WHAT IS THE ADDITIVE INVERSE? PROPERTIES AND EXAMPLES - MATHS

The additive inverse of a number is its opposite, that is, it is that number that, when added to itself, using 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.

The additive inverse is the neutral element that is used in an addition to achieve a result equal to 0. Within the natural numbers or numbers that are used to count elements in a set, all have an additive inverse minus the "0", since it is itself its additive inverse. In this way 0 + 0 = 0.

The additive 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 the additive inverse

First property

The main property of the additive inverse is that from which its name is derived. This indicates that if a whole number - numbers without decimals - is added its additive inverse, 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 subtraction, which indicates that if we add the same amount to the minuend and the subtrahend, the difference in the result must be maintained. That is to say:

3 - 1 = -

2 = -

2 = 2

In this way, when modifying the location of any of the values to the sides of the equal, its sign would also be modified, thus being able to obtain the additive inverse. So:

2 - 2 = 0

Here the “2” with a positive sign is subtracted from the other side of the equal, becoming the additive inverse.

This property makes it possible to transform a subtraction into an addition. In this case, as they are integers, it is not necessary to perform additional procedures to carry out the process of subtracting elements.

Third property

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

5 x (-1) = -5

So the additive inverse of "5" will be "-5".

Examples of additive inverse

a) 20 - 5 = -

25 = -

15 = 15

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

b) 18 - 6 = -

12 = -

12 = 12

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

c) 27 - 9 = -

18 = -

18 = 18

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

d) 119 - 1 = -

118 = -

118 = 118

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

e) 35 - 1 = -

34 = -

34 = 34

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

f) 56 - 4 = -

52 = -

52 = 52

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

g) 21 - 50 = -

-29 = -

-29 = -29

-29 - (29) = 0. The additive inverse of “-29” will be “29”.

h) 8 - 1 = -

7 = -

7 = 7

7 - 7 = 0. The additive inverse of “7” will be “-7”.

i) 225 - 125 = -

100 = -

100 = 100

100 - 100 = 0. The additive inverse of “100” will be “-100”.

j) 62 - 42 = -

20 = -

20 = 20