Category: Vedic Mathematics

Make Math fun and interesting with these tricks and shortcuts..

Vertically and Crosswise Multiplication

This is an extremely useful method for high school students while learning multiplication of larger numbers. A lot of time is spent on performing multiplication operations and multiplication is an integral concept in Mathematics. Using this method, multiplication of larger numbers can be performed in a single line. It can done as follows:

  1. For two digit numbers, follow an ‘X’ shape. We can proceed from either left to right or right to left. Here, let us see from right to left. Consider 63 * 83. It can be done as follows:

ð  3 * 3 = 9.

ð  (6*3) + (8*3) = 42.

ð  6 * 8 = 48.

ð  It becomes 48 42 9 =  5229

  1. For three digit numbers, eg, 421 * 123, proceed as follows:

ð  3 * 1 = 3

ð  (3*2) + (2*1) = 8

ð  (3*4) + (1*1) + (2*2) = 17

ð  (4*2) + (2*1) = 10

ð  4 * 1 = 4

ð  It becomes 4 10 17 8 3 = 4 117 8 3 = 51783

  1. For four digit numbers, eg, 1234 * 5631, proceed as follows:

ð  4 * 1 = 4

ð  (3*1) + (4*3) = 15

ð  (2*1) + (3*3) + (4*6) = 35

ð  (1*1) + (2*3) + (3*6) + (4*5) = 45

ð  (1*3) + (2*6) + (3*5) = 30

ð  (1*6) + (2*5) = 16

ð  1 * 5 = 5

ð  It becomes 5 16 30 45 35 15 4 = 5 16 30 45 3654 = 5 16 30 48654 = 5  16 348654 = 5 1948654 = 6948654.

Huge multiplications in a single line. Now that’s simple, isn’t it? 🙂

P S It’s also my favorite. This was what got me hooked !

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My experience with Vedic Math – Fun & Learning

I wish I had gotten hooked to it much earlier than I did. Well, better late than never. I started learning about Vedic Math and the different tricks and shortcuts involved in it, thanks to my mom. She was the one to initiate interest. When she decides to do something, there’s no stopping her. She spent hours together reading up from the internet and books, practicing and solving on paper and finding out new techniques to perform lengthy calculations. She did successfully come up with new tricks of her own.

The next thing that she did was organize a Fun with Math summer camp for kids of the locality. She planned and re-planned the week long camp. She chalked out the entire programme, which had to be done in a systematic manner cos it had to be a combination of fun and learning to sustain the interest of the kids. Well, it was summer holidays and they were doing Math, so it was a big deal and I don’t blame them. 😉 The camp was a huge success.

In short, mom managed to get a whole bunch of kids excited and interested in the topic except her own. Initially, neither my brother, nor I showed much interest when she passionately rambled on about the different Math shortcuts that could make our life easier. She persisted. And well, I’m glad she did. We slowly started tuning ourselves to what she was saying, learning new tricks of the trade and applying them to our calculations.  Who knew then that I would go on to become a Math teacher who would be trying  to convince a whole bunch of kids to listen to what I was saying. This was where the concepts I had learned in Vedic Math came handy. It was always a welcome change to regular classwork, helped solve problems faster and got kids excited. It was one of those moments I silently thanked mom for nagging us. 🙂

Vedic Mathematics is a system of Mathematics that has its roots in the Vedas. This ancient Indian system of calculations had gotten buried and was later rediscovered in the early 20th century (1911-1918) by the great Indian scholar Sri Bharati Krsna Tirthaji. After detailed study of the Indian scriptures, he concluded that the whole of Vedic Mathematics was based on sixteen basic Sutras and sub-Sutras.

This system makes use of Mental Mathematics and helps us perform long and tedious calculations in a quick and simple manner even without the need for a paper and pen. It is also considered to be more coherent and integrated in approach. The concepts are interrelated and unified such that reversal of division leads to multiplication, reversal of squares leads to square roots and so on.

I’ll be using this section on Vedic Mathematics to introduce some of the tricks and methods learned by me, hoping to make lives of many more easier. Looking forward to sharing and spreading the knowledge of this ancient, immensely useful and fun system. I would be more than happy to receive your contributions on the same.

“While Learning adds excitement and meaning, Sharing what you know with your world adds purpose to what we all refer to as Life.”

All from 9 and Last from 10 (To perform large subtractions)

Performing large subtractions fast could be a cumbersome for some. This method can be used for subtracting numbers from 10, 100, 1000, 10000 and so on and from 30, 500, 6000, 20000 and so on. Consider we want to subtract 376 from 1000 and 10905 from 100000. This can be done as follows:

  1. Subtract the last digit from 10 (compliment) and the rest of the digits from 9. i.e., 3 would become 6, 7 would become 2 and 6 would become 4. Thus 1000 – 376 would result in 624.
  2. Similarly 10905 would become 89095 by subtracting the last digit 5 from 10 and the rest of the digits from 9.

Note that applying this to any number ending in 0 should be done by performing the above operations ignoring the 0 and then adding the 0 in the end. Suppose we want to subtract 71840 from 100000, we get 28160 by subtracting 4 from 10 and the rest from 9 and finally adding a 0 to the end.

Also note that the formula All from nine and last from ten subtracts numbers from the next highest base number. Eg: 1000 – 864, 100 – 78 etc. Suppose we had 1000 – 67. 1000 has three 0s, but 67 is a two digit number. This can be done as 1000 – 067 and then applying the formula we get, 933.

Now consider 700 – 46. Here we have 700 instead of 100. This can be done as follows:

  1. Apply the regular formula like it is done for 100 – 46. We get 54 by subtracting 6 from 10 and 4 from 9.
  2. Now 7 is reduced to 6. Thus we get the answer as 654.
  3. Subtraction using  All from 9 and last from 10

Consider the example, 4652. Applying the Sutra, All from nine and last from ten we get 5348 as 4 6 and 5 are taken from 9 and the last digit 2 is taken from 10. Note that if 0 is present in the end, we perform the steps for rest of the number and then add the 0 to the end. Consider the example, 3450. Applying the Sutra we get, 6550. This method can be used when the numbers are close to a base (10, 100, 1000 etc) or multiples of a base (60, 200, 4000 etc). Note that we subtract numbers from the next highest unity. Thus 1000 – 462 = 538 and 10000 – 3672 = 6328.

  1. Consider the example, 1000 – 47

ð  The next highest unity for 47 is 100, but we have to subtract it from 1000. This is done by adding a 0 in front of 47 to make it a 3 digit number. Thus we write it as 1000 – 047.

ð  Now applying the Sutra, we get 953.

  1. Consider the example 4000 – 243.

ð  Consider the unity to be 1000 and solve as usual. Thus we get the answer as 757.

ð  Now since we are subtracting 243 from 4000, it will reduce to 3000 and we get the final answer as 3757.

  1. Consider other cases with subtraction not involving unity or multiples of unity. We can perform these subtractions in a single line without taking borrow or carry forward concept that we have been taught in school. Consider the example, 476 – 248.

ð  Subtracting each column from left to right  (or right to left) we get 4 – 2 = 2 ; 7 – 4 = 3 ; 6 – 8 = -2.

ð  The answer that we got by performing the above subtraction is 23(-2)

ð  When we see a negative number, we take its compliment (All from 9 and Last from 10) and reduce the previous digit by 1 since we are subtracting from it. Thus here 23(-2) becomes 228