**Multiplicative Inverse of 3 by -5**

To find the multiplicative inverse of 3 by -5, we need to determine a number that, when multiplied by 3 by -5, will result in the multiplicative identity, which is 1. In other words, we are looking for a number that, when multiplied by 3 by -5, will give us 1 as the product.

Let's break down the process step by step:

**Step 1: Understanding the Multiplicative Inverse**
The multiplicative inverse, also known as the reciprocal, of a number 'a' is denoted as 1/a. The product of a number and its multiplicative inverse is always equal to 1.

**Step 2: Determining the Multiplicative Inverse of 3 by -5**
To find the multiplicative inverse of 3 by -5, we need to divide 1 by 3 by -5. In other words, we need to find the number that, when multiplied by 3 by -5, will result in 1.

**Step 3: Calculation**
To calculate the multiplicative inverse, we divide 1 by 3 by -5.

1 / (3 x -5)

The product of 3 and -5 is -15.

1 / -15

Therefore, the multiplicative inverse of 3 by -5 is -1/15.

**Step 4: Verification**
To verify that -1/15 is indeed the multiplicative inverse of 3 by -5, we can multiply them together and check if the product is equal to 1.

(3 x -5) x (-1/15)

The product of 3 and -5 is -15.

-15 x (-1/15)

The -15 and -1/15 will cancel each other out, resulting in:

1

Since the product is equal to 1, we have correctly determined the multiplicative inverse of 3 by -5 to be -1/15.

Therefore, the multiplicative inverse of 3 by -5 is -1/15, as explained above.

-5/3