In math, what does reciprocal mean?

A reciprocal, or multiplicative inverse, is simply one of a pair of numbers that, when multiplied together, equal 1. If you can reduce the number to a fraction, finding the reciprocal is simply a matter of transposing the numerator and the denominator. To find the reciprocal of a whole number, just turn it into a fraction in which the original number is the denominator and the numerator is 1.

For example, the reciprocal of 2/3 is 3/2 (or 1-1/2) , because 2/3 x 3/2 = 1. The reciprocal of 7 is 1/7 because 7 x 1/7 = 1.

Decimal numbers, too, have reciprocals. To find the reciprocal of a decimal number, divide 1 by that number. For instance, to find the reciprocal of 1.25, divide 1 by 1.25:

1 ÷ 1.25 = 0.8

The multiplicative inverse of 1.25, therefore, is 0.8.

Understanding reciprocals can simplify many math problems when you understand that dividing by a number is the same as multiplying by the reciprocal of that number. For example

5 ÷ 1/4

is the same as

5 x 4/1 (which is simply 5 x 4, which of course equals 20)

Try it out for yourself. See if you can solve these problems in your head by multiplying the first number by the reciprocal of the second number:

  • 8 ÷ 1/5
  • 10 ÷ 1/10
  • 3 ÷ 3/8

(Hint: All the answers will be whole numbers.)