What number should be added to `(-5)/(8)` so as to get `(-3)/(2)`?

Answer

To solve the problem of what number should be added to \(-\frac{5}{8}\) to get \(-\frac{3}{2}\), we can follow these steps:

### Step 1: Set up the equation
Let the number to be added be \(X\). According to the problem, we can write the equation:
\[ -\frac{5}{8} + X = -\frac{3}{2} \]

### Step 2: Isolate \(X\)
To find \(X\), we need to isolate it on one side of the equation. We can do this by adding \(\frac{5}{8}\) to both sides:
\[ X = -\frac{3}{2} + \frac{5}{8} \]

### Step 3: Find a common denominator
To add the fractions \(-\frac{3}{2}\) and \(\frac{5}{8}\), we need a common denominator. The least common multiple (LCM) of 2 and 8 is 8. We can convert \(-\frac{3}{2}\) to have a denominator of 8:
\[ -\frac{3}{2} = -\frac{3 \times 4}{2 \times 4} = -\frac{12}{8} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ X = -\frac{12}{8} + \frac{5}{8} = \frac{-12 + 5}{8} = \frac{-7}{8} \]

### Step 5: Conclusion
Thus, the number that should be added to \(-\frac{5}{8}\) to get \(-\frac{3}{2}\) is:
\[ X = -\frac{7}{8} \]

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