Find the multiplicative inverse of : (i) `(-3)/(4)` (ii) `(11)/(4)`

Answer

To find the multiplicative inverse of a rational number, we need to understand that the multiplicative inverse of a number \( a \) is \( \frac{1}{a} \). In simpler terms, if you multiply a number by its multiplicative inverse, the result is 1.

Let's find the multiplicative inverse of the given rational numbers step by step.

### Step 1: Find the multiplicative inverse of \(-\frac{3}{4}\)

1. **Identify the number**: The number is \(-\frac{3}{4}\).
2. **Write the multiplicative inverse**: The multiplicative inverse of \(-\frac{3}{4}\) is obtained by flipping the fraction and changing the sign. Therefore, it becomes \(-\frac{4}{3}\).
3. **Conclusion**: The multiplicative inverse of \(-\frac{3}{4}\) is \(-\frac{4}{3}\).

### Step 2: Find the multiplicative inverse of \(\frac{11}{4}\)

1. **Identify the number**: The number is \(\frac{11}{4}\).
2. **Write the multiplicative inverse**: The multiplicative inverse of \(\frac{11}{4}\) is obtained by flipping the fraction. Therefore, it becomes \(\frac{4}{11}\).
3. **Conclusion**: The multiplicative inverse of \(\frac{11}{4}\) is \(\frac{4}{11}\).

### Final Answers:
- The multiplicative inverse of \(-\frac{3}{4}\) is \(-\frac{4}{3}\).
- The multiplicative inverse of \(\frac{11}{4}\) is \(\frac{4}{11}\).

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