Which operation is described by multiplying a number by its multiplicative inverse?

Which operation is described by multiplying a number by its multiplicative inverse?

• A. Addition resulting in zero
• B. Multiplication resulting in one
• C. Division resulting in zero
• D. Subtraction resulting in one

Answer: (B)

Multiplying a number by its multiplicative inverse results in one. The multiplicative inverse of a number \( x \) is \( \frac{1}{x} \), which means that when you multiply \( x \) by \( \frac{1}{x} \), the product will always equal one, as long as \( x \) is not zero. This operation is based on the fundamental properties of multiplication and is essential in various mathematical contexts, including solving equations and understanding fractions. For example, if you take the number 5, its multiplicative inverse is \( \frac{1}{5} \). Multiplying these together: \[ 5 \times \frac{1}{5} = 1 \] This idea underpins many operations in algebra and demonstrates how multiplying by a reciprocal restores balance or identity in multiplication, specifically leading to the product of one. In contrast, addition resulting in zero, division resulting in zero, and subtraction resulting in one do not accurately reflect the behavior described in the question. Therefore, the operation of multiplying a number by its multiplicative inverse correctly leads to the result of one.

Multiplying a number by its multiplicative inverse results in one. The multiplicative inverse of a number ( x ) is ( \frac{1}{x} ), which means that when you multiply ( x ) by ( \frac{1}{x} ), the product will always equal one, as long as ( x ) is not zero. This operation is based on the fundamental properties of multiplication and is essential in various mathematical contexts, including solving equations and understanding fractions.

For example, if you take the number 5, its multiplicative inverse is ( \frac{1}{5} ). Multiplying these together:

[

5 \times \frac{1}{5} = 1

]

This idea underpins many operations in algebra and demonstrates how multiplying by a reciprocal restores balance or identity in multiplication, specifically leading to the product of one.

In contrast, addition resulting in zero, division resulting in zero, and subtraction resulting in one do not accurately reflect the behavior described in the question. Therefore, the operation of multiplying a number by its multiplicative inverse correctly leads to the result of one.