The Inverse Properties
Additive Inverse Property
Inverse Property for
a + (-a) = 0 and –a + a = 0
Additive inverses are called opposites.
When you add a number to its additive inverse, the result is 0.
Other terms that are synonymous with additive inverse are negative and opposite.
Write the opposite (or additive inverse) of -3.
The opposite of -3 is 3, since -3 + 3 = 0.
Example: Write the opposite (or additive inverse) of 1/5.
The opposite of 1/5 is -1/5, since 1/5 + (-1/5) = 0.
Multiplicative Inverse Property
Inverse Property for Multiplication:
Multiplicative inverses are called reciprocals.
When you multiply a number by its multiplicative inverse the result is 1.
A multiplicative inverse or reciprocal of a real number a (except 0) is found by “flipping” a upside down.
The numerator of a
becomes the denominator of the reciprocal of a and the denominator of a becomes
the numerator of the reciprocal
Example: Write the reciprocal (or multiplicative inverse) of -3.
The reciprocal of -3 is -1/3, since -3(-1/3) = 1.
Example : Write the reciprocal (or multiplicative inverse) of 1/5.
The reciprocal of 1/5 is 5, since 5(1/5) = 1.