L8 : Associative Property - Whole Numbers , Maths, Class 6 Video Lecture

hello friends this video on whole
numbers but eight is brought to you by
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let's move on to the third property that
is associative property so what do you
think are we going to talk about an
associative property of addition of
whole numbers no associative property
that means some kind of association
between two or more numbers some kind of
connection or some kind of bonding
between two or more numbers so let us
have a look at associative property now
an associative property we are going to
consider three numbers so let's say 13
plus 6 plus 2 so where 13 plus 6 is
inside bracket now how would you
calculate this value now the simple way
we calculate this first we do the
operation which is inside the brackets
so 13 plus 6 is 19 plus 2 that is 21 now
what if I change the positions of these
three digits or not earlier in
commutative property we had two numbers
so we just exchange the Airports
positions but now we have three numbers
so there are different ways in which we
can change their position so we
basically do not change the position
what we do is so you see the position
remains the same we just change the
position of the bracket so now we put
the bracket here the moment we put the
bracket here what happens how to be
calculated we now perform the operation
which is inside bracket first so it
becomes 13 plus so this operation will
be done first which is 8 and the result
is still 21 so when we have to add three
numbers whether we add the first two
numbers first and then add the sum to
the third or we add the second and third
numbers first and then add yourself to
the first in both the cases we get the
same result now let us take one more
example
verify this fact let's say we consider
three numbers five zero and one so the
result here would be 5 plus 1 which is
equal to 6 now if the same thing we
perform in a little different way so
what happens in this case also we see
that the result is the same
so therefore what do we conclude we
conclude that if we have three whole
numbers ABC then a plus B plus C is
equal to a plus B plus C so this is what
we have concluded so the conclusion is
addition is associative so this means
this is a kind of association between
the three whole numbers this is the kind
of association between the two addition
operations whether you perform the
addition of the first two numbers first
or the last two numbers first the result
will remain the same
and that is why we say addition is
associative so in a similar way for
associative property also we will look
at the other operations so let us start
with subtraction so here also
subtraction is not associative let us
illustrate this with an example
so let's say 13 minus 5 minus 2 so we
have considered three whole numbers 13 5
& 2 in this case so what would how would
we calculate this 13 minus 5 is 8 minus
2 so this is equal to 6 now let us
change the position of the brackets that
is 13 minus 5 minus 2 so this becomes 5
minus 2 is 3 so the result here is 10 so
we observe that here in this case the
results in the two cases are not same so
we observed that a minus B minus C is
not equal to a minus B minus C so this
is not true for subtraction therefore
subtraction is not
so she ativ let's talk about
multiplication so in multiplication
again we see that it is associative that
means if we take something like this 2
into 3 into 5 so all do we get 6 into 5
which is equal to 13 now if the same
thing we do it like this 2 into 3 into 5
so 3 into 5 is 15 so 2 into 15 is 30 so
we get the same result in both the cases
sorry so this is one example let us take
another example let's say 1 into 0
multiply it by 3 so 1 into 0 is 0 into 3
which is equal to 0 now the same thing
with a different format 1 into 0 into 3
would be 1 into 0 which is equal to 0 so
in both of these cases what we observe
is a into B into C is equal to a into B
into C so basically multiplication is
associative in whole numbers I hope you
would have guessed by now that division
is also not associative because till now
we have been observing that
multiplication and addition they go
hand-in-hand and a subtraction and
division they go together so let's look
at some examples here so let's say 10
divided by 5 divided by 1 so this
becomes 2 divided by 1 which is equal to
2 now the same thing we perform in
different order that is 10 divided by 5
divided by 1 so what do you get you get
10 divided by 5 so as a result you get 2
Wow you have got same results in both
the cases so does that mean that
division is associative what do you
think do you want to give it a thought
ok let's give it a thought and let's try
it out with some other example so this
is one example
is tried out with another example so
let's take this example 16 divided by 4
divided by 2 so what do you get 4
divided by 2 which is equal to 2 now the
same thing let's perform it in this way
16 divided by 4 divided by 2 so this is
16 divided by 2 and this is equal to 8
oh so now again you are getting
different results so the if because if
division is associated it has to hold
true for all the examples that we
consider now in one example we got it
right in another example we didn't get
it right
so should we give a try to the third
example ok let's give a try let's say 32
divided by 4 divided by 2 so this is 8
divided by 2 which is equal to 4
now 32 divided by 4 divided by 2 this is
32 divided by 2 so this is equal to 16
so in this case also we arrived at
different results so that means division
is not associative now you might ask
that if division is not associated then
why the reserves are the same in this
case because this is just a matter of
chance that for the certain set of data
it might hold true but overall
universally does not hold true for all
whole numbers therefore we see that a
divided by B divided by C is not equal
in a divided by B divided by C so this
is our overall result thank you please
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