One of the categories of plotting the rational numbers on the number line,
is when the numerators are less than the denominators.
Let's try to plot '1 by 2' and 'minus 1 by 2' on the number line.
First, we see how we can plot '1 by 2'.
The numerator 1, is less than the denominator 2.
When the numerator is less than the denominator,
the positive rational number will be between 0 & 1.
So we draw the number line like this.
The number '1 by 2' has to lie somewhere between '0 & 1'.
Now we divide the length between 0 & 1 into equal parts.
How many equal parts is the question.
The denominator tells us the number of equal parts.
The denominator is 2. So we divide it into two equal parts.
This line divides this region into two equal parts.
But what does the numerator tell us?
It tells us the number of parts starting from 0.
The numerator is 1.
And therefore we take one part from '0' and mark '1 by 2' here.
We can use the same procedure to mark 'minus 1 by 2' on the left side of 0.
Divide it into two parts,
and mark 'minus 1 by 2', one part away from '0'.
Just as integers had corresponding values,
Rational numbers too have Corresponding values.
In our example, 'minus 1 by 2' corresponds to '1 by 2'.
Let us look at another example where the numerator
is less than the denominator.
We have to plot '3 by 4' and 'minus 3 by 4'.
Let us plot '3 by 4' first.
Since the numerator is less than the denominator,
we know that the number will be between 0 & 1.
So we draw the number line like this. With just 0 & 1 plotted.
Remember, the denominator tells us the number of equal parts.
Since the denominator is 4.
We divide the length between '0 & 1' into 4 equal parts
Drawing these three lines gives us four equal parts.
Now we move to the numerator.
The numerator tells us the number of parts from the number zero
Since the numerator is three we move three equal parts from zero.
One, two, and three.
So we mark 'three by four' here.
Now let us plot 'minus three by four'.
Since 3 is less than 4. And the Rational number is negative,
we know that will come between '0 and minus 1'.
We divide this length into four equal parts as the denominator is 4.
And we mark 'minus 3 by 4', 3 parts away from zero.
That's it. We have plotted the points.
But let me ask you a question.
You have plotted the numbers '3 by 4' and 'minus 3 by 4'.
But do you know which numbers are plotted on these points?
Here's your answer.
Since this is one part, we mark '1 by 4' here.
Since these are two parts, we mark '2 by 4' here.
Similarly, we can plot 'minus 1 by 4'. And 'minus 2 by 4' here.
This was just for your understanding.
And you don't need to mark all the points if you're asked
to mark just '3 by 4' and 'minus 3 by 4'.
In the next video we will look at an example,
in which the numerator is greater than the denominator.
