An elegant way of multiplying numbers using a simple pattern.
* 21 x 23 = 483
This is normally called long multiplication but
actually the answer can be written straight down
using the VERTICALLY AND CROSSWISE
formula.
We first put, or imagine, 23 below 21:
There are 3 steps:
a) Multiply vertically on the left: 2 x 2 = 4.
This gives the first figure of the answer.
b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8
This gives the middle figure.
c) Multiply vertically on the right: 1 x 3 = 3
This gives the last figure of the answer.
And thats all there is to it.
* Similarly 61 x 31 = 1891
* 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1
Try these, just write down the answer:
- 14
21 x
2) 22
31 x
3) 21
31 x
4) 21
22 x
5) 32
21 x
Total Correct =
Multiply any 2-figure numbers together by mere mental arithmetic!
If you want 21 stamps at 26 pence each you can
easily find the total price in your head.
There were no carries in the method given above.
However, there only involve one small extra step.
* 21 x 26 = 546
The method is the same as above
except that we get a 2-figure number, 14, in the
middle step, so the 1 is carried over to the left
(4 becomes 5).
So 21 stamps cost £5.46.
Practise a few:
- 21
47 x
2) 23
43 x
3) 32
53 x
4) 42
32 x
5) 71
72 x
Total Correct =
* 33 x 44 = 1452
There may be more than one carry in a sum:
Vertically on the left we get 12.
Crosswise gives us 24, so we carry 2 to the left
and mentally get 144.
Then vertically on the right we get 12 and the 1
here is carried over to the 144 to make 1452.
- 32
56 x
7) 32
54 x
8) 31
72 x
9) 44
53 x
10) 54
64 x
Total Correct =
Any two numbers, no matter how big, can be
multiplied in one line by this method.
DIVISION
The above left to right method can be simply reversed to give us a one line division method.
Suppose we want to divide 1452 by 44. This means we want to find a number which, when multiplied by 44 gives 1452, or in other words we want a and b in the multiplication sum:
Since we know that the vertical product on the left must account for the 14 on the left of 1452, or most of it, we see that a must be 3.
This accounts for 1200 of the 1400 and so there is a remainder of 200. A subscript 2 is therefore placed as shown.
Next we look at the crosswise step: this must account for the 25 (25), or most of it. One crosswise step gives: 3×4 = 12 and this can be taken from the 25 to leave 13 for the other crosswise step, b×4. Clearly b is 3 and there is a remainder of 1:
We now have 12 in the last place and this is exactly accounted for by the last, vertical, product on the right. So the answer is exactly 33.
It is not possible in this short article to describe all the variations but the method is easily extended for
a) dealing with remainders,
b) dividing any two numbers,
c) continuing the division (if there is a remainder) to any number of figures,
d) dividing polynomial expressions.
The multiplication method described here simplifies when the numbers being multiplied are the same, i.e. for squaring numbers. And this squaring method can also be easily reversed to provide one line square roots: easy to do, easy to understand.
And yeah, I have a task for you.
Find a way to multiply multi digit numbers and write it down here.
Solve these, and check if you were right.
This was just one ‘‘Vedic math’’ method.
It’s mental math used 3000 years ago.
But later about that.
So, what I’m asking you to do is after you learn how to multiply, do it in your brain.You will have to imagine all the numbers there and remember all of them.
This improves memory AND your ability to visualize.
Practice it!
I will post more ways to increase your memory and brainpower.
EDIT: You can measure how long it takes you to multiply these numbers.
Maybe I’ll post some other Vedic Maths ‘‘Sutras’’
