Magical Multiplication - Vedic Maths tricks Video Lecture | Improve Your Calculations: Vedic Maths (English) - Class 6

Let us now see a special case of
multiplying two numbers both of which
are entirely made up of only 3's ,6's or 9's.
Let's begin by something which we
all know, 3x 3 gives us 9. Let us put it as as 09. Now what if it was 33
x 33. It is still very simple. Let's
take the answer of 3x3 which is 09 and
make some improvisations.We will add one
blank each to the left of the digit of the
answer the one left to the nine will be
decreased by one and the one left to the
zero will be increased by one
thereby giving us 1089 as our answer.Let us extend it a bit further by trying
333 x 333. Now, since we
have two extra 3's , we will add two extra
blanks to the left of 9 and 2 blanks
to the left of 0 . We will proceed as earlier. The two
blanks to the left of 9 will be
decreased by 1 and the two blanks to the
left of 0 will be increased by 1, thereby
giving us 110889 as our answer. So far we
have seen the multiplicand and the
multiplier were same. Now let us see when they are different but still made up of same
digits. Let us begin by taking 333x 33 as an
example. We will first treat it as 33x 33. So we'll put down 0 9 add one
blank each to the left of 9 and 0 ,then we
will decrease 9 by one and put it
to the left of it, we will increase 0 by one
and put one to the left of it. Now for
the extra 3 we will insert one 9 in the
middle there
fore
we will have 10989 as our answer. Now let us
try 3333 x 33 again we will treat it as
33x 33 first , so we can put down 0 9, add 1 blank each to the left of nine and zero then
decrease 9 by one and put 8 to the
left of it increases 0 by one and put
1 to the left of it and for the extra
two-digits we will add 2 extra 9 in the
middle
therefore giving us our answer as 109989.
Let us take 3333 x 333
Now we'll treat it as 333 x
333, so we will put 0 9 and add two
blanks each to the left of 9 and 0
Now we can decreased 9 by one and put 8
in the first blank similarly will again
decreased 9 by one and put another 8
in the second blank. Now we will increase 0 by
one and put one in the first blank to
the left of zero and will put another
one by increasing 0 and putting it in
this second blank to the left of 0. Now
for the extra of one 3 will put a 9 in
the middle ,therefore giving us 1109889
as our final answer. So far we have seen
that our multiplicand and multiplier were
made up of same digits, now let us take
some examples where they are made up of
different digits. Let us begin by a very
simple example 6x3 which we all know
is 18. Now let us try 66x 33 again it
would be very similar to what we have
learnt in previous examples. We will put
down the answer of 6x 3, 18 and then
add one
blank each to the left of 8 and 1.
Next step would be to
decrease 8 by one and write to the left
of it and then we will increase 1 by
one and write to the left of it thereby
giving us our final answer as 2178. Let
us now try 666x 333. Here again
the process would be very similar. We will first write down 6x3 , 18 and add 2
blanks each to the left of 8 and
1. Now the 2 blanks to the left of
8 will be filled by decreasing 8 by
one and two blanks to the left of 1
will be filled by increasing 1 by one
thereby giving us our final answer
that's 221778. Let us take some examples
of our multiplicand and multiplier are
different and also the number of digits
in them are different. Let us begin
by 666x 33
as an example. Here we will proceed by thinking it as 66 x33. So we will
put down 1 8 and put one blank each to the
left of 8 and 1. Now we can fill
them by first decreasing 8 by 1
and putting it to the left of it and
increasing 1 by one and putting it to the
left of it.Now for the extra six we will
put one 9 in the middle
thereby giving us 21978. Now, let us
take 6666 x 33 as an example. Again we
will proceed by thinking it as 66x 33.
So we will first put down 1 8 and now we will insert
one blank each to the left of 8 and 1.
Now we will decrease 8 by one and fill the
blank left to it by 7 similarly will
increase 1 by one and fill the blank
left to it by 2. Now we have two extra 6 to
take care of , for that we will insert two 9's
in the middle
thereby giving us 219978 as our final
answer. Now let us take one more example
6666x
333. Now we will proceed by thinking it as
666x
333. So first let us put down 1 8 an insert two blanks each to
to the left off 8 and 1. We will
now fill the blanks left to 8 by one
less than it. So both the blanks will
get 7 and the blanks left to 1 will each
get one more than 1.So both will get 2.
Now we have one extra six to take care
of , for which we will insert a 9 in the middle
thereby giving us 2219778 as our answer.
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