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!

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Squaring Two-Digit Numbers Quickly

Using this math trick, you will be able to square any two digit number very quickly.  With a little practice you can do it in your head, or you can do it on paper and still impress others with your math skills.  This method of squaring is very easy, and I will be using as an example squaring the number 23.

First, determine the closest number to your number that ends in a zero.  In this example, the number is 20.  Next, determine the difference between your number and the closest number with the zero.  In this case, it will be (23 – 20) = 3.  Add the result to your number (23 + 3 = 26).  Now, multiply the number with the zero by the sum of your number and the difference you determined:

20 x 26 = 520

Now square the difference you determined before, and add it to the result above:

(3 x 3) + 520 = 529

Presto!  There is the square of your number!

Here are some more examples:

The Square of 25

Closest zero number:  20 (note – 30 will also work in this example)

Difference:  25 – 20 = 5

Sum:  25 + 5 = 30

Answer:  (5 x 5) + (20 x 30) = 25 + 600 = 625

The Square of 37

Closest zero number:  40

Difference:  37 – 40 = -3

Sum:  37 + -3 = 34

Answer:  (-3 x -3) + (40 x 34) = 9 + 1360 = 1369

The Square of 81

Closest zero number:  80

Difference:  81 – 80 = 1

Sum:  81 + 1 = 82

Answer:  (1 x 1) + (80 x 82) = 1 + 6400 + 160 = 6561

Noticed how I broke down the (80 x 82) into (80 x 80) + (2 x 80)!

The Square of 12

Closest zero number:  10

Difference:  12 – 10 = 2

Sum:  12 + 2 = 14

Answer:  (2 x 2) + (14 x 10) = 4 + 140 = 144

This math trick can sometimes be very useful, and is one that I recommend that you practice on your own.  One day you just might come upon a situation where you need to square a two digit number without a calculator.  I know – you can use your smart phone… but with practice, you can solve the problem before your run your calculator app!

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Going through a recent search on Pi, I came across many pages that had listed values of Pi to many places.  For example, one page listed the value of Pi to 1000 places:

3.141592653589793238462643383279502884197169399375105820974944592
3078164062862089986280348253421170679821480865132823066470938440
9550582231725359408128481117450284102701938521105559644622948954
9303819644288109756659334461284756482337867831652712019091456485
6692346034861045432664821339360726024914127372458700660631558817
4881520920962829254091715364367892590360011330530548820466521384
1469519415116094330572703657595919530921861173819326117931051185
4807446237996274956735188575272489122793818301194912983367336244
0656643086021394946395224737190702179860943702770539217176293176
7523846748184676694051320005681271452635608277857713427577896091
7363717872146844090122495343014654958537105079227968925892354201
9956112129021960864034418159813629774771309960518707211349999998
3729780499510597317328160963185950244594553469083026425223082533
4468503526193118817101000313783875288658753320838142061717766914
7303598253490428755468731159562863 82353787593751957781857780532
171226806613001927876611195909216420199

LOL – I have not confirmed this, but there is no reason for me to think that it is incorrect – or correct for that matter.

It turns out that there are many ways to determine Pi, and some of these methods are outlined here.  Has anybody used a method that they feel is better than others?

Sure, it is not a very useful exercise to calculate the value of Pi out to so many places, but it sure is cool!

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Number Wheel Math Tricks – 4s and 6s

Here is a cool video from Mister numbers.  It shows you a method of obtaining the multiplication tables for 4s and 6s using a number wheel:

Clever way of getting the series of numbers, and generates a pattern too!

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