Which of the following numbers are in ascending order ?

Options

A. `(12)/(19), (12)/(25), (12)/(29), (12)/(37)`
B. `(12)/(29), (12)/(37), (12)/(19), (12)/(25)`
C. `(12)/(37), (12)/(29), (12)/(19), (12)/(25)`
D. `(12)/(37), (12)/(29), (12)/(25), (12)/(19)`

Answer

To determine which of the given fractions are in ascending order, we will compare the fractions step by step.

### Step-by-Step Solution:

1. **Identify the Fractions**:
We have the following fractions to compare:
- \( \frac{12}{19} \)
- \( \frac{12}{25} \)
- \( \frac{12}{29} \)
- \( \frac{12}{37} \)

2. **Understand Ascending Order**:
Ascending order means arranging the numbers from the smallest to the largest.

3. **Compare the Fractions**:
Since all the fractions have the same numerator (12), we can determine their values by looking at their denominators. The smaller the denominator, the larger the fraction, and vice versa.

4. **List the Denominators**:
The denominators are:
- 19
- 25
- 29
- 37

5. **Order the Denominators**:
Arranging the denominators from smallest to largest gives us:
- 19 (smallest)
- 25
- 29
- 37 (largest)

6. **Determine the Corresponding Fractions**:
Based on the order of the denominators, the fractions in ascending order are:
- \( \frac{12}{37} \) (smallest)
- \( \frac{12}{29} \)
- \( \frac{12}{25} \)
- \( \frac{12}{19} \) (largest)

7. **Final Ascending Order**:
Thus, the fractions in ascending order are:
- \( \frac{12}{37} < \frac{12}{29} < \frac{12}{25} < \frac{12}{19} \)

8. **Identify the Correct Option**:
From the options provided, the correct answer is the one that lists the fractions in the order we derived above.