Find the additive inverse of: (i) `(7)/(-10)` (ii) `(8)/(5)`

Answer

To find the additive inverse of a rational number, we need to determine what number, when added to the original number, results in zero. The additive inverse of a number \( x \) is simply \( -x \).

Let's solve the given problem step by step.

### Step 1: Find the additive inverse of \( \frac{7}{-10} \)

1. **Identify the number**: The given number is \( \frac{7}{-10} \).
2. **Rewrite the number**: We can rewrite \( \frac{7}{-10} \) as \( -\frac{7}{10} \) (since a negative sign in the denominator can be moved to the numerator).
3. **Determine the additive inverse**: The additive inverse of \( -\frac{7}{10} \) is \( \frac{7}{10} \) because:
\[ -\frac{7}{10} + \frac{7}{10} = 0 \]

### Step 2: Find the additive inverse of \( \frac{8}{5} \)

1. **Identify the number**: The given number is \( \frac{8}{5} \).
2. **Determine the additive inverse**: The additive inverse of \( \frac{8}{5} \) is \( -\frac{8}{5} \) because:
\[ \frac{8}{5} + \left(-\frac{8}{5}\right) = 0 \]

### Final Answers:

(i) The additive inverse of \( \frac{7}{-10} \) is \( \frac{7}{10} \).

(ii) The additive inverse of \( \frac{8}{5} \) is \( -\frac{8}{5} \).

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