Algebra/Chapter 3/Inverses

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What are Equations? Algebra
Chapter 3: Solving Equations
Section 2: Inverses of Numbers
Properties of Equality

Numbers have two inverses: additive inverses, or opposites, and multiplicative inverses, or reciprocals. All real numbers besides 0 have both of these inverses.

Additive Inverses

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The additive inverse of a number is such that a number added to its additive inverse is zero. It is also called an opposite. To find a number's additive inverse, find if the number is positive, negative, or neither. If a number n is positive, then its additive inverse is -n. Likewise, the additive inverse of -n is n. 0 is the additive inverse of itself.

Multiplicative Inverses

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The multiplicative inverse of a number is such that a number multiplied by its multiplicative inverse is 1; that is, unity. It is also called a reciprocal. The multiplicative inverse of a number n is 1/n. To find a number's multiplicative inverse you may also write it as a fraction and reverse its numerator and denominator; recall that any number divided by 1 is itself. 0 has no multiplicative inverse; it would be 1/0, but numbers can not be divided by zero.