Lecture 3 : Rational Numbers - Mathematics, Class 7 Video Lecture

welcome back to the third video in the
series of the videos we are discussing
on rational number it's quite the cold
morning today and let's start this
lecture with a cup of coffee so now on
rational numbers the next topic is to
discuss the basic mathematical
operations on rational number to start
with it is an addition so let's take up
an example draw a number line and try to
solve that example on the number line so
the example is minus 4 by 7 plus 5 by 7
so let's first put the numbers on the
left hand side we have the negative
rational numbers so minus 1 by 7 2 by 7
minus 3 by 7 minus 4 by 7 on the right
hand side of the zero we have the
positive rational numbers so we'll put 1
by 7 2 by 7 3 by 7 and 4 by 7 we have to
add 5 by 7 2 minus 4 by 7 now a minus 4
by 7 is here to add something positive
to it the rule is we move towards the
right hand side so we add 1 2 by 7 then
this becomes 3 by 7 this becomes 4 by 7
and which are pure
to get or we jumped five bison complete
five Western and answer we get here is
one by civil now let's do this in the
way we have done for the fractions the
denominator is common keep the
denominator as it is and we just add up
the numerators so this gives us more
quicker and a more easier manner 5 minus
4 is 1 by 7 that we have right through
the rule what we had applied for the
factions the same rule we are praying
here for the rational numbers the
denominator is same we just go up and
add the numerators now I take one more
example the next example is let's add 3
by 7 minus 5 by 7 not in love with 5
let's make it here 6 to give a small
change so here we have a minus 6 by 7 to
be added with 3 by 7 so we have here 3
by 7 now the rule is if you have a
negative number to be added to any
positive integer what do we do is we
jump on the left hand side so we jump
here 1 2 3 so we have already jumped
minus 3 by 7 4 5 & 6 so if I have so the
answer which we have got to the number
line is minus 3 by 7 what have done is
to 3 by 7
I have jumped 1 one step of minus 1 by 7
that is I have jumped 1 by 7 in the left
inside to get the answer as minus 3 by 7
let's check that the same thing can be
achieved through the method of
simplified method of fraction 3-6 here
we get minus 3 and yes the answer is the
same minus 3 by 7 so the rule here is
very simple if you want to add two
rational numbers with the denominator as
same just add up the numerators and you
will get the answer so let's take the
third example in the same form we have
here minus 2 by 8 plus 6 by 8 so it
comes to 8 in the denominator and here
minus 2 plus 6 so that gives me 4 by 8
and the reduced form of 4 by 8 is 1 by 2
so this was how do we add the rational
numbers with the help of a number line
and directly with them
Go Fish data Clee with the fraction
method let's go to the next example
the next example here is let's see if
the denominators are same we just add up
the numerator but what if the
denominators are different let's take an
example here that I have minus 7 by 5 I
have to add that with minus 2 by 3 how
do I do that
so in the fractions we have already
learned that in this kind of scenarios
if we have to add these two we have to
find the least common multiples of the
denominator so the least common multiple
of 5 and 3 is 15 and we have to convert
the number into such a manner that the
denominators are least common multiple
so here we have 15 so minus 7 by 5 into
3 by 3 gives me
and the same thing if I have to do here
- 2 by 3 into 5 by 5 this 5 by 5 is 1 so
I'm actually just getting an equivalent
form of the rational number - 10 by 15
now if I had to add - 7 by 5 plus minus
2 by 3 it is I have to add minus 21 by
15 plus minus 10 by 15 now where have
the denominators same I'm back to the
previous situation where I just add up
the numerators so it is which gives me -
31 by 15 so this is how we go on we go
on doing the addition if the
denominators are different let's take
one more example - 10 by 15 plus 6 by 3
now if you see I can directly first
reduce this into a common number so I
can he'll have I'll have here 2 by 3 I'm
just dividing it by 5 here in the
numerator and denominator and this will
give me 6 by 3 we'll let's keep it 6 by
3 because anyway we have to add that we
have to keep the denominators same so
this gives me 3 - 2 plus 6 that is 4 by
3 so this is how we do an addition if
have a denominator different and in the
previous section we learn how to do for
the dive and the denominators are same
let
take one more example here fatty we are
minus 4 by 7 and here I have plus 4 by 7
C would say oh this is quite simple
I will hear how minus 4 plus 4 by 7 and
the answer would be 0 by 7 or it's 0 Y
had thickened this example is not for
their addition but to show here that
when I add minus 4 by 7 plus 4 by 7 I
get an answer of 0 recall what we have
learned for the integers that if I have
a minus 2 and a plus 2 and if I get 0 by
adding minus 2 and plus 2 we call them
as additive inverse for integers the
same rule applies here minus 4 by 7 and
4 by 7 will become additive inverse
rational numbers the same rule applies
even if I convert this into 12 by 21
just multiplying it by 4 into 3 7 into 3
so that it's again a different rational
number altogether and 4 by 7th still if
I add them minus 12 by 21 plus 4 by 7 so
again I can reduce into 4 by 7 and 4 by
7 and they become the additive inverse
this is just to emphasize that even if
they are not in the standard form still
they become an additive inverse of each
other so this is foil today's topic in
the next topic we will be talking more
about rational numbers with a different
operation like multiplication thank you