Associative Property Rational Number (Part - 10) - Rational Numbers , Maths, Class 8 Video Lecture

hello friends this video on rational
numbers 510 is brought to you by exam
feel calm no over here from exam let us
now talk about the third property that
is the associative property for rational
numbers now again associative property
when it comes to addition addition is
associative and what exactly is
associative property so this property
takes into consideration three different
rational numbers so let's say we have
three rational numbers ABC so as per
associative property it tells that a
plus B plus C is equal to a plus B plus
C so basically what we have garland's
when we have to add three rational
numbers so even if we change the order
of how we are adding it that is we add
the first two and then add the sum to
the third or we add the second and third
and then add the sum to the first C
whatever order we add them the sum would
remain the same so that that's what it
tries to say so addition is associative
but when it comes to subtraction it is
not associative that is a minus B minus
C is not equal to a minus B minus C so
this is not equal because when you
subtract rational numbers they are not
like as we saw they are not even
commutative so basically the value
changes the moment you change the order
when it comes to multiplication again it
is associative that is a multiplied by B
into C is equal to a multiplied by B
multiplied by C so changing the order
remains it keeps the product same
division a divided by B divided by C is
not equal to a divided by B divided by C
so this also we see that only addition
and multiplication are associative
others are not so again we will prove
the same things taking examples of
rational numbers so first let's start
with the associative property for
addition so let's consider one rational
number a as 1 by 5 let's consider B as
-2 by 7
and let's consider see as 3x5 so
considering these three rational numbers
let us first calculate a plus B plus C
so this comes out to be 1 by 5 minus 2
by 7 plus 3 by 5 now why this is minus
because this is plus of minus 2 by 7 so
plus minus this minus so that's y minus
2 by 7 so this will come out to be Mac 7
minus 10 divided by 35 plus 3 by 5 so
this comes out to be minus 3 by 35 plus
3 by 5 and this comes out to be 18 by 35
so this is the value that we get for
English B plus C now let us try to
calculate a plus B plus C so this comes
out to be 1 by 5 plus minus 2 by 7 plus
3 by 5 so this comes out to be 1 by 5
plus minus 10 plus 21 divided by 35 so
this is equal to 1 by 5 plus 11 by 35 so
this comes out to be 18 by 35 again so
if you compare these two values what do
you see we see that a plus B plus is
equal to a plus B plus C so we see that
the associative property holds true for
addition of rational numbers let's look
at the associative property for
subtraction so here again we consider 3
rational numbers as 1 by 5 minus 2 by 7
and 3 by 5 now when we will first
calculate a minus B minus C so this
would be 1 by 5 minus -2 by 7 minus 3 by
5 so this would be equal to 1 by 5 plus
2 by 7 minus 3 by 5 this comes out to be
17 by 13
five minus three by five which is equal
to seventeen minus twenty-one divided by
35 and this is equal to minus four by 35
so this is the value that we get now in
a similar way if we calculate a minus B
minus C we find one by five minus minus
2 by 7 minus 3 by 5 so this comes out to
be 1 by 5 minus minus 10 minus 21
divided by 35 and this comes out to be 1
by 5 plus 30 1 by 35 this is equal to 38
5 35 so now you compare the two values
are they equal they are not so therefore
we conclude that a minus B minus C is
not equal to a minus B minus C so the
commutative property property doesn't
hold true for subtraction of rational
numbers let's talk about multiplication
so for this also we will include we'll
consider 3 rational numbers as 1 by 5
minus 2 by 7 and 3 by 5 so first we will
calculate a multiplied by B multiplied
by C so that is 1 by 5 into minus 2 by 7
into 3 by 5 so this comes out to be 1 by
5 in 2 minus 6 by 35 so this is equal to
minus 6 by 175 so now let us calculate a
into B into C which is equal to 1 by 5
in 2 minus 2 by 7 this multiplied it by
3 by 5 so this is equal to minus 2 by 35
83 by 5 so this is equal to minus 6 by
175 so compare the two values and the
equal therefore we can say that a into B
into C is equal to a into B into C so we
will now look at the associative
property for division so for division
again a B is considered as one by five B
is -2 by 7 and C is three by five so
considering the three values we will
again calculate a divided by B divided
by C which is equal to 1 by 5 divided by
-2 by 7 divided by 3 by 5 so this can be
written as 1 by 5 divided by this would
be minus 2 by 7 divided by 3 by 5 so
this would be equal to minus 2 by 7 into
5 by 3 so this comes out to be 1 by 5
divided by 10 minus 10 by 21 or this is
equal to 1 by 5 into 21 by minus 10 so
this is how we divide right so this
comes out to be 21 by minus 50 now again
in a similar way let us try to calculate
the other value so we have made some
space here so let us calculate a divided
by B divided by C so this would be 1 by
5 divided by minus 2 by 7 this divided
by 3 by 5 so this comes out to be 1 by 5
into 7 by minus 2 this divided by 3 by 5
so this comes out to be 7 by minus 10
into 5 by 3 so this comes out to be 35
divided by minus 30 or we can write it
as 7 6 so this can be written as 7 by
six so if you compare the two values
they are not equal so we can say that
associative property does not hold true
for division so this is how we have
looked at three properties that disclose
your property commutative property and
associative property and we saw that
some of them are true for addition some
of them as true for subtraction some for
multiplication and some for division
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