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Reciprocal




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In mathematics, the reciprocal (or multiplicative inverse) of a number is 1 divided by the number, or equivalently, the number raised to the power of -1 (as in [math]\tfrac{1}{x}[/math] and [math]x^{-1}[/math]).[1][2] All numbers have a reciprocal except zero, since no number times 0 is 1. Two numbers are reciprocal of each other if and only if their product is 1.[3] For example:

  • 2.5 and 0.4 are reciprocals, because 2.5 × 0.4 = 1.
  • -0.2 and -5 are reciprocals, because -0.2 × -5 = 1.
  • 1 and -1 are their own reciprocals, because 1 × 1 = 1 and -1 × -1 = 1.

To find the reciprocal of a fraction, swap the numerator and the denominator. Whole numbers can be thought as having a denominator of 1.[2] For example:

  • The reciprocal of 8 is 1/8 (or 0.125).
  • The reciprocal of 5/3 is 3/5 (or 0.6).
  • The reciprocal of 1/7 is 7.
  • The reciprocal of -9/4 is -4/9.

Dividing a fraction is the same as multiplying its reciprocal and vice versa.

Related pages

References

  1. "Compendium of Mathematical Symbols" (in en-US). 2020-03-01. https://mathvault.ca/hub/higher-math/math-symbols/. 
  2. 2.0 2.1 "Reciprocal". https://www.mathsisfun.com/reciprocal.html. 
  3. Weisstein, Eric W.. "Reciprocal" (in en). https://mathworld.wolfram.com/Reciprocal.html#:~:text=Two%20numbers%20are%20reciprocals%20if,number,%20the%20smaller%20its%20reciprocal..