Examples Patterns in Whole Numbers Video Lecture - Advance Learner Course

hello friends this video on whole
numbers part 13 is brought to you by
exam for your calm no more fear from
exam so learning about this dots pattern
let us now look at some of the magical
questions of whole numbers which of the
following will not represent 0 1 + 0 1 +
0 would be what now 0 is the additive
identity when 0 is added to anything the
number remains the same so 1 + 0 will
remain 1 so it will not represent 0 0
into 0 anything multiplied by 0 is
always 0 so this represents 0 0 by 2 so
0 divided by anything is also 0 +
anything divided by 0 is always not
defined question number 2 if the product
of two whole numbers is 0 can we say
that one or both of them will be 0
justify through examples now if the
product is 0 that means that one of them
is definitely 0 because even if one of
them is 0 the product is going to be 0
because anything multiplied by 0 gives a
0 there is now if none of them are 0 in
that case the product will never be 0
because if you have two nonzero numbers
getting multiplied in that case the
product can never become 0 but if both
of them are 0 then also the product of 0
if one of them is 0 then also the
product is 0 question number 3 if the
product of two whole numbers is 1 can we
say that one or both of them will be 1
justify through examples now since we
are talking about only whole numbers
that both the Holum both the numbers
which are being multiplied are whole
numbers now in order to get a product of
one both whole numbers must be one so
they need to be one only then the
product would be one because otherwise
if you have any other nonzero number and
if you multiply it with one you would
get the same on zero numbered you take
any number only when it is 1 then only 1
into 1 would be 1 otherwise any other
number when multiplied with 1 will give
the same number if 0 gets multiplied
with 1 then it gives 0 so every time
because that is why 1 is the
multiplicative identity when 1 is
multiplied to any number that number
retains its identity
question number 4 find using
distributive property 5000 437 multiply
it by 1000 1 now here we can write 1001
we can break 1001 as 1,000 plus 1 so now
by distributive property this is a into
B plus C so what do we know that by
distributive property a into B plus C is
equal to a into B plus C 2 C so we can
say 5 4 3 7 into 1000 plus 5 4 3 7 into
1 so this would be equal to five four
three seven zero zero zero plus 5 4 3 7
so this becomes equal to 5 4 4 2 4 3 7
so this would be the answer question
number 5 study the pattern 1 into 8 plus
1 is equal to 9 1 2 into 8 plus 2 is
equal to 98 123 into 8 plus 3 is equal
to 9 8 7 now when you look at the
pattern what's happening earlier it was
1 then it became one two then it became
1 2 3 then it become 1 2 3 4
one two three five and also this number
which is getting added is also
increasing gradually one two three four
five and so on and the beautiful thing
is that the result that you are getting
that is also changing in a very
beautiful way first of course 9 then it
is nine eight the nine eight seven the
nine eight seven six nine eight seven
six five and so on
so can we write the next two steps yes
we can the next step would be one two
three four five six one more number
added into eight plus this would be six
is equal to nine eight seven six five
four what would be the next step it
would be one two three four five six
seven into 8 plus 7 is equal to nine
eight seven six five four three so that
is the pattern that we can see on the
screen now can you see how whether the
pattern works at all or not I mean are
we just writing it for the sake of it or
if you be calculated we will get this of
course we will get this but do you know
how it works so let us try to understand
this so let us take this step which we
have written at first that is 1 2 3 4 5
6 now when you look at this number 1 2 3
4 5 6 what do you see you would see that
this 6 is at the unit's place or once
please so how will you get a 6 in order
to get a 6 you have to add 1 6 times so
when you add 1 6 times you would get a 6
how would you get a 5 when you add 1 5
times how would you get a 4 when you add
1 4 times 3 3 times 2 2 times and one
one time so when you actually add these
numbers what do you get you get 1 2 3 4
5 6 right so now in this let's take
example of this one so in this what we
do is we replace this number with this
expansion so we basically write it as 1
1 1 1 1 1 plus 1 1 1 1 1 plus 1 1 1 1
plus 1 1 1 plus 1 1 plus 1 so we write
it like this and this gets multiplied
with 8 as a whole so when this entire
thing gets multiplied with 8 what do we
get we get something like this 8 8 8 8 8
8 plus 8 8 8 8 8 plus 8 8 8 8 plus 8 88
plus 88 Plus 8 and now we add 6 to this
entire thing so when you sum it up you
get 9 8 7 6 4 8 plus 6 which is equal to
9 8 7 6 5 4 so what is this value this
value is nothing but this value so it
works so this is one simple way of
simplifying it now instead of
multiplying this big big numbers
together you can write it in this form
and then you can see this magical
phenomena so these are some of the magic
with whole numbers so you can play
around with whole numbers and you can
try and define them making use of the
various properties that we have learned
in this lesson
so with this we have reached towards the
end of this lesson and I hope that this
lesson on whole numbers would have
helped you try to solve more and more
questions focus mainly on the concepts
do not memorize anything understand them
and then try to solve questions I hope
this lesson would have helped you see
you all in the next lesson thank you
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