Reciprocal

The reciprocal of a nonzero number is the number that multiplies with it to give 1. For a number x, its reciprocal is 1/x.

Multiplicative inverse: An element that multiplies with another element to produce the identity element. A reciprocal is the multiplicative inverse of a nonzero number.
Real number: A number on the continuous number line, including rational and irrational numbers. Every nonzero real number has a reciprocal that is also real.
Proportion: An equation stating that two ratios are equal. Reversing a ratio replaces it with its reciprocal and can reveal an equivalent relation.
Additive inverse: The number that adds to a given number to produce zero. It undoes addition, whereas a reciprocal undoes multiplication.
Division: An arithmetic operation that partitions a quantity or determines how many times one quantity contains another. Dividing by a nonzero number is equivalent to multiplying by its reciprocal.
Rational number: A number expressible as a ratio of integers with a nonzero denominator. The reciprocal of a nonzero rational number is rational.
Unit conversion: The process of expressing a measurement in different units without changing its quantity. Conversion factors often use reciprocal units to cancel the original unit.
Square root: A number whose square equals a given number. Taking a reciprocal reverses multiplication by a factor; taking a square root reverses squaring.
Multiplicative identity: The number 1, which leaves any number unchanged when multiplied by it. A number and its reciprocal multiply to this identity.
Exponentiation: The operation of raising a base to a power. A reciprocal can be written as a negative first power: x⁻¹ = 1/x.

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