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

Hi! I am Samir and now we will learn a
trick to multiply two numbers called
one-line multiplication. It is generally
used in cases where no other more elegant
trick can be used.
Here the idea is to
understand the process first and then we will
proceed to see how we can write down the answer
in 1 line. Pay extra attention to each and
every step.Please notice carefully the movement
of arrows to understand the flow better. Let's
begin
Let us use 26 * 34 as an example
Here the answer would be in 3 parts , we will
begin by 3rd part  which is the product of
4 and 6 giving us 24, the second part would
be the sum of cross products of 2 & 4 and
6 & 3 giving us 2 into 4 =eight and adding
to it would be 3 into 6 =18  ,giving us a
total of 26, and
The first part would be product of 2*3 giving
us 6
Please note that the number of digits in 2nd
and 3rd part would be 1
So the extra 2 in the third part will be moved
to the second part making it 26 + 2=28 , leaving
behind 4 in the 3rd part,  similarly the
extra 2 in the second part will be moved to
the first part making it 6 plus 2 , 8 leaving
 behind  8 in the second part .Now we can
finally get the answer as  884
Having understood the process let us  proceed
to see how we can write down the answer in
one line. For this we will have 2 boxes one
would be called the answer box and the other
would be called the carry over box.
The answer box would contain the final digits
of the answer whereas the carry over box will
show the calculation that goes on in our mind
to arrive at the answer.
We can begin from the right hand side,  4*
6 , 24 we can put down 4 in the answer box
and carry over 2, next step would be to multiply
4 with 2 and add to it the carry over making
it 8 + 2, 10 now to this we will add 3 into
6 , 18 which will give us  18+10 , 28,  now
we can put down the 8 in the answer box and
keep 2 in the carry over box.Finally we will
multiply 3 and  2 to get 6 and to this
we will add the carried over 2 giving us 8.
Now,We can write down our final answer is
884.
Having understood the process for two digit
numbers let us try to extend it to the 3 digit
numbers. Again our aim would be first to understand
the process and then try to write down the
answer in one line. Here the answer would
have 5 parts. Let us begin by fifth part which
should be 7 into 3 giving us  21,  4th part
would be (2 * 3 = 6 )+( 4 * 7 = 28) giving
us a total of 34, for the   3rd part, it
would be the product of 5 and 3 which will
give us 15, to this we will add 2 into 4 which
is 8 ,and then  add 8 into 7 , 56. Now adding
all this will get 79 .
Now for the second part , we will have the
product of 5 and 4 giving us 20 and to this
we  will add the product of 8 and 2 , 16
, giving us a total of 36 and finally  for
the first part will have 8 into 5 equal to
40 . Please note that the number of digits
 in 2nd ,3rd, 4th, and 5th part each would
be one. So beginning from 5th part will have
to move the extra 2 to the 4th part making
it  34 + 2, 36 and leaving behind one in
the 5th part. Now again the extra 3 in  the
4th part will be moved to the 3rd part giving
us 79 + 3, 82 in the third part and leaving
behind 6 in the 4th part. Again, the extra
8 in the third part will be moved to the second
part making the second part as 36 + 8, 44
and leaving behind 2 in the third part .finally
extra 4 in the second part will be moved to
the first part therefore giving us 44 in the
first part and leaving behind 4 in the second.
Now we can Club all these and write down our
final answer as 4 4 4 2 6 1
Let's proceed to write down the answer in
one line, again we will have 2 boxes. One
would be called the answer box and the other
would be called the carry over box.
The answer box would contain the the final
digits of the answer whereas the carry over
box will show the calculation that goes on
in our mind to arrive at the answer.
We can begin  by multiplying 7 and 3 giving
us  21 ,we can put down one in the answer
box and take 2 to the carry over box. Next
 we will multiply 2 & 3 to get 6. And to
this we will add the carry over 2 making it
8 ,to this we add 4 into 7, 28 giving us 28
+ 8 = 36 as total for this part, we can put
down 6 in the answer box and take 3 as carry
over.
For the next part  we will start by 5*3=
15, to this we will add the carry over 3,
making it 18. To this will also have to add
2*4 =8, making it 26, and finally we add
7*8 =56 , giving us a total of 82 for this
part. So we can put 2 in the answer box and
carry 8 to the next part, which we will begin
by multiplying 5 and 4 which gives us 20,
and adding the carry over 8 makes it 28,
to this we will also add 8*2 ,16 making it
28+16, 44
Now we can put down 4 in the answer box and
carry the remaining 4 to the carry over box
for the final part. We can now multiply 5
& 8 giving us 40  to this we add the carry
over 4 for the last time, giving us 44. Now
we can write down our final answer as 444261
Let us now try one more example to see how
good our understanding is. We will write down
only the answer this time
So let us try 624 x 753
Let's proceed to try to write down the answer
in one line, again we will have 2 boxes. The
answer box and  the carry over box. And the
answer would have 5 parts. We will begin from
right hand side by  multiplying 4 and 3 giving
us  12 ,we can put down 2 in the answer box
and take 1 to the carry over box. Next  we
will multiply 2 & 3 and get  6. And to this
we will add the carry over 1 making it 7 ,now
to this we add 5 x 4 =20 making it 20 +
7 , 27.We can put down 7 in the answer box
and take 2 as the carry over.
For the next part  we will start by 6x 3,
18, to this we will add the carry over 2,
making it 20. Now we will add 2x5 , 10 to it
 making it 10+20, 30 .Finally we will add
7x4 , 28 to it , giving us 58 as total for
this part. So we can put 8 in the answer box
and carry over  5 to the next part, which
we will begin by multiplying 6 and 5 giving
us 30,  and to it we will add the carry over
5 making it 35, and finally  we will add
7x2 , 14 , making it 14+35= 49
Now we can put down 9 in the answer box and
carry 4 to the carry over box for the final
part. We can finally multiply 6 & 7 giving
us 42 and to this we will add the final carry
over 4 for the last time, giving us 46
Now we can write down our final answer as
469872
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