What number should be subtracted from `(-2)/(3)` to get `(-1)/(6)` ?

Options

A. `-(3)/(2) `
B. `-(1)/(2) `
C. `-(7)/(2) `
D. `-(9)/(2) `

Answer

To solve the problem, we need to find the number \( x \) that should be subtracted from \(-\frac{2}{3}\) to get \(-\frac{1}{6}\).

### Step-by-step Solution:

1. **Set up the equation**:
We start with the equation based on the problem statement:
\[ -\frac{2}{3} - x = -\frac{1}{6} \]

2. **Isolate \( x \)**:
To find \( x \), we can rearrange the equation:
\[ -x = -\frac{1}{6} + \frac{2}{3} \]
Now, we need to simplify the right side.

3. **Find a common denominator**:
The denominators are 6 and 3. The least common multiple (LCM) of 6 and 3 is 6. We can rewrite \(\frac{2}{3}\) with a denominator of 6:
\[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]

4. **Substitute and simplify**:
Now substitute \(\frac{4}{6}\) back into the equation:
\[ -x = -\frac{1}{6} + \frac{4}{6} \]
Combine the fractions:
\[ -x = \frac{4 - 1}{6} = \frac{3}{6} \]
Simplifying \(\frac{3}{6}\) gives:
\[ -x = \frac{1}{2} \]

5. **Solve for \( x \)**:
Multiply both sides by -1 to solve for \( x \):
\[ x = -\frac{1}{2} \]

### Final Answer:
The number that should be subtracted from \(-\frac{2}{3}\) to get \(-\frac{1}{6}\) is:
\[ \boxed{-\frac{1}{2}} \]