CLASS-7
PROPERTIES OF ADDITION OF RATIONAL NUMBERS
PROPERTIES OF ADDITION OF RATIONAL NUMBERS -
The addition of rational numbers follows several properties that make the arithmetic consistent and predictable. Here are the key properties:
- Closure Property:- The sum of two rational numbers is always a rational number. In other words, if a and b are rational numbers, then a+b is also a rational number.
- Associative Property:- Addition of rational numbers is associative, meaning that the grouping of the numbers does not affect the result. For any rational numbers a, b, and c, (a+b)+c = a+(b+c).
- Commutative Property:- Addition of rational numbers is commutative, meaning that the order of the numbers does not affect the result. For any rational numbers a and b, a+b = b+a.
- Identity Property:- The identity element for addition in rational numbers is 0. For any rational number a, a+0 = 0+a = a.
- Inverse Property:- Every rational number has an additive inverse, which when added to the number gives the identity element 00. For any rational number a, there exists another rational number −a such that a+(−a) = (−a)+a = 0.
- Additive Property of Zero:- Adding zero to any rational number leaves the number unchanged. For any rational number a, a+0 = 0+a = a.
These properties ensure that addition of rational numbers behaves predictably and consistently, making it easier to perform arithmetic operations and solve equations involving rational numbers.