What should be added to `(-7)/(8)` to get `(5)/(9)`?

Answer

To solve the question "What should be added to \(-\frac{7}{8}\) to get \(\frac{5}{9}\)?", we can follow these steps:

### Step 1: Set up the equation
We need to find a number \(x\) such that:
\[ -\frac{7}{8} + x = \frac{5}{9} \]

### Step 2: Isolate \(x\)
To isolate \(x\), we can move \(-\frac{7}{8}\) to the other side of the equation. When we do this, we change its sign:
\[ x = \frac{5}{9} + \frac{7}{8} \]

### Step 3: Find a common denominator
To add the fractions \(\frac{5}{9}\) and \(\frac{7}{8}\), we need a common denominator. The least common multiple (LCM) of 9 and 8 is 72.

### Step 4: Convert the fractions
Now we convert each fraction to have the common denominator of 72:
- For \(\frac{5}{9}\):
\[ \frac{5}{9} = \frac{5 \times 8}{9 \times 8} = \frac{40}{72} \]
- For \(\frac{7}{8}\):
\[ \frac{7}{8} = \frac{7 \times 9}{8 \times 9} = \frac{63}{72} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ x = \frac{40}{72} + \frac{63}{72} = \frac{40 + 63}{72} = \frac{103}{72} \]

### Step 6: Conclusion
Thus, the number that should be added to \(-\frac{7}{8}\) to get \(\frac{5}{9}\) is:
\[ \frac{103}{72} \]

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