Vedic mathematics is simple
VEDIC MATHEMATICS simplifies multiplication, divisibility, complex numbers, squaring, cubing, square and cube roots. It essentially involves the use of a large set of algorithms, for both simple as well as complex computations.
It is an ancient system of mathematics that was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krishna Tirthaji (1884-1960). It is based on 16 sutras and 13 sub-sutras or word-formulae. The accent is on the natural working of the mind and a methodical approach to any calculation. It allows for mental calculations through some simple methods and allows ample scope for innovation in the sense that you can invent your own method. Research is being carried out in many areas including the effects of learning Vedic mathematics on children and developing easy and powerful applications of the sutras in geometry, calculus, computing etc.
Vedic mathematics is based on certain sutras or principles that are general in nature and can be applied in many ways to solve actual problems.
The Main Sutras
All from 9 and the last from 10
All the Multipliers
By Addition and by Subtraction
By one more than the one before.
By One Less than the One Before
By the Completion or Non-Completion
By the Deficiency
Differential Calculus
If One is in Ratio the Other is Zero
If the Samuccaya is the Same it is Zero
Specific and General
The Product of the Sum
The Remainders by the Last Digit
The Ultimate and Twice the Penultimate
Transpose and Apply
Vertically and Cross-wise
The Sub Sutras
By Alternative Elimination and Retention
By Mere Observation
By Osculation
For 7 the Multiplicand is 143
Last Totalling 10
Lessen by the Deficiency
On The Flag
Only the Last Terms
Proportionately
The First by the First and the Last by the Last
The Product of the Sum is the Sum of the Products
The Remainder Remains Constant
The Sum of the Products
Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency
To get an idea of the methodical and simplistic way to solve mathematical problems, here are a few samples:
Sutra All from 9 and the last from 10 can be used to perform instant subtractions for numbers consisting of 1 followed by zeroes like 100, 1000, 10,000 etc. For example, to calculate 1000-269, take each figure in 269 and subtract from 9 and the last figure from 10. In this case, you need to subtract 2 from 9, 6 from 9 and 9 from 10 and you get the answer 731. Basically, you start using the first zero in the number and then subtract 9. In the case of a number in which we have more zeros than figures in the numbers being subtracted, like say 1000-76, take it as is 076 and apply the same rule.
Sutra "By one more than the one before" is used to square numbers that end in 5. Take for instance 852=7225. There are two parts here, 72 and 25. The last part is always 25. The first part is the first number 8 multiplied by the number "one more," which is 9 (8+1) and 8 x 9 = 72. So, you have the answer: 7225.
Sutra "Vertically and Cross-wise" can be used in multiplying numbers close to 100. For instance, if you have to multiply 90 and 92, 90 is 10 less than 100 and 92 is 8 less than 100.
The answer is 8280 which is got by subtracting 8 from 90 (82) and the last part of the number is 80 that is derived as 10 multiplied by 8 (80). So you have 8280.
There is an easy method for dividing by 9. For example, if you want to divide 23 by 9, the answer is 2 remainder 5. The first figure of 23 is 2, and this is the answer. The remainder is just 2 and 3 added up.
To find the square of a number that is closer to 10, 100, 1000, use the following principle: The square of 99 is 9801. Subtract the number from its nearest `0' number, 100-99=1 in this case. Then subtract the number obtained with the base number; you get (99-1) 98 in this case. This forms the first two digits of you answer. The last two digits are obtained by the square of difference between the nearest `0' number and the base number; (100-99)to the power of 2=01.
How to get the square of a number that is not closer to 10, 100, 1000 etc? The square of 43 is 1849. Add the number to the second digit. 43+3=46 in this case. Multiply the first digit of the number with number obtained in (i); you get 4x46=184. This is the first part of your answer. Square the last digit; 3 to the power of 2=9 in this case. This is the last part of your answer. Therefore, the answer is 1849
Now for multiplication with the multiplier-digits consisting entirely of nines. For example, 666 multiplied by 999 is 665,334. To derive this, subtract one from the multiplier's digits i.e. 666-1=665. Subtract from 9 each of the digits of the number obtained; 9-6,9-6 and 9-5 gives 334.
To multiply any number by any number, for example 64x92 is 5888. First multiply 6 by 9 and then add 6*2 & 4*9 and then multiply 4 by 2 which is 54 (12+36) 8; So you get three sets of numbers... 54 48 08. To get the answer, add the first number (54) to the first digit of the second number (4). You get 58 (54+4). These are the first two digits of the answer. Add the second digit (8) of the second number (48) to the first digit of the third number (0). You get 8 (8+0). This is the third digit of the answer. The last digit of the third number is the fourth digit of the answer (8). So you get 5888.
The above are just a few examples of the applications of this wonderful science. The scope of the subject is indeed vast. Vedic Mathematics is being taught in some of the most prestigious institutions in England and Europe. It has also been used in the area of artificial intelligence.
So next time, maybe you don't need to reach for that calculator.
Bindu Gopal Rao
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