Rational Number-Introduction

Rational Number Introduction

In Mathematics, we frequently come across simple equations to be solved. For example,

the equation x + 2 = 13                                         (1)

is solved when x = 11, because this value of x satisfies the given equation. The solution

11 is a natural number. On the other hand, for the equation

x + 5 = 5                                                                 (2)

the solution gives the whole number 0 (zero). If we consider only natural numbers,

equation (2) cannot be solved. To solve equations like (2), we added the number zero to

the collection of natural numbers and obtained the whole numbers. Even whole numbers

will not be sufficient to solve equations of type

x + 18 = 5                                                                 (3)

Do you see ‘why’? We require the number –13 which is not a whole number. This

led us to think of integers, (positive and negative). Note that the positive integers

correspond to natural numbers. One may think that we have enough numbers to solve all

simple equations with the available list of integers. Now consider the equations

2x = 3                                                                         (4)

5x + 7 = 0                                                                   (5)

for which we cannot find a solution from the integers. (Check this)

We need the numbers 3/2 to solve equation (4) and 7/5 to solve equation (5). This leads us to the collection of rational numbers.

We have already seen basic operations on rational numbers. We now try to explore some properties of operations on the different types of numbers seen so far.