subject: Introduction For Inverse Property Of Addition [print this page] The inverse property of addition is most useful in solving arithmetic expressions. Inverse property of addition to easily check the real number is additive inverse or not. The summation of a real number (x) and its addition inverse (-x), or opposite, gives the result is 0.Here, zero (0) is the additive identity.
Definition of Inverse Property of Addition:
The inverse property of addition encloses for any real number of variable x, there is a unique real number, denoted by -x.
OR
The inverse property of addition is when you add a real number and its additive inverse and you get the identity element (0).
a + (-a) = 0.
(- a)+ a =0.
Inverse Property of Addition:
The inverse property of addition has the following properties,
Associative Property of Addition
Commutative Property of Addition
Identity Property of Addition
Distributive Property of Multiplication over Addition
In mathematically, the addition notation is involved in commutative and associative, therefore the order in which the terms are added doesnt matter.
In identity property of addition, the identity factor of addition is labeled the additive identity. That is zero (0), adding zero to any real number will give up that same real number.
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As well as the inverse factor of addition or the additive inverse is the opposite of any real number.
For example, the opposite of a number 7 is (-7), therefore 7 + (-7) = 0.
Examples for Inverse Property of Addition:
Determine the additive inverse of the following real numbers, 6, 3x, (2y + 1), -3 and 1/5 by using the inverse property of addition.
Solution:
1. 6 + (- 6) = 0, so the additive inverse of 6 is -6.
2. 3x + (-3x) = 0, so the additive inverse of 3x is -3x.
3. [(2y + 1)] + [-(2y + 1)] =0, so the additive inverse of (2y + 1) is -(2y + 1)
4. Write the opposite (or additive inverse) of -3.
The opposite of -3 is 3, since -3 + 3 = 0.
5. Write the opposite (or additive inverse) of 1/5.
The opposite of 1/5 is -1/5, since 1/5 + (-1/5) = 0.
The inverse property of addition states that for every number n, n + (-n) = 0.
The inverse property of multiplication states that for every non-zero number n, n * (1/n) = 1. (note the non-zero part is important or else we would be dividing by zero and we are not allowed to do that)
So division is the inverse operation of multiplication and
subtraction is the inverse operation of addition.
One use of these properties is in solving equations.
For example:
Solve: 2x + 4 = 0
Subtract 4 on both sides; but this is really adding -4 so it uses negation (deriving -4 from 4), which is the inverse of addition.
2x = -4.
Divide both the sides by 2; but this is really multiplying by 1/2 so it uses inversion (getting from 2 to 1/2), which is the inverse property of multiplication.
