Vedic Mathematics - Easy Multiplication

Mathematics as always is a challenging yet interesting subject. Moreover quick and accurate calculations is the key to success in most competitive exams. Multiplication is one of the most common operation and when done using conventional method is a time consuming process. Mental multiplication is an impossible task for ordinary heads when dealing with large numbers. With a few secrets from Vedic mathematics all these statements can be rewritten. Mental multiplication will no longer be a challenge with the techniques discussed below.

The entire discussion is categorized into three sections:

Special Case 1
Special Case 2
General Method

Special Case 1
Prerequisites:

Both numbers should have equal number of digits.
Sum of last digits should be always 10.
Rest of the digits should be the same.

Example:
23*27 : Sum of last digits 3+7=10 and both numbers begin with 2.
86*84 : Sum of last digits 6+4=10 and both numbers begin with 8.
125*125 : Sum of last digits 5+5=10 and both numbers begin with 12.

Procedure:
Consider the multiplication of numbers PQ*PR. Here Q+R=10. P forms the first part of the number.

Step 1 : Multiply Q and R. This forms the last part of the answer.
Step 2 : Multiply P and P+1. This forms the first part of the answer.

To make it clear lets try a few examples:
23 * 27 = ?
3 * 7 = 21
2 * (2+1) = 6
23 * 27 = 621
Simple..!!

86 * 84 = 8*(8+1)/6*4 = 8*9/6*4 = 72/24 = 7224.
Now I think you can do this in a single step.

125 * 125 = 12*13/5*5 = 156/25 = 15625.

Try with a few more examples on your own to master the technique..!

Special Case 2
Prerequisites:

The number should be close to 100.

Example:

102*106

96*98

97*103

Procedure:

Step 1 : Write the two numbers one below the other.

Step 2 : Find the difference of the number from 100 and write it against the number.

Step 3 : Add the first number with the difference of second number from 100 or vice versa. This forms first part of the answer.

Step 4 : Multiply the two differences to get the second part of the answer.

To make it clear try a few examples:

102 * 106 = ?

102 +2

106 +6

----------------

102+6 or 106+2 / +2*+6

-----------------

108/12 = 10812.

Another example

96 * 98 = ?

96 -4

98 -2

--------------

94/08 = 9408.

From the above examples, it can be noted that the answer is formed as :

(First part)*100 + (Second part)

Now try this example

97 * 103 = ?

97 -3

103 +3

------------

100/-9

Here the second part is a negative number. Using above formula, the answer can be obtained as:

100/-9 = (100)*100 + (-9) = 10000-9 = 9991.

It may seem a bit complex at first but this method is definitely time saving once mastered.

General Method

Prerequisites:

None

Procedure:
For 2*2

Consider the multiplication PQ*RS.

---------------

P*R/P*S+Q*R/Q*S

Example:

---------------

12/15+16/20 = 12/31/20

Solving this is a bit tricky. This process can be represented as shown:
12 +
31 +
20
-----------
1530

34 * 45 = 1530.

For 3*3
Consider the multiplication PQR*STU.
PQR
STU
-------------------
P*S/P*T+Q*S/P*U+R*S+Q*T/Q*U+R*T/R*U

Example:
132
245
-------------------------
1*2/1*4+3*2/1*5+2*2+3*4/3*5+4*2/2*5 = 2/4+6/5+4+12/15+8/10 = 2/10/21/23/10 = 32340.

Using similar logic any number can be easily multiplied.

Reading these techniques alone does not make any difference. Use them whenever and wherever possible to gain maximum benefit.