Quickly Calculating the Product of Two 2-Digit Numbers

A resource about math tricks would not be complete without mention of the techniques of Vedic mathematics.  Vedic math was introduced by Bharati Krishna Tirthaji Maharaja in the first half of the 1900s, and are a collection of sutras which allow the user to quickly solve mathematical problems very efficiently.  Tirthaji claimed that these sutras were found while studying ancient Hindu writings, but confirmation of his explanation has never been made.

Vedic math can be used such that calculations can be performed mentally or very quickly using single-line notation.  This article will demonstrate the Vedic math technique of quickly calculating the product of two 2-digit numbers.

In this example, 32 will be multiplied by 43:

32
x43

First take the product of the right-most digits and multiply them.  Then, write the result under and to the right of the multiplication set:

32
  |
43
6

Next, take the product of each diagonal digits and add them together.  Write the sum to the left of the first result.  I will show this step in two parts:

32
 X
43
(3×3)+(4×2)   6

Which is the same as:
32
 X
43
17  6

Lastly, take the product of the left-most digits, and write the result to the left of the first two results:

32
 |
43
12  17  6

Almost done – now if you have any remainder in the tens columns, be sure to add it to the ones columns to the result to the left.  In our example, the “17” has a remainder of “1” in the tens columns, so add 1 to 12:

32
43
13  7  6

Now just “squeeze” the results together, and you will have your answer:

32
43
1376

And, indeed, if you use a calculator, you will find that 32 x 43 = 1376.

 

And now for a few more examples:

12×16:

12
16
1   2+6   12

12
16
1  8  12

192 answer

 

16×36:

16
36
3   24   36

16
36
3   24   36

16
36
3  27  6

16
36
5  7  6

576 answer

 

25×97:

25
97
18  45+14  35

25
97
18  59  35

25
97
18  62  5

25
97
24  2  5

2425 answer
Practice some more of your own on paper to get the technique down, and then try to do some in your head.  With a little practice, you will be able to do two-digit calculations quickly in your head!

Tags: Math Tricks, mental math, multiply 2 digit numbers, Tirthaji, two digit numbers, vedic math, vedic mathematics