`(3)/(-4)` ________ `(-5)/(6)` compare

Options

A. `ge`
B. `lt`
C. `gt`
D. `=`

Answer

To compare the two rational numbers \(-\frac{3}{4}\) and \(-\frac{5}{6}\), we can follow these steps:

### Step 1: Write the two fractions together
We have the two fractions:
\[ -\frac{3}{4} \quad \text{and} \quad -\frac{5}{6} \]

### Step 2: Cross-multiply the fractions
To compare the two fractions, we can cross-multiply:
\[ (-3) \times 6 \quad \text{and} \quad (-5) \times 4 \]
Calculating these gives:
\[ -18 \quad \text{and} \quad -20 \]

### Step 3: Compare the results
Now, we compare \(-18\) and \(-20\):
Since \(-18\) is greater than \(-20\), we can conclude that:
\[ -\frac{3}{4} > -\frac{5}{6} \]

### Conclusion
Thus, the final comparison is:
\[ -\frac{3}{4} \quad \text{is greater than} \quad -\frac{5}{6} \]

### Final Answer
The answer is:
\[ -\frac{3}{4} > -\frac{5}{6} \]

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