Find the inverse of a number

There are two ways to find the inverse of a number. The first way is to look for the opposite or additive inverse of the number. The second way is to look for the reciprocal or multiplicative inverse of the number.

  • The additive inverse or opposite of any number x is -x. The sum of opposites is equal to zero.
  • The multiplicative inverse or reciprocal of any nonzero number a is 1/a. The product of reciprocals is equal to one.

Examples showing how to find the inverse of a number

Find the opposite and reciprocal of these numbers: -6, 5/6, 4 1/5, -0.02, and 5x.

a. -6

The opposite of -6 is -(-6) = 6

The reciprocal of -6 is 1/-6

b. 5/6

The opposite of 5/6 is -(5/6) = -5/6

The reciprocal of 5/6 is 1/(5/6) = 1 x 6/5 = 6/5

c. 4 1/5

The opposite of 4 1/5 is -(4 1/5) = - 4 1/5

The reciprocal of 4 1/5 is 1/(4 1/5) = 1/(21/5) = 1 x 5/21 = 5/21

d. -0.02

The opposite of -0.02 is -(-0.02) = 0.02

The reciprocal of -0.02 is 1/(-0.02) = 1/(-2/100) = 1 x (-100/2) = 1 x (-50) = -50

e. 5x

The opposite of 5x is -(5x) = -5x

The reciprocal of 5x is 1/(5x) = 1/5x

Properties of real numbers