What should be subtracted from `(-3)/(4)` to get `(5)/(6)` ?

Answer

To solve the problem of what should be subtracted from \(-\frac{3}{4}\) to get \(\frac{5}{6}\), we can follow these steps:

### Step 1: Set up the equation
Let \(x\) be the number that should be subtracted from \(-\frac{3}{4}\). The equation can be set up as:
\[ -\frac{3}{4} - x = \frac{5}{6} \]

### Step 2: Rearrange the equation
To isolate \(x\), we can rearrange the equation:
\[ -x = \frac{5}{6} + \frac{3}{4} \]
Now, we can multiply both sides by -1 to solve for \(x\):
\[ x = -\left(\frac{5}{6} + \frac{3}{4}\right) \]

### Step 3: Find a common denominator
To add the fractions \(\frac{5}{6}\) and \(\frac{3}{4}\), we need a common denominator. The least common multiple (LCM) of 6 and 4 is 12.

### Step 4: Convert the fractions
Convert \(\frac{5}{6}\) and \(\frac{3}{4}\) to have the denominator of 12:
\[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \]
\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ \frac{10}{12} + \frac{9}{12} = \frac{10 + 9}{12} = \frac{19}{12} \]

### Step 6: Substitute back into the equation
Now substitute back to find \(x\):
\[ x = -\frac{19}{12} \]

### Final Answer
Thus, the value that should be subtracted from \(-\frac{3}{4}\) to get \(\frac{5}{6}\) is:
\[ \boxed{-\frac{19}{12}} \]

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