What number should be added to `(-7)/(8)` to get `(4)/(9)` ?

Options

A. `(94)/(72)`
B. `(93)/(72)`
C. `(95)/(72)`
D. `(96)/(72)`

Answer

To solve the problem of what number should be added to \(-\frac{7}{8}\) to get \(\frac{4}{9}\), we can follow these steps:

### Step 1: Set up the equation
Let \(x\) be the number we need to find. We can set up the equation as follows:
\[ x + \left(-\frac{7}{8}\right) = \frac{4}{9} \]

### Step 2: Rearrange the equation
To isolate \(x\), we can add \(\frac{7}{8}\) to both sides of the equation:
\[ x = \frac{4}{9} + \frac{7}{8} \]

### Step 3: Find a common denominator
To add the fractions \(\frac{4}{9}\) and \(\frac{7}{8}\), we need to find a common denominator. The least common multiple (LCM) of 9 and 8 is 72.

### Step 4: Convert the fractions
Now, we convert both fractions to have the common denominator of 72:
\[ \frac{4}{9} = \frac{4 \times 8}{9 \times 8} = \frac{32}{72} \]
\[ \frac{7}{8} = \frac{7 \times 9}{8 \times 9} = \frac{63}{72} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ x = \frac{32}{72} + \frac{63}{72} = \frac{32 + 63}{72} = \frac{95}{72} \]

### Step 6: Conclusion
Thus, the number that should be added to \(-\frac{7}{8}\) to get \(\frac{4}{9}\) is:
\[ x = \frac{95}{72} \]