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 fractions to decimals
1. Convert \(-\frac{5}{6}\):
\[ -\frac{5}{6} \approx -0.8333 \]

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

### Step 2: Identify the range
Now we know that:
\[ -0.8333 < x < 0.875 \]
This means any number that lies between \(-0.8333\) and \(0.875\) is valid.

### Step 3: Evaluate the options
Assuming the options are:
1. \(-0.75\)
2. \(0.8\)
3. \(0.9\)
4. \(-0.5\)

Now we will check each option to see if it lies within the range.

- **Option 1: \(-0.75\)**
\[ -0.8333 < -0.75 < 0.875 \quad \text{(valid)} \]

- **Option 2: \(0.8\)**
\[ -0.8333 < 0.8 < 0.875 \quad \text{(valid)} \]

- **Option 3: \(0.9\)**
\[ -0.8333 < 0.9 \quad \text{and} \quad 0.9 > 0.875 \quad \text{(not valid)} \]

- **Option 4: \(-0.5\)**
\[ -0.8333 < -0.5 < 0.875 \quad \text{(valid)} \]

### Conclusion
The number that does not lie between \(-\frac{5}{6}\) and \(\frac{7}{8}\) is **\(0.9\)**.