Problem 125 - Introductory Algebra for College Students

Question

Explain how to find the multiplicative inverse of a number.

Step-by-Step Solution

Answer

The multiplicative inverse of a number is its reciprocal- if the number is \( a \), its multiplicative inverse is \( \frac{1}{a} \) or \( a^{-1} \). Multiply the original number with its multiplicative inverse to check the result- the answer should be 1.

Step 1: Understand the Problem

The multiplicative inverse of a number is the number that, when multiplied by the original number, gives a product of 1. Essentially, they 'cancel out' each other in multiplication.

Step 2: Identify the Number

Identify the number for which you need to find the multiplicative inverse.

Step 3: Calculate the Reciprocal

To find the multiplicative inverse of the number, calculate its reciprocal. The reciprocal of a number \( a \) is \( \frac{1}{a} \). This can also be expressed as \( a^{-1} \), where '-1' is the exponent, indicating the reciprocal.

Step 4: Check the Result

To verify if the result is correct, multiply the original number by its multiplicative inverse. The product should be equal to 1.