In this video,
we will try to plot Rational numbers whose numerators
are greater than their denominators.
Let us plot '7 by 4' and 'minus 7 by 4'.
We try to plot '7 by 4' first.
The first step in such kind of problems,
where the numerator is greater than the denominator
is to convert it into a mixed fraction form.
You would have learned this in your earlier classes,
but let me quickly show you how.
We only have to divide '7 by '4.
We get the quotient as 1 and the remainder as 3.
So we write the mixed fraction as 'quotient remainder by divisor'.
This is the whole part, and this is the fractional part.
So we can write '7 by 4' as '1, 3 by 4'.
1 is called the whole number part.
And '3 by 4' is called the proper fraction part.
Each of the 3 numbers ,
1, 3 & 4
tell us something about where '7 by 4' is plotted on the number line.
The whole number part tells us the position of '7 by 4'.
So 1 tells us that the rational number '7 by 4'
is between itself and the next whole number.
The next whole number is 2.
So we know that '7 by 4' is between 1 & 2.
So we draw the number line accordingly with just 0 ,1 & 2 marked.
The denominator of the proper fraction part tells us
the number of equal parts this segment is divided into.
Since it is 4 we divide this segment into 4 parts.
This segment between 1 & 2 is divided into four equal parts.
The numerator of the proper fraction tells us the number of parts
from the first whole number.
So it is 3 parts away from 1.
So we mark '7 by 4' here!
What about 'minus 7 by 4'?
We can write 'minus 7 by 4' as 'minus 1, 3 by 4'.
Now the number minus 1 tells us that 'minus 7 by 4'
is between itself and the next number.
Make note of the fact that the next number ,
will be on the left hand side
since 'minus 7 by 4' is a negative rational number.
So the next number is minus 2.
Now we can say that 'minus 7 by 4' is between 'minus 1 and minus 2'.
The denominator tells us the number of equal
parts this length is divided into.
So we divide it into four equal parts by marking three lines.
The number three tells us the number of parts,
from the number minus one.
So leaving three parts from minus one,
we mark 'minus 7 by 4' here.
With that we are done with the topic of plotting positive
and negative rational numbers.
Please practice this concept thoroughly,
and make note of the summary
which appears at the end of this video.
