MULTIPLICATION TABLE -
    REMEMBERING MADE EASY
    BY SIMPLE TECHNIQUE

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        For traditional way of learning
        with a number of tips, go to

        Multiplication Tables.

        Here, we follow a method which is very simple
        to understand and very easy to follow.

        The method is based on "Nikhilam"
        sutra of vedic mathematics.

        Our aim is to remember the entries
        in the following table.

x12345678910
112345678910
22468101214161820
336912151821242730
4481216202428323640
55101520253035404550
66121824303642485460
77142128354249566370
88162432404856647280
99182736455463728190
10102030405060708090100


        In the above Multiplication Table, we remember
        the easier ones and arrive at the difficult ones
        using the technique we are going to learn.

        consider the sum of multiplicand and multiplier.
        Remember the values for the sum < 10 and arrive
        at the values for the sum > 10 using the simple
        technique from Vedic Mathematics.

        Let us first see the Multiplication Table by
        posting the entries which we have to get by heart.

x12345678910
1123456789 
2246810121416  
336912151821   
44812162024    
5510152025     
66121824      
771421       
8816        
99         
           


You have to memorise the values in the
above Multiplication Table, which are easy.

If you find it difficult, here is a solution.













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Now let us learn the technique with which we arrive
at the other values in the Multiplication table.

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Example 1 :

Suppose, we have to find 9 x 6.

First we write one below the other.

          9
          6

Then we subtract the digits from 10 and
write the values (10-9=1; 10-6=4) to the
right of the digits with a '-' sign in between.

          9 - 1
          6 - 4
The product has two parts. The first part is the
cross difference (here it is 9 - 4 = 6 - 1 = 5).

The second part is the vertical product
of the right digits (here it is 1 x 4 = 4).

We write the two parts seperated by a slash.

          9 - 1
          6 - 4
          -----
           5/4
          -----

So, 9 x 6 = 54.

Let us see one more example.













Example 2:

To find 7 x 6

By following the above procedure,
we may write as follows.

          7 - 3
          6 - 4
          -----
           3/12
          -----

The first part = 7 - 4 = 6 - 3 = 3.

The second part here is 3x4 = 12.
It has two digits. we retain the units' digit
and carry over the other digit to the left.

To indicate the carry over, we write the digit
to be carried over in small letters as follows.

          7 - 3
          6 - 4
          -----
          3/12
          -----

So, the answer becomes (3+1)/2 = 4/2

Thus, 7 x 6 = 42.

I hope you have followed the technique.

Now, we apply the technique to find all the
remaining entries in the above multiplication Table.











Calculation of Entries in the Multiplication Table :

The entries of the multiplication table
are calculated as shown below.

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9 times table :

    9 - 1      9 - 1      9 - 1      9 - 1      9 - 1      9 - 1      9 - 1      9 - 1      9 - 1      
    2 - 8      3 - 7      4 - 6      5 - 5      6 - 4      7 - 3      8 - 2      9 - 1     10 - 0
    -----      -----      -----      -----      -----      -----      -----      -----     ------
     1/8        2/7        3/6        4/5        5/4        6/3        7/2        8/1        9/0
    -----      -----      -----      -----      -----      -----      -----      -----     ------
    9x2=18     9x3=27     9x4=36     9x5=45     9x6=54     9x7=63     9x8=72     9x9=81    9x10=90




8 times table :

    8 - 2      8 - 2      8 - 2      8 - 2      8 - 2      8 - 2      8 - 2      8 - 2      
    3 - 7      4 - 6      5 - 5      6 - 4      7 - 3      8 - 2      9 - 1     10 - 0
    -----      -----      -----      -----      -----      -----      -----     ------
     1/14       2/12       3/10        4/8        5/6        6/4        7/2        8/0
    -----      -----      -----      -----      -----      -----      -----     ------
    8x3=24     8x4=32     8x5=40     8x6=48     8x7=56     8x8=64     8x9=72    8x10=80




7 times table :

    7 - 3      7 - 3      7 - 3      7 - 3      7 - 3      7 - 3      7 - 3      
    4 - 6      5 - 5      6 - 4      7 - 3      8 - 2      9 - 1     10 - 0
    -----      -----      -----      -----      -----      -----     ------
     1/18       2/15       3/12        4/9        5/6        6/3        7/0
    -----      -----      -----      -----      -----      -----     ------
    7x4=28     7x5=35     7x6=42     7x7=49     7x8=56     7x9=63    7x10=70




6 times table :

    6 - 4      6 - 4      6 - 4      6 - 4      6 - 4      6 - 4      
    5 - 5      6 - 4      7 - 3      8 - 2      9 - 1     10 - 0
    -----      -----      -----      -----      -----     ------
     1/20       2/16       3/12        4/8        5/4        6/0
    -----      -----      -----      -----      -----     ------
    6x5=30     6x6=36     6x7=42     6x8=48     6x9=54    6x10=60


5 times table :

    5 - 5      5 - 5      5 - 5      5 - 5      5 - 5      
    6 - 4      7 - 3      8 - 2      9 - 1     10 - 0
    -----      -----      -----      -----     ------
     1/20       2/15       3/10        4/5        5/0
    -----      -----      -----      -----     ------
    5x6=30     5x7=35     5x8=40     5x9=45     5x10=50    


4 times table :

    4 - 6      4 - 6      4 - 6      4 - 6      
    7 - 3      8 - 2      9 - 1     10 - 0
    -----      -----      -----     ------
     1/18       2/12        3/6        4/0
    -----      -----      -----     ------
    4x7=28     4x8=32     4x9=36     4x10=40    


3 times table :

    3 - 7      3 - 7      3 - 7      
    8 - 2      9 - 1     10 - 0
    -----      -----     ------
     1/14       2/7        3/0
    -----      -----     ------
    3x8=24     3x9=27     3x10=30    


2 times table :

    2 - 8      2 - 8      
    9 - 1     10 - 0
    -----     ------
     1/8        2/0
    -----     ------
    2x9=18     2x10=20    






To find the multiplication table
for two digit numbers, go to
Vedic mathematics.

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