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Types of Numbers

Types of Numbers

At a Glance - Multiplicative Inverses

Every fraction with a nonzero numerator has a multiplicative inverse, which is simply the number we can multiply our fraction by to get 1. Basically, we're striving to get back to 1 or to "achieve oneness." It's like the math version of meditation.

Sample Problem

What's the multiplicative inverse of ?

In other words, what can we multiply this fraction by to turn it into 1? Since () × (-4) = 1, our multiplicative inverse is just -4.

Sample Problem

What's the multiplicative inverse of  ?

It's , since  ×  = 1.

The multiplicative inverse of a fraction is called the reciprocal, and it's the upside-down version of that fraction. Don't take us too literally here—you don't need to stand on your head or anything. Instead, you're just pulling the old switcheroo on the numerator and denominator.

To find the multiplicative inverse of an integer or mixed number, write the integer or mixed number as a fraction first, and then make the switch. It's like one of those bad movies on ABC Family where someone wakes up in someone else's place and has to figure out how to get back.

Why can't a fraction with a zero in its numerator like  have a multiplicative inverse? Here's why: , so  There's no way to multiply  by something and get 1 as an answer. It has no multiplicative inverse. It's like it has a case of multiplicative amnesia. It should probably go to a multiplicative hospital. Okay, we've officially beaten that word to death. We'll get it to a multiplicative morgue, stat.

Example 1

What's the multiplicative inverse of ?


Example 2

What's the multiplicative inverse of -4?


Exercise 1

What's the multiplicative inverse of ?


Exercise 2

What's the multiplicative inverse of -2?


Exercise 3

Find the multiplicative inverse of the final answer:


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