All of us know what a number line is.
And the numbers we see here on the number line
are called integers.
On the right side of zero we have positive integers
and on its left we have negative integers.
Integers, we are familiar with. But what about numbers like these?
1 by 3, 5 by 6 or 'minus 7' by 12.
Each of these are numbers,
but we don't use them as often as we use counting numbers.
Such numbers are called Rational numbers.
But we need to define them well!
We cannot say numbers like these are rational numbers.
We say that they are of the form 'p' by 'q'.
One number in the numerator and one in the denominator.
But there are a few conditions we need to know.
'p' and 'q' should be integers.
We can have only integers in place of 'p' and 'q'.
And there is another important condition
'q' should not be equal to 'zero'.
Why do we have the second condition?
Say I asked you to calculate 3 divided by 0.
What would be the quotient?
'0' multiplied by what will give you 3? There is no such number.
This value is undefined.
So this is the basic definition of rational numbers.
It is a number of the form 'p' by 'q' where 'p' and 'q' are integers.
And 'q' is not equal to '0'?
There are many questions that should pop up in your head
when you see this definition.
What is the difference between rational numbers and fractions?
Are integers classified as rational numbers?
What about '0'? How do we plot such numbers on a number line?
And how do we compare two rational numbers?
For example if you are asked to compare
1 and 5 you could easily say that 5 is greater of the two.
But what if you are asked to compare numbers
like 6 by 7 and 13 by 15?
How would you find out which one is greater?
Don't worry about it! All these questions
will be answered in our videos on Rational numbers.
