What is the Inverse Additive?

He Inverse additive Of a number is its opposite, that is to say, it is that number that when added with itself, making use of an opposite sign, yields a result equivalent to zero.

In other words, the additive inverse of X would be Y if and only if X + Y = 0 (Online Course On Integer Numbers, 2017).

The inverse additive is the neutral element that is used in an addition to achieve a result equal to 0 (Coolmath.com, 2017).

Within the natural numbers or numbers that are used for counting elements in a set, all have an additive inverse minus the"0", since it itself is its inverse additive. In this way 0 + 0 = 0 (Szecsei, 2007).

The inverse of a natural number is a number whose absolute value has the same value, but with an opposite sign. This means that the additive inverse of 3 is -3, because 3 + (-3) = 0.

Properties of Additive Inverse

First Property

The main property of the additive inverse is that from which its name is derived (Freitag, 2014).

This indicates that if an integer-numbers without decimals- is added its inverse additive the result must be"0". So:

5 - 5 = 0

In this case, the additive inverse of"5"is"-5".

Second property

A key property of the additive inverse is that the subtraction of any number is equivalent to the sum of its additive inverse.

Numerically this concept would be explained as follows:

3 - 1 = 3 + (-1)

2 = 2

This property of the additive inverse is explained by the property of the subtraction which indicates that if we add the same amount to the minuend and the subtract, the difference in the result must be maintained. That is to say:

3 - 1 = [3 + (-1)] - [1 + (-1)]

2 = [2] - [0]

2 = 2

Thus, by modifying the location of any of the values ​​on the sides of the equals, it would also be modifying its sign, thus being able to obtain the additive inverse. So:

2 = 2 = 0

Here the"2"with positive sign happens to subtract to the other side of the equal, becoming the inverse additive.

This property makes it possible to transform a subtraction into a sum. In this case, since it is an integer, it is not necessary to perform additional procedures to carry out the process of subtraction of elements (Burrell, 1998).

Third Property

The additive inverse is easily calculated by using a simple arithmetic operation, which consists of multiplying the number whose additive inverse we want to find by -1. So:

5 x (-1) = -5

Then, the additive inverse of"5"will be"-5".

Examples of Additive Inverse

A) 20-5 = [20 + (-5)] - [5 + (-5)]

25 = [15] - [0]

15 = 15

15-15 = 0. The inverse additive of"15"will be"-15".

B) 18-6 = [18 + (-6)] - [6 + (-6)]

12 = [12] - [0]

12 = 12

12 - 12 = 0. The inverse additive of"12"will be"-12".

C) 27-9 = [27 + ​​(-9)] - [9 + (-9)]

18 = [18] - [0]

18 = 18

18-18 = 0. The inverse additive of"18"will be"-18".

D) 119 - 1 = [119 + (-1)] - [1 + (-1)]

118 = [118] - [0]

118 = 118

118 - 118 = 0. The inverse of"118"will be"-118".

E) 35-1 = [35 + (-1)] - [1 + (-1)]

34 = [34] - [0]

34 = 34

34 - 34 = 0. The inverse additive of"34"will be"-34".

F) 56-4 = [56 + (-4)] - [4 + (-4)]

52 = [52] - [0]

52 = 52

52 - 52 = 0. The inverse additive of"52"will be"-52".

G) 21-50 = [21 + (-50)] - [50 + (-50)]

-29 = [-29] - [0]

-29 = -29

-29 - (29) = 0. The inverse of"-29"will be"29".

H) 8-1 = [8 + (-1)] - [1 + (-1)]

7 = [7] - [0]

7 = 7

7 - 7 = 0. The inverse additive of"7"will be"-7".

I) 225-125 = [225 + (-125)] - [125 + (-125)]

100 = [100] - [0]

100 = 100

100 - 100 = 0. The inverse additive of"100"will be"-100".

J) 62 - 42 = [62 + (-42)] - [42 + (-42)]

20 = [20] - [0]

20 = 20

20-20 = 0. The inverse additive of"20"will be"-20".

K) 62 - 42 = [62 + (-42)] - [42 + (-42)]

20 = [20] - [0]

20 = 20

20-20 = 0. The inverse additive of"20"will be"-20".

L) 62 - 42 = [62 + (-42)] - [42 + (-42)]

20 = [20] - [0]

20 = 20

20-20 = 0. The inverse additive of"20"will be"-20".

M) 62 - 42 = [62 + (-42)] - [42 + (-42)]

20 = [20] - [0]

20 = 20

20-20 = 0. The inverse additive of"20"will be"-20".

N) 62 - 42 = [62 + (-42)] - [42 + (-42)]

20 = [20] - [0]

20 = 20

20-20 = 0. The inverse additive of"20"will be"-20".

O) 655 - 655 = 0. The inverse additive of"655"will be"-655".

P) 576-576 = 0. The inverse additive of"576"will be"-576".

Q) 1234 - 1234 = 0. The inverse additive of"1234"will be"-1234".

R) 998 - 998 = 0. The inverse additive of"998"will be"-998".

S) 50 - 50 = 0. The inverse additive of"50"will be"-50".

T) 75 - 75 = 0. The inverse of"75"will be"-75".

U) 325 - 325 = 0. The inverse additive of"325"will be"-325".

V) 9005 - 9005 = 0. The inverse additive of"9005"will be"-9005".

W) 35 - 35 = 0. The inverse additive of"35"will be"-35".

X) 4 - 4 = 0. The inverse additive of"4"will be"-4".

Y) 1 - 1 = 0. The inverse of"1"will be"-1".

Z) 0 - 0 = 0. The inverse of"0"will be"0".

Aa) 409 - 409 = 0. The inverse additive of"409"will be"-409".

References

  1. Burrell, B. (1998). Numbers and Calculating. In B. Burrell, Merriam-Webster's Guide to Everyday Math: A Home and Business Reference (Page 30). Springfield: Merriam-Webster.
  2. Coolmath.com. (2017). Cool Math . Obtained from The Additive Inverse Property: coolmath.com
  3. Online Course on Whole Numbers . (June 2017). Obtained from Inverse Additive: eneayudas.cl
  4. Freitag, M.A. (2014). Inverse Additive. In M. A. Freitag, Mathematics for Elementary School Teachers: A Process Approach (Page 293). Belmont: Brooks / Cole.
  5. Szecsei, D. (2007). The Algebra Matrices. In D. Szecsei, Pre-Calculus (Page 185). New Jersey: Career Press.


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