Inverse Property of Addition / Multiplication
Inverse Property of Addition (InversePA)
When you add opposites you always end up with zero. Opposites always cancel each other out. (The additive inverse of a number is its opposite.)
Inverse Property of Addition
(Opposites always cancel)
a + -a = 0
8 + -8 = 0
(a + b) + -(a + b) = 0
-z + z = 0
-(3 + y) + (3 + y) = 0
0 = -7 + 7


Inverse Property of Multiplication (InversePM)
When you multiply anything by its reciprocal you always end up with one. The product of reciprocals is always one. (The multiplicative inverse of a number is its reciprocal.)
Inverse Property of Multiplication
(The product of reciprocals is one)
a • 1/a = 1
8 • 1/8 = 1
ab • 1/(ab) = 1
(x + y) • 1/(x + y) = 1
1/(3y) • 3y = 1
1/5 • 5 = 1