NCERT Class 8 Mathematics Text Book for Blind and Visually Impaired Students made Screen Readable By Professor T K Bansal.

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)

On solving we get, x= 0. If we consider only the 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 are not 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.

We 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)

5 x + 7 = 0 .. .. (5)

for these equations we cannot find a solution from the list of integers. (Do check this yourself)

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.