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

Options

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

Answer

To solve the problem of what should be subtracted from \(-\frac{2}{3}\) to get \(\frac{3}{4}\), we can follow these steps:

### Step 1: Set up the equation
We need to find a number \(x\) such that:
\[ -\frac{2}{3} - x = \frac{3}{4} \]

### Step 2: Rearrange the equation
To isolate \(x\), we can rearrange the equation:
\[ -x = \frac{3}{4} + \frac{2}{3} \]
Now, multiply both sides by -1:
\[ x = -\left(\frac{3}{4} + \frac{2}{3}\right) \]

### Step 3: Find a common denominator
To add the fractions \(\frac{3}{4}\) and \(\frac{2}{3}\), we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12.

### Step 4: Convert the fractions
Convert \(\frac{3}{4}\) and \(\frac{2}{3}\) to have the common denominator of 12:
\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]
\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ \frac{9}{12} + \frac{8}{12} = \frac{9 + 8}{12} = \frac{17}{12} \]

### Step 6: Substitute back to find \(x\)
Now substitute back into the equation for \(x\):
\[ x = -\frac{17}{12} \]

### Conclusion
Thus, the number that should be subtracted from \(-\frac{2}{3}\) to get \(\frac{3}{4}\) is:
\[ \boxed{-\frac{17}{12}} \]