What should be subtracted from `(-2)/(3)` to get `(3)/(4)`?

Options

A. `(-11)/(12)`
B. `(-13)/(12)`
C. `(-5)/(4) `
D. `(-17)/(12)`

Answer

To solve the problem, we need to find the value of \( x \) that should be subtracted from \( -\frac{2}{3} \) to get \( \frac{3}{4} \).

Let's set up the equation based on the information given:

1. **Set up the equation**:
\[ -\frac{2}{3} - x = \frac{3}{4} \]

2. **Isolate \( x \)**:
To isolate \( x \), we can rearrange the equation:
\[ -x = \frac{3}{4} + \frac{2}{3} \]
Now, we need to find a common denominator to add the fractions on the right side.

3. **Find a common denominator**:
The denominators are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12. We will convert both fractions to have a denominator of 12.
\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]
\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]

4. **Add the fractions**:
Now we can add the two fractions:
\[ -x = \frac{9}{12} + \frac{8}{12} = \frac{17}{12} \]

5. **Solve for \( x \)**:
To find \( x \), we multiply both sides by -1:
\[ x = -\frac{17}{12} \]

Thus, the number that should be subtracted from \( -\frac{2}{3} \) to get \( \frac{3}{4} \) is \( -\frac{17}{12} \).