**Multiplicative Inverse of -3/4**

To find the multiplicative inverse of a fraction, we need to find another fraction that, when multiplied by the given fraction, gives a product of 1. In other words, the multiplicative inverse of a fraction is the reciprocal of that fraction.

**Step 1: Understanding the given fraction**

The given fraction is -3/4. This means that the numerator is -3 and the denominator is 4.

**Step 2: Writing the reciprocal**

To find the reciprocal of a fraction, we interchange the numerator and the denominator. Therefore, the reciprocal of -3/4 is 4/-3.

**Step 3: Simplifying the reciprocal fraction**

To simplify the reciprocal fraction, we need to simplify the numerator and the denominator separately.

- The numerator, 4, is already in its simplest form.
- The denominator, -3, can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1. Dividing -3 by 1 gives us -3.

Therefore, the simplified reciprocal of -3/4 is 4/-3 or -4/3.

**Step 4: Verifying the multiplicative inverse**

To verify that -3/4 and -4/3 are multiplicative inverses, we need to multiply them together and check if the product is equal to 1.

- Multiplying -3/4 by -4/3 gives us (-3 * -4) / (4 * 3) = 12/12.
- Simplifying the product gives us 1.

Since the product of -3/4 and -4/3 is equal to 1, we can conclude that -4/3 is indeed the multiplicative inverse of -3/4.

In summary, the multiplicative inverse of -3/4 is -4/3.

Multiplicative inverse of -3/4 is -4/3