Zero - 4 (Base no. multiplication Extension)

Dear all,

Continuing with our blogs on Speed Math. All these techniques are to be practiced daily for at least 15 minutes to get full advantage of them.

{ Sharing - recently lost someone very dear. Please bear with me. So took a break from blogging. But one has to continue working. As this topic is very useful for students, teachers and parents. It is futuristic as it addresses and refines our fundamentals. Once simple calculations can be handled in the mind, our study in various Science subjects becomes easier. 

Planning to cover different topics in competitive Mathematics so as to get the best methods to the reader }

Base method multiplication extension

20 as base number

+3   +6                -2   +1            +2   +11
23 x 26                18 x 21            22 x 31
----------------       ------------------         ------------------
23+6 / (3x6)    18+1 / (-2*1)        31+2 / (2*11)
29   / 18            19   / -2                33  / 22
(29x2) / 18        19*2  / -2            33*2 / 22
58  / 18                38 / -2                66  / 22    
598                       37 / 8                682
                            378

So, as is obvious, the left side of the result is arrived by adding diagonally. The right side is the product of the difference above or below the base numbers. Then the left side is to be doubled as 20=10x2. Only one digit is to be left on the right side.

The expansions are:-

23 x 26 = (23+6)20 + (3x6) = 29*20 + 18 = 580 + 18 = 598
18 x 21 = (18+1)20 + (-2x1) = 9*20 -2 = 380 - 2  = 378
22 x 31 = (31+2)20 + (2x11) = 33*20 + 22 = 660+22 = 682

The expansion is for knowledge purposes only. The above method of separating left and right side of the answer by a slash gives one speed. 

Thinking further, we can take any base number that is generally a multiple of 10. If the base number is 30 we do x3 for the left hand side, if 40 we do x4, if 70 we do x7 and so on. Generally, it is best to take base number between the given numbers. The whole idea is to avoid the pen and still be right. But taking the subject in capsules makes it easy to digest.

Lots more to explore. Vedic Maths is unlimited.

Another way of adding numbers 

          +25                +5   +10
Ex:     125+85+90+105+110
                  -15  -10 

Take 100 as the average. Above and below mark the differences. The net difference is 15 {+10 and -10 just cancel out}. Now we have five 100's that make 500. Adding 15 gives the final answer as 515.
Averaging and adding is much better than running for the pen, writing in columns and then adding. With practice, this can easily be done in the mind. 

                    +39       +15.50
Ex:     45.50+89+32+65.50+17
          -4.50        -18               -33

Take the average as 50. Managing the differences, 15.5-18 gives -2.5, -4.5-2.5 gives -7, 39-7 gives 32 and 32-33 gives -1. So as we have five 50's that make 50x5=250. Taking -1 out of it gives us the final answer as 249.

This is one of the best ways of adding numbers. Its no fun running for the rough paper time and again.

With Regards,

Jeeves