Which of the following numbers does not lie between `(-5)/(6)` and `(7)/(8)` ?

Options

A. `(-17)/(24)`
B. `(5)/(6)`
C. `(-3)/(4)`
D. `(-11)/(12)`

Answer

To determine which of the given numbers does not lie between \(-\frac{5}{6}\) and \(\frac{7}{8}\), we will first convert these fractions into decimal form and then compare them with the options provided.

### Step 1: Convert the boundary fractions to decimal
1. **Convert \(-\frac{5}{6}\)**:
\[ -\frac{5}{6} \approx -0.8333 \]

2. **Convert \(\frac{7}{8}\)**:
\[ \frac{7}{8} = 0.875 \]

### Step 2: List the options and convert them to decimal
Now, we will convert each option to decimal:

1. **Option A: \(-\frac{17}{24}\)**:
\[ -\frac{17}{24} \approx -0.7083 \]

2. **Option B: \(\frac{5}{6}\)**:
\[ \frac{5}{6} \approx 0.8333 \]

3. **Option C: \(-\frac{3}{4}\)**:
\[ -\frac{3}{4} = -0.75 \]

4. **Option D: \(-\frac{11}{12}\)**:
\[ -\frac{11}{12} \approx -0.9167 \]

### Step 3: Compare the values
Now we will compare these decimal values with the boundaries \(-0.8333\) and \(0.875\):

- **Option A: \(-0.7083\)** lies between \(-0.8333\) and \(0.875\).
- **Option B: \(0.8333\)** lies between \(-0.8333\) and \(0.875\).
- **Option C: \(-0.75\)** lies between \(-0.8333\) and \(0.875\).
- **Option D: \(-0.9167\)** does not lie between \(-0.8333\) and \(0.875\) (it is less than \(-0.8333\)).

### Conclusion
The number that does not lie between \(-\frac{5}{6}\) and \(\frac{7}{8}\) is:
\[ \text{Option D: } -\frac{11}{12} \]