Class 8 Maths- Addition of rational numbers and its properties

Addition of rational numbers and its properties

Addition of rational numbers: Let and be any two rational numbers.

Then we define =  

Thus, in order to add two rational numbers with the same denominator, we simply add their numerators and divide the sum by the common denominator.

Properties of addition of rational numbers:

Closure property: The sum of any two rational numbers is always a rational number. Thus, if  and are any two rational numbers, then is also a rational number.

The name – ‘closure property’ – is chosen to indicate whether rational numbers are a closed group when added or they are open (to becoming ‘non-ration’ numbers too).  

Commutativity: The addition of rational numbers is commutative i.e. if  and are any two rational numbers, then 

Commutative is the property which indicates the ‘ability to commute or travel’ i.e. changes places without any change in the net value of the addition.

Associativity: The addition of rational numbers is associative i.e. if , and are any three rational numbers, then = + 

The word “associativity” comes from “associative” or “group” and the associative property is about what happens to a group of numbers if within the group are interchanged.