What is the inverse of 5 under multiplication?

• A. 5
• B. 0
• C. 1/5
• D. 2

Answer: (C)

In the context of multiplication, the inverse of a number is defined as a value that, when multiplied by the original number, results in the multiplicative identity, which is 1.

For the number 5, to find its multiplicative inverse, you need to determine what number, when multiplied by 5, gives you 1. This can be expressed mathematically as:

5 * x = 1

To find x, you can rearrange this equation:

x = 1/5

When you multiply 5 by 1/5, you indeed get:

5 * (1/5) = 5/5 = 1

This confirms that 1/5 is the multiplicative inverse of 5, thus making it the correct answer. Understanding this principle is crucial in operations involving multiplicative inverses, especially in areas such as algebra and finite mathematics.