The sum of two rational numbers is `-5/8` If one of them is `7/16` find the other.

Answer

To find the other rational number when the sum of two rational numbers is \(-\frac{5}{8}\) and one of them is \(\frac{7}{16}\), we can follow these steps:

### Step 1: Set up the equation
We know that:
\[ \frac{7}{16} + x = -\frac{5}{8} \]
where \(x\) is the other rational number we need to find.

### Step 2: Isolate \(x\)
To find \(x\), we can rearrange the equation:
\[ x = -\frac{5}{8} - \frac{7}{16} \]

### Step 3: Find a common denominator
The denominators are \(8\) and \(16\). The least common multiple (LCM) of \(8\) and \(16\) is \(16\). We need to convert \(-\frac{5}{8}\) to have a denominator of \(16\):
\[ -\frac{5}{8} = -\frac{5 \times 2}{8 \times 2} = -\frac{10}{16} \]

### Step 4: Substitute back into the equation
Now we can substitute this back into our equation for \(x\):
\[ x = -\frac{10}{16} - \frac{7}{16} \]

### Step 5: Combine the fractions
Now that both fractions have the same denominator, we can combine them:
\[ x = \frac{-10 - 7}{16} = \frac{-17}{16} \]

### Step 6: Conclusion
Thus, the other rational number is:
\[ x = -\frac{17}{16} \]