Addition and Its Properties

Addition is one of the four basic mathematical operations that refer to combination of collections of objects towards forming a larger number. For example: Mother bought two Pigeon baby products for Rs. 220 and three baby toys from Fisher Price India brand for Rs. 350. How much she paid in total for Max online shopping. Adding, Rs. 220 + Rs. 350 = Rs.  570. Thus, mother paid Rs. 570 in total for Max online shopping for the baby. This is called addition operation in mathematics. There are five properties of addition, namely

• Identity Property
• Commutative Property
• Associative Property
• Property of Opposites
• Property of Opposite of a Sum

Identity Property: According to the identity property of addition, there is a unique real number zero for every real number a, b or c etc. Zero is referred as the identity elements in addition. For example: Mother bought one powder (suppose a) from pigeon baby products. Mathematically implementing identity property of addition, a + 0 = a and 0 + a = a.

Commutative Property: According to the commutative property of addition, for all real numbers, the order of addition does not change the result. For example: Mother bought 3 baby toys (suppose a) from Fisher Price India brand and 7 baby products (suppose b) from Pigeon baby brand. Mathematically, 3 + 7 = 10 and 7+3 = 10. Therefore, a + b = b + a

Associative Property: This property of addition states that when three real numbers are added, the grouping or association doesn’t change the result. Example is similar to the previous one. Therefore, (a + b) + c = a + (b + c).

Property of Opposites: This property of addition states that against every real number, suppose a, there is a unique real number, i.e, -a. A number and its opposite are called additive inverses and the addition of additive inverses is equal to zero. Therefore, a + (-a) = 0.

Property of Opposite of a Sum: This property of addition states that the opposite of a sum of real numbers is equal to the sum of the opposites. For example: - (2+3) = (-2) + (-3) = 5. That is, - (a + b) = (-a) + (-b).
These are the properties of addition.