What should be subtracted from `-(3)/(8)` to get `(5)/(6)` ?

Answer

To solve the problem of what should be subtracted from \(-\frac{3}{8}\) to get \(\frac{5}{6}\), we can follow these steps:

### Step 1: Set Up the Equation
Let \(x\) be the number that needs to be subtracted from \(-\frac{3}{8}\). We can write the equation as:
\[ -\frac{3}{8} - x = \frac{5}{6} \]

### Step 2: Rearrange the Equation
To find \(x\), we can rearrange the equation:
\[ -x = \frac{5}{6} + \frac{3}{8} \]
Now, multiply both sides by -1:
\[ x = -\left(\frac{5}{6} + \frac{3}{8}\right) \]

### Step 3: Find a Common Denominator
To add the fractions \(\frac{5}{6}\) and \(\frac{3}{8}\), we need a common denominator. The least common multiple (LCM) of 6 and 8 is 24.

### Step 4: Convert the Fractions
Convert \(\frac{5}{6}\) and \(\frac{3}{8}\) to have a denominator of 24:
\[ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \]
\[ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \]

### Step 5: Add the Fractions
Now we can add the two fractions:
\[ \frac{5}{6} + \frac{3}{8} = \frac{20}{24} + \frac{9}{24} = \frac{29}{24} \]

### Step 6: Substitute Back to Find \(x\)
Now substitute back to find \(x\):
\[ x = -\left(\frac{29}{24}\right) = -\frac{29}{24} \]

### Final Answer
The number that should be subtracted from \(-\frac{3}{8}\) to get \(\frac{5}{6}\) is:
\[ \boxed{-\frac{29}{24}} \]

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