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Chapter 1: Problem 125

Explain how to find the multiplicative inverse of a number.

Short Answer

Expert verified
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 by step solution

01

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.
02

Identify the Number

Identify the number for which you need to find the multiplicative inverse.
03

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.
04

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.

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