# Inverse Property of Addition : Definition, Example and Questions

## What is Inverse Property of Addition?

The property says that adding a number with its negative number results in number 0.

Inverse addition property can be expressed as:

Where A can be any number possible.
And [-A] is the negative version of A.

How to find the negative version of any number?

By simply adding negative sign to the front you can convert any number into negative form.

Let us try to find the negative version of some number

Example 01
A = 9
[-A] = -9

Example 02
A = 74
[-A] = -74

Example 03
A = -6
[-A] = -(-6) = 6

Note: Negative version of any negative version is a positive number

Example 04
A = 0
[-A] = 0
Negative version of number 0 is zero

### Inverse Property of Addition Example

Given below are some example of the above property. It will help you understand the concept better.

Example 01
Let A = 98 and [-A] = -98
⟹ A + [-A]
⟹ 98 – 98 = 0

Example 02
Let A = -3
[-A] = – (-3) = 3

⟹ A + [-A]
⟹ -3 + 3 = 0

Example 03
Let A = 10
[-A] = – 10

⟹ A + [-A]
⟹ 10 -10 = 0

Example 04
Let A = 0
[-A] = 0

⟹ A + [-A]
⟹ 0 + 0 = 0

From the above examples you can observe that adding number with its negative variant results in 0

### Understanding inverse property of Addition using number line

Here we will use number line to understand the process behind the property.

Let A = 6
Negative variant of A = [-A] = -6

⟹ A + [-A]
⟹ 6 + [-6]
⟹ 0

Understanding the calculation using number line

### Does the inverse property of addition works when number is negative?

Yes!!
Let us take negative number [A] = -9
The negative version of [A] will be [-A] = -(-9) = 9

Now checking for inverse addition property
⟹ A + [-A]
⟹ -9 + 9
⟹ 0

hence, inverse property of addition works if number taken is negative

### Do we have any inverse property for multiplication?

Yes!!

In Inverse Multiplication Property we multiply numbers with its reciprocal to get 1 as final result.

The property is expressed as:

Important Point
For addition, the inverse of any number is its negative variant.
And for Multiplication, the inverse of number is its reciprocal.

Let us see some examples:

Example 01

\mathtt{Let\ A\ =\ 11}\\\ \\ \mathtt{Then\ \frac{1}{A} \ =\ \frac{1}{11}}\\\ \\ \mathtt{Multiplying\ A\ \&\ \frac{1}{A}}\\\ \\ \mathtt{\Longrightarrow \ A\ \times \ \frac{1}{A\ }}\\\ \\ \mathtt{\Longrightarrow \ 11\ \times \ \frac{1}{11\ }}\\\ \\ \mathtt{\Longrightarrow \ 1}\\\ \\

Example 02
\mathtt{Let\ A\ =\ } -29\\\ \\ \mathtt{Then\ \frac{1}{A} \ =\ \frac{-1}{29}}\\\ \\ \mathtt{Multiplying\ A\ \&\ \frac{1}{A}}\\\ \\ \mathtt{\Longrightarrow \ A\ \times \ \frac{1}{A\ }}\\\ \\ \mathtt{\Longrightarrow \ 29\ \times \ \frac{-1}{29\ }}\\\ \\ \mathtt{\Longrightarrow \ 1}\

### How are inverse property of addition & multiplication different?

In Inverse property of addition we add number with its negative variant, while in multiplication we multiply the number with its reciprocal.

In Inverse property of addition the end result is 0
But in inverse property of multiplication, the final result is 1

### How is inverse property different from identity property of addition?

In Identity property of addition we add the number with 0, so that the identity of number remain intact.
A + 0 = A

While in inverse property we add the number with its inverse to get 0
A + (-A) = 0

### Difference between Inverse and Commutative Property

In Commutative Property of addition, the change in arrangements of number in addition do not effect the final result.

A + B = B + A

While in inverse property of addition, we get number 0 on adding negative variant of number

A + (-A) = 0

## Questions on Inverse Property of Addition

(01) What is additive inverse of 11

(a) 1/11
(b) -1/11
(c) -11
(d) -10

The additive inverse of number 11 is -11

Option (c) is the right answer

(02) What is additive inverse of -6

(a) 6
(b) 1/6
(c) -1/6
(d) 0

The additive inverse of -6 is 6

Option (a) is the right answer

(03) Find the additive inverse of (-1/10)

(a) 1
(b) 1/10
(c) 10
(d) -10

The additive inverse of (-1/10) is (1/10)

Option (b) is the right answer

(04) What is the property used for below expression
6 + 3 = 3 + 6

(b) Associative Property
(c) Commutative Property
(d) Identity Property

The given expression is of commutative property which is expressed as:
a + b = b + a

Option (c) is the right answer

(05) How to get negative variant of any number?

(b) Multiply 0
(c) Multiply 2
(d) Multiply -1