Games with Numbers: Reversing the Digits Video Lecture - Class 8

hello friends this video on playing with
numbers part two is brought to you by
example calm no more peer from exam so
let us first look at this some trick
like like the example which I had shown
just now where you take it take a number
the worse the digits add them and then
looking at the sum you can tell whether
it is divisible by a particular number
or not so how do we do the sum trip so
let us take any two-digit number so here
first we will discuss about it into
these numbers so let's take any two
digit number net so in general we are
considering right now so let's
scientific 2552 1.15 1392 these our two
digit numbers who in general we are
considering that we have a two digit
number where a and b are integers now
how can you write a B so when you look
at this number D is as a unit place and
a is a percentage so you can write it
like this
a into 10 plus B into 1 which is equal
to a into 10 would be 10 a and B into 1
is V B so you can write the number a B
as 10 a leftie now so our first step was
just to think of a number to be thought
of a number a B now in the second step
we were asked to reverse the digit now
what happens when you reverse the digits
a B becomes da you just interchange the
position of the two digits a and B so
this becomes d into 10 plus a into 1
because in this case a is a
and be elected MP so this is equal to 10
B plus a so be a candidate and f10 D
plus 8 now what well what when we ask in
the third step in the third step we have
to find out the sum of these two digits
typically we needed to add the two
digits that is a B plus B so what is a B
a B is 10 a plus B and B a is 10 D plus
8 now if you look at this 10 a plus 8
how much would be that that would be 11
8 similarly 10 B plus B D is 1 D
threatens 11 D so here 11 is a common
factor so this can be written as 11 into
a plus B so when you look at this
factored form what does it show it shows
that 11 is an exact physical strength
which shows that the sum the sum of
these two numbers is equal to 11 into a
plus B which means 11 exactly divides
the Sun similarly a plus B what I'd like
to son
so here we are interested only in 11 we
looking at this going by this general to
this we see that 11 would be a number
that would always divide the sum exactly
no matter whatever your number it now
here we have considered everything in
genders like a a BA D so this a could be
any digit B would also be any digit so
you can just think of any number and if
you follow these steps
the result would always be completely
visible guys 11th so that is how the
trees work now in a similar way you can
also play the a symmetric with the
difference of two numbers for example in
let us consider any two-digit numbers so
let's say that the number that we
considered is AD so how can we write ad
as we did in the last night it can be
written as 10 8 plus B now when you
report the digit then it becomes B 8 and
B a can be written as
B plus a now instead of adding them what
you do you subtract them
now when you subtract then it becomes a
B minus B a so this can be written as 10
a plus B minus nd plus 8 so this can be
written as M ay plus B minus 10 t minus
8
now all these are how we add and
subtract and Hendrick expressions and we
have already discussed during one of our
previous lessons so I am sure that you
are putting is comfortable with all of
these calculations by now when you look
at this same position 10 enh append a
minus 1 K would be minus 8
similarly plus 1 D minus 10 be just
minus 9 B right because minus 10 plus 1
so minus 10 in figures therefore minus 9
and 10 minus 1 is 9 so minus 90 if you a
9 is the common factor so this looking
down into a minus B so when you are
trying to place a different trait at
that time at the last step you have to
tell your friend to divide the
difference by nine steps because in this
case 9 is an exact division right if you
look at this more deeply you will see
that in any case in any values of a and
B the difference so whatever you are
taking right now is the difference
between the two numbers the difference
will always be divisible by 9 for
example if a is greater than T in that
case what happens the different spins
divisible by 9 that is that if a is
greater than B that is a minus B is any
positive number
now let us say if their sample scenario
by T is less than B so if a is less than
B in fact if your difference would be 9
into B minus 8 which will again be
divisible by 9
now you see you come across a situation
where a and B are same that is a is
equal to B for example if you choose a
number X 53 or 22 or amendment in that
will go
digital editing so a and B are same so
impact is what can happen in that case
your difference will be equal to zero
nothing's difference is equal to zero
again if you divided zero by nano and
ultimately the remainder there would be
no remainder so the remainder is zero at
that time also so we see that this
general trick applying for any two bands
of A and B does not matter whether a is
greater than B on the internet or any of
a and B are equal so this plea to that
being able to all of them thank you
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