Write the additive inverse of :
(i) `(3)/(8)`
(ii) `(-8)/(15)`
(iii) `(4)/(-13)`
(v) `(-6)/(-11)`

Answer

To find the additive inverse of a rational number, we need to understand that the additive inverse of a number \( x \) is the number that, when added to \( x \), results in zero. This means that the additive inverse of a number \( \frac{a}{b} \) is \( -\frac{a}{b} \).

Now, let's find the additive inverses for the given rational numbers step by step.

### Step 1: Find the additive inverse of \( \frac{3}{8} \)
- The additive inverse of \( \frac{3}{8} \) is \( -\frac{3}{8} \).

### Step 2: Find the additive inverse of \( -\frac{8}{15} \)
- The additive inverse of \( -\frac{8}{15} \) is \( \frac{8}{15} \) (since the negative sign will cancel out).

### Step 3: Find the additive inverse of \( \frac{4}{-13} \)
- The additive inverse of \( \frac{4}{-13} \) is \( -\frac{4}{-13} \), which simplifies to \( \frac{4}{13} \) (the negatives cancel out).

### Step 4: Find the additive inverse of \( -\frac{6}{-11} \)
- The additive inverse of \( -\frac{6}{-11} \) is \( \frac{6}{-11} \), which simplifies to \( -\frac{6}{11} \) (the negatives cancel out).

### Summary of Results:
1. Additive inverse of \( \frac{3}{8} \) is \( -\frac{3}{8} \).
2. Additive inverse of \( -\frac{8}{15} \) is \( \frac{8}{15} \).
3. Additive inverse of \( \frac{4}{-13} \) is \( \frac{4}{13} \).
4. Additive inverse of \( -\frac{6}{-11} \) is \( -\frac{6}{11} \).