 12 and 26.
- The GCD is 2.
- Simplify: \(-\frac{12 \div 2}{26 \div 2} = -\frac{6}{13}\).
- This fraction can be simplified, so it is not in standard form.

2. **Check Option 2: \(-\frac{49}{70}\)**
- Find the GCD of 49 and 70.
- The GCD is 7.
- Simplify: \(-\frac{49 \div 7}{70 \div 7} = -\frac{7}{10}\).
- This fraction can also be simplified, so it is not in standard form.

3. **Check Option 3: \(-\frac{9}{16}\)**
- Find the GCD of 9 and 16.
- The GCD is 1 (since they have no common factors).
- Since the GCD is 1, \(-\frac{9}{16}\) is already in standard form.

4. **Check Option 4: \(\frac{28}{-105}\)**
- Find the GCD of 28 and 105.
- The GCD is 7.
- Simplify: \(\frac{28 \div 7}{-105 \div 7} = \frac{4}{-15}\).
- This fraction can be simplified, so it is not in standard form.

### Conclusion:
Among the four options, only Option 3, \(-\frac{9}{16}\), is in standard form.