ADDITIVE INVERSE

In mathematics, the additive inverse of a number is the number itself with opposite sign.

That is,

• Additive inverse of a positive number is the number itself with negative sign. 
• Additive inverse of a negative number is the number itself with positive sign. 

Examples : 

Additive inverse of '+3' is '-3'.

Additive inverse of '-7' is '+7'.

Additive inverse of '-0.023' is '+0.023'.

Additive Inverse of a Fraction :

Additive inverse of a positive fraction is the same fraction with negative sign.

Additive inverse of a negative fraction is the same fraction with positive sign.

Examples :

Additive inverse of '+2/5' is '-2/5'.

Additive inverse of '-3/4' is '+3/4'.

Additive Inverse of Zero :

Additive inverse of zero is zero.

The number '0' is the only number with its additive inverse being itself. 

Note : 

The sum of a number and its additive inverse is always zero.

Examples : 

+3 + (-3)  =  0

-2 + (+2)  =  0

(+2/5) + (-2/5)  =  0

Practice Questions

Question 1 :

Find the additive inverse of '-15'. 

Answer :

The given number is a negative number.

Then, its additive inverse is the number itself with positive sign.

So, additive inverse of '-15' is

+15

Question 2 :

Find the additive inverse of '-0.3'. 

Answer :

The given number is a negative number.

Then, its additive inverse is the number itself with positive sign.

So, additive inverse of '-0.3' is

+0.3

Question 3 :

Find the additive inverse of '3'. 

Answer :

The given number is a positive number.

Then, its additive inverse is the number itself with negative sign.

So, additive inverse of '3' is

-3

Question 4 :

Find the additive inverse of '8,964'. 

Answer :

The given number is a positive number.

Then, its additive inverse is the number itself with negative sign.

So, additive inverse of '8,964' is

-8,964

Question 5 :

Find the additive inverse of '1/7'. 

Answer :

The given number is a positive number.

Then, its additive inverse is the number itself with negative sign.

So, additive inverse of '1/7' is

-1/7

Question 6 :

Simplify : 

(-9) + 9

Answer :

The numerical expression '(-9) + 9' is the sum of '-9' and its additive inverse '+9'.

We know the fact that the sum of a number and its additive inverse is zero. 

So, 

(-9) + 9  =  0

Question 7 :

Simplify : 

7 + (-7)

Answer :

The numerical expression '7 + (-7)' is the sum of '7' and its additive inverse '-7'.

We know the fact that the sum of a number and its additive inverse is zero. 

So, 

7 + (-7)  =  0

Question 8 :

Given : 

5 + x  =  0

Find the value of 'x'.

Answer :

It is given that the sum of '5' and 'x' is zero.

Then, additive inverse of '5' is 'x'. 

But, additive inverse of '5' is '-5'

So, 

x  =  -5

Question 9 :

Given : 

(-7/8) + (x/8)  =  0

Find the value of 'x'.

Answer :

It is given that the sum of '-7/8' and 'x/8' is zero.

Then, additive inverse of '-7/8' is 'x/8'. 

But, additive inverse of '-7/8' is '7/8'

So, 

x/8  =  7/8

x  =  7

Question 10 :

Given : 

(2/3) + (x/6)  =  0

Find the value of 'x'.

Answer :

It is given that the sum of '2/3' and 'x/6' is zero.

Then, additive inverse of '2/3' is 'x/6'. 

But, additive inverse of '2/3' is '-2/3'

So, 

x/6  =  -2/3

Multiply each side by 6.

x  =  -4

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