Property of Opposites

Introduction of Property of Opposites:

The property of opposites is the number changing its sign, that is positive being change to negative and negative being change to positive. I like to share this Associative Property Addition with you all through my article.

For Example: Let the number be ‘’a’’ and the property of opposites of the number ‘’a’’ is ‘’-a’’.

Let we see this property of opposites are applicable for addition, subtraction, multiplication and division. In this article, we see about how the property of opposites used for solving Problems.

Property of Opposites:

Case 1: Property of Opposites in Addition

Statement: Add the number and its property of opposites is zero

Example: A + (-A) = 0

Case 2: Property of Opposites in Subtraction

Statement: difference between number and its opposites is equal to the twice of that number.

Example: A – (-A) = A + A = 2A

Case 3: Property of Opposites in Multiplication

Statement: Multiply the number and its opposites, we get negative square of that number.

Example: A × (-A) = - A2

Case 4: Property of Opposites in Division

Statement: Divide a number by it opposites or vice versa, we get -1

Example:

A ÷ (-A) = -1

(-A) ÷ (A) = -1

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Example Problems – Property of Opposites:

Example 1:

Write the value of the sum of the number 5 and its opposites.

Solution:

Given: addition of the number 5 and its opposites

Expression: 5 + (-5)

We know that sum of any number and its opposites we get 0

5 + (-5) = 0

Answer: 0

Example 2:

Multiply the number 3 and its opposites

Solution:

Given: 3 × (-3)

Formula:

A × (-A) = - A2

3 × (-3) = - 32 = -9

Answer: 3 × (-3) = -9

Practice Problems – Property of Opposites

Problem 1:

What is the value of difference between the number 6 and its opposites?

Answer: 12

Problem 2:

What is the value when the number and its opposites comes under the division operation?

Answer: -1