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# 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. You'll find that we are very often striving to get back to one or to "achieve oneness." Om...

Sample Problem

The multiplicative inverse of  is -4, since () × (-4) = 1

Sample Problem

The multiplicative inverse of   is , since  ×  = 1.

The multiplicative inverse of a fraction is called the reciprocal, and is the upside-down version of that fraction. Don't take us too literally here—you won't be converting to a fraction on its head. 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. Or a really good movie, like The Change-Up.

Why can't the fraction  have a multiplicative inverse? , so  There's no way to multiply  by something and get 1 as an answer. It has no multiplicative identity. 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.