LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

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.**