Which of the following sets of fractions is in the correct sequence of ascending order of their values?

Options

A. `-1/2,5/6,(-4)/(-9)`
B. `-3/7,(-5)/6,3/5`
C. `(-1/2,-4/9,5/6)`
D. `(-4/9,5/6,1/6)`

Answer

To solve the problem of determining which set of fractions is in the correct sequence of ascending order, we will analyze the given fractions step by step.

### Step-by-Step Solution:

1. **Identify the Fractions**:
Let's assume we have the following fractions to compare:
- A: -3/7
- B: -5/6
- C: 5/6
- D: 4/9
- E: 1/6

2. **Understanding Ascending Order**:
Ascending order means arranging the fractions from the smallest to the largest value. Negative fractions are smaller than positive fractions.

3. **Compare Negative Fractions**:
- First, compare -3/7 and -5/6.
- To compare these, we can cross-multiply:
\[ -3 \times 6 \quad \text{and} \quad -5 \times 7 \]
This gives us:
\[ -18 \quad \text{and} \quad -35 \]
- Since -18 is greater than -35, we conclude that:
\[ -5/6 < -3/7 \]

4. **Compare Positive Fractions**:
- Now, we compare the positive fractions 5/6 and 4/9.
- Cross-multiply:
\[ 5 \times 9 \quad \text{and} \quad 4 \times 6 \]
This gives us:
\[ 45 \quad \text{and} \quad 24 \]
- Since 45 is greater than 24, we conclude that:
\[ 4/9 < 5/6 \]

5. **Combine Results**:
- From the comparisons, we have:
\[ -5/6 < -3/7 < 4/9 < 5/6 \]
- This indicates that the correct ascending order of the fractions is:
\[ -5/6, -3/7, 4/9, 5/6 \]

6. **Final Check**:
- Ensure that all comparisons are correct and that the order is maintained.
- Since we have confirmed the order, we can conclude that the correct ascending order is indeed:
\[ -5/6, -3/7, 4/9, 5/6 \]

### Conclusion:
The correct ascending order of the fractions is:
\[ -5/6, -3/7, 4/9, 5/6 \]