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
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