**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

Adding both the numbers

⟹ A + [-A]

⟹ 6 + [-6]

⟹ 0

Understanding the calculation using number line

**Frequently asked Question on Inverse Property of Addition**

**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

Read Solution

The additive inverse of number 11 is -11

Option (c) is the right answer

Option (c) is the right answer

**(02) What is additive inverse of -6**

(a) 6

(b) 1/6

(c) -1/6

(d) 0

Read Solution

The additive inverse of -6 is 6

Option (a) is the right answer

Option (a) is the right answer

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

(a) 1

(b) 1/10

(c) 10

(d) -10

Read Solution

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

(a) Additive Inverse Property

(b) Associative Property

(c) Commutative Property

(d) Identity Property

Read Solution

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?**

(a) Add 1

(b) Multiply 0

(c) Multiply 2

(d) Multiply -1

Read Solution

Multiply the number with (-1) to get negative variant of number.

Example

Find negative variant of number 5

5 x (-1) = -5

**Option (d) is the right answer**