Multiplication, Division Rational Numbers - Rational Numbers , Maths, Class 7 Video Lecture

hello friends this video on rational
numbers part 16 is brought to you by
exam feel calm no more fear from exam so
now let us quickly look at
multiplication of rational numbers we
will also look at it on the number nine
so multiplication is pretty simple here
we just follow a simple logic multiply
the numerators multiply the denominators
so let us look at an example let's say
you have to multiply 3 by 2 by 5 so how
will you do that so 5 is nothing but 5
by 1 so you multiply the numerators
which is 3 into 5 that is 15 and then
you multiply the denominators 2 into 1
is 2 so the result is 15 by 2 now if you
want to have a look at this
multiplication on the number line here
you go let's say this is 0 1 2 3 4 5 and
so on so what does this mean 3 by 2 into
5 that means you take 5 3 by 2 is added
five times this actually means that 3 by
2 you are adding 3 by 2 5 times so what
does that mean that actually means that
you take 5 times 5 jumps that each jump
is 3 by 2 so 3 by 2 is 1 and a half so
this is one jump 3 by 2 so the next jump
of 3 by 2 would be here the next jump of
3 by 2 would be here again the next jump
would be somewhere here now the entire
thing is not visible on the screen but
when you actually take 5 jumps where
each jump is 3 by 2 you reach 15 by 10
which is nothing but 7 and 1/2 so 15 by
2 lies between 7 & 8 so try to do this
yourself so in the similar way let us
try to perform some more multiplication
let's say minus 3 by 2 multiplied by 1
by minus two so this gives minus G by
minus 4/7 le-tree by 2 multiplied by 1
by minus 6 so multiply the numerators
which is 3 multiply the denominators
which is minus 12 so this becomes 3 by
minus 2 X so in this fashion you perform
multiplication of rational numbers so
when we talk about multiplication like
how we have the concept of additive
inverse in a similar way we have a
concept of multiplicative identity as
well so that is where it comes the
concept of reciprocal so reciprocal of a
number is that number which when
multiplied by the number gives one so
let us take some examples let's say you
have a number 3 by 2 do you think that
you can have a number which can
multiplied by 3 by 2 gives you 1 can you
have any such number yes you can have
just think of this number 2 by 3 so if
you multiply 2 by 3 with 3 by 2 what
will you get you'll get nothing but 1
right so this is called the reciprocal
of 3 by 2 so 2 by 3 is the reciprocal of
3 by 2 so what is actually reciprocal it
is that number which when multiplied by
the given number gives you much the
widest concept of reciprocal X's that's
because 1 is the multiplicative identity
like how we saw that a 0 is an additive
identity that means when you add 0 to a
number the number remains the same
similarly when you multiply 1 to a
number the number remains the same 3 by
2 multiplied by 1 who gives you 3 by 9
minus 15 by 3 multiplied by 1 gives you
minus 15 by 3 0 multiplied by 1 gives
you 0 so any number multiplied by 1
gives you the same number so that is why
one is called a multiplicative identity
and because of this concept we see that
we always come across a number which
when multiplied by another number gives
you 1
okay so the simple thing to remember
when you want to find a reciprocal is
that just make the numerator as
denominator and the denominator as
numerator so basically interchange the
numerator and denominator so let us try
to find reciprocals 51 so what would be
the reciprocal of 51 so here the
numerator is 51 and denominator is one
so just interchange them so 1 by 51
would be the reciprocal 10 by 24 so here
tens the numerator and 24 is the
denominator just reverse the order
so 24 by 10 would be the reciprocal - 11
by 6 so here minus 11 is numerator and 6
is debater so change it it would be 6 by
- 11 - 9 by minus 3 so in this case also
just change the numerator and
denominator so minus 3 by minus 9 would
be the reciprocal so let us now look at
the division of rational numbers now
when we talk about dividing a rational
number it is the same as multiplying it
with the reciprocal of the other
rational number now what again what does
that mean let's say you have a rational
number - 3 by 5 and you want to divide
it by 2 so dividing it by 2 is same as
multiplying it with reciprocal of 2 so
multiplying it with 1 by 2 so that is
what the meaning of division is like how
in case of subtraction subtraction means
for adding the additive inverse
similarly here division means
multiplying the reciprocal so you might
now multiplication is pretty simple
multiply the numerators which is minus 3
multiply the denominators which is 10 so
their answer would be minus 3 by 10 in a
similar way let's take another example -
7 by 12 / - 2 by 13 so dividing - 2 by
13 is same as multiplying
team by minus two so here minus 7 into
13 would be minus 90 112 into minus 2
would be minus 24 so minus minus will
cancel out so you would get 91 by 24 so
this would be the answer so you see this
is pretty simple whenever you want to
divide two rational numbers that
actually means you multiply with the
reciprocal of one of the numbers thank
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