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The multiplicative inverse of a number is simply 1 divided by that number—for example, the multiplicative inverse of 2 is 1/2. This concept matters because multiplying any number by its multiplicative inverse always gives you 1, which is useful for solving equations and performing calculations in mathematics and science.
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Encyclopedic overview
The reciprocal function, y = 1/x. For every non-zero x coordinate, the corresponding y coordinate on the graph represents its multiplicative inverse. The graph forms a rectangular hyperbola.
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. Dividing 1 by a real number yields its multiplicative inverse. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).
Excerpted from Wikipedia’s “multiplicative inverse” article, available under the CC BY-SA 4.0 licence.