Operations with Integers and Rational Numbers

If we look at any Integer say -7, we find that -7 can be written as -7 /1, where -7 and 1 both are integers and the denominator 1 < > 0. So -7 is absolutely expressed in form of a rational number. Now, in this we are going to learn about operations with integers and Rational Numbers. All mathematical operations namely addition, subtraction, multiplication and division can take place with both integers and rational numbers.

As integers all the properties of addition namely closure, commutative, associative satisfy with rational numbers too. There exist an additive identity 0 (zero), such that we add 0 to any rational number, the rational number remains unchanged.

Similarly, there exists an additive inverse for every rational number such that the sum of the number and its additive inverse is zero. In the same way, all subtraction properties of integers satisfy with rational numbers.  

To divide one rational number by another, we will convert the dividend to its reciprocal and then the sum of division converts to the simple sum of multiplication, which can be solved easily.  

When we find the sum or the difference of any two rational numbers, we need to first find the LCM of the denominators. On finding the LCM of denominators, we change the rational number to its equivalent rational number such that the denominator becomes equal to the LCM.

Finally addition or subtraction of the numerator can be done. Moreover to find the product of two rational numbers is very easy. To look into it, we simply need to multiply the numerator with the numerator and the denominator with the denominator. On getting the new rational number as the product, we convert it to the standard form.