What should be subtracted from ` (-7)/(8) ` to get `(5)/(12)` ?

Options

A. `(-31)/(24)`
B. `(31)/(24)`
C. `(35)/(24)`
D. `(-35)/(24)`

Answer

To solve the problem of what should be subtracted from \(-\frac{7}{8}\) to get \(\frac{5}{12}\), we can follow these steps:

### Step 1: Set up the equation
We need to find a number \(x\) such that:
\[ -\frac{7}{8} - x = \frac{5}{12} \]

### Step 2: Rearrange the equation
To isolate \(x\), we can rearrange the equation:
\[ -x = \frac{5}{12} + \frac{7}{8} \]
Now, we will change the sign:
\[ x = -\left(\frac{5}{12} + \frac{7}{8}\right) \]

### Step 3: Find a common denominator
To add \(\frac{5}{12}\) and \(\frac{7}{8}\), we need a common denominator. The least common multiple (LCM) of 12 and 8 is 24.

### Step 4: Convert fractions to have the same denominator
Convert \(\frac{5}{12}\) and \(\frac{7}{8}\) to have a denominator of 24:
\[ \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} \]
\[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ \frac{10}{24} + \frac{21}{24} = \frac{10 + 21}{24} = \frac{31}{24} \]

### Step 6: Substitute back into the equation
Now substitute back into the equation for \(x\):
\[ x = -\frac{31}{24} \]

### Final Answer
Thus, the value that should be subtracted from \(-\frac{7}{8}\) to get \(\frac{5}{12}\) is:
\[ \boxed{-\frac{31}{24}} \]

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