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Inverse properties

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The concept of inverse properties states that "when a number is combined with its inverse, it is equal to its identity." There are two forms of inverse properties with which we are concerned: multiplicative inverse and additive inverse. The additive inverse property states that x + (-x) = 0. A positive integer added to its negative counterpart will always equal zero. In the case of the multiplicative inverse property, however, the result will always be one. We can express this through the formula a x 1/a = 1. But why is this? Keep in mind that a = a/1. When we multiply two fractions in which each fraction's numerator is equal to the denominator of the other, and each fraction's denominator is equal to the other, we invariably end up with a product of 1.

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