Sum of two rational numbers is -8 if one number is `(3)/(4),` then find other number.

Options

A. `(-4)/(35)`
B. `(-35)/(4)`
C. `(35)/(4)`
D. `(4)/(35)`

Answer

To find the other rational number when the sum of two rational numbers is -8 and one of the numbers is \( \frac{3}{4} \), we can follow these steps:

### Step 1: Set up the equation
Let the other rational number be \( x \). According to the problem, we have:
\[ x + \frac{3}{4} = -8 \]

### Step 2: Isolate \( x \)
To find \( x \), we need to isolate it on one side of the equation. We can do this by subtracting \( \frac{3}{4} \) from both sides:
\[ x = -8 - \frac{3}{4} \]

### Step 3: Convert -8 to a fraction
To perform the subtraction, we need to express -8 as a fraction with the same denominator as \( \frac{3}{4} \). We can write -8 as:
\[ -8 = -\frac{8 \times 4}{4} = -\frac{32}{4} \]

### Step 4: Substitute and simplify
Now substitute this back into the equation:
\[ x = -\frac{32}{4} - \frac{3}{4} \]
Combine the fractions:
\[ x = -\frac{32 + 3}{4} = -\frac{35}{4} \]

### Conclusion
Thus, the other rational number is:
\[ \boxed{-\frac{35}{4}} \]