Question

what is the difference between a multiplicative inverse and a reciprocal?
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Answer 1

When the product of two numbers is one, they are called reciprocals or multiplicative inverses of each other. For example, equation image indicator and equation image indicator are reciprocals because equation image indicator. This is the motivation for the following property of fractions.

Inverse Property for Fraction Multiplication

equation image indicator where a and b are nonzero. The fraction equation image indicator is called the multiplicative inverse of equation image indicator (or reciprocal) and vice versa.

Notice that a reciprocal (multiplicative inverse) can be formed from any common fraction by exchanging the positions of the numerator and denominator. The reciprocal of equation image indicator is equation image indicator, of equation image indicator is equation image indicator, and equation image indicator is equation image indicator. The reciprocal (multiplicative inverse) for a mixed number is found by first changing the mixed number to an improper fraction. For example, equation image indicator so the reciprocal of equation image indicator is equation image indicator.

Answer 2

Answer:

There is no difference