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Is Negative Number a Rational Number?


In a number system we have dealt with Natural Numbers which are also called counting numbers, The series of numbers 1, 2, 3, …… which are used to count the existence of anything are called natural numbers. Whole numbers, which include 0 (zero) followed the series of natural numbers which are used to measure the units like weight, speed, height etc . So they are also called Measuring numbers. So, the series 0, 1, 2, …….. are called whole numbers The series of numbers which have Natural numbers, 0 and the negatives of natural numbers are called Integers. Integers are from The Range -∞…….. -5, -4, -3, -2, -1, 0, +1, +2, +3, ………+∞

Now, the question arises that are the Negative numbers a Rational Numbers. For this we first look at a glance that what are rational numbers. All numbers which can be expressed in form of p/q, where both p and q are integers such that q≠ 0 belong to the family of rational numbers. Some examples of rational numbers are -3/4, 5/9, 2/-6 etc. If we take any negative number say -6, we can also write it as -6/1. Comparing -6/1 with the rational number, we observe that it is also written in form of p/q, where p= -6 and q=1. Further we see that q≠ 0. We also notice that all the properties of integers i.e. addition and multiplication closure, commutative property, associative property also satisfy for the rational numbers.

Moreover, multiplicative and additive inverse also exists for both negative integers and Rational numbers. We also check that there exists a number 0, which when added with either negative Integer or rational numbers will not change the number, and if multiplied with it, will result to zero (0). Thus we conclude that every negative number is a Rational Number.