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Vedic mathematic techniques

• 2. Numbers below a base number  ! 88 × 97 = 8536  We notice here that both numbers being multiplied are close to 100: 88 is 12 below 100, and 97 is 3 below it. -12 -3 88 × 97 = 85/36  The deficiencies (12 and 3) have been written above the numbers (on the flag – a sub-sutra), the minus signs indicating that the numbers are below 100. The answer 8536 is in two parts: 85 and 36.  The 85 is found by taking one of the deficiencies from the other number.  That is: 88 – 3 = 85 or 97 – 12 = 85 (whichever you like), and the 36 is simply the product of the deficiencies: 12 × 3 = 36.  It could hardly be easier.
• 3. Splitting numbers  18 For eg. 18 18 * 7 9 2 We can write it as : 7 * 9 * 2 = 63 * 2 = 126
• 4. Multiplying by 4  For eg. 4 53 * 4 2 * 2 53 * 4 = 53 * 2 *2 Double of 53 = 106 Double of 106 = 212 Hence , 53 * 4 = 212
• 5. The sutras  8 By the Completion or Non-Completion  12 The Remainders by the Last Digit  13 The Ultimate and Twice the Penultimate  14 By One Less than the One Before  15 The Product of the Sum  16 All the Multipliers
• 6. Sutra 8, By the Completion or Non-Completion : The technique called completing the square’ for solving quadratic equations is an illustration of this Sutra. But the Vedic method extends to ‘completing the cubic’ and has many other applications
• 7. Sutra 11,  Specific and General is useful for finding products and solving certain types of equation. It also applies when an average is used, as an average is a specific value representing a range of values. So to multiply  57×63 we may note that the average is 60 so we find 602 – 32 = 3600 – 9 =3591.  Here the 3 which we square and subtract is the difference of eachnumber in the sum from the average (
• 8. Sutra 12,  The Remainders By the Last Digit is useful in converting fractions to decimals. For example if you convert 17to a decimal by long division you will get the remainders 3, 2, 6, 4, 5, 1 . . . and if these are multiplied in turn by  the last digit of the recurring decimal, which is 7, you get 21, 14, 42, 28, 35, 7 .  . . The last digit of each of these gives the decimal for 17  = 0.142857 . . .  The remainders and the last digit of the recurring decimal can be easily obtained
• 9. Sutra 13,  The Ultimate and Twice the Penultimate can be used for testing if a number is divisible by 4. To find out if 9176 is divisible by 4 for example we add the ultimate which is 6 and twice the penultimate, the 7. Since:  6 + twice 7 = 20 and 20 is divisible by 4 we can say 9176 is divisible by 4.  Similarly, testing the number 27038 we find 8 + twice 3 which is 14.  As 14 is not divisible by 4 neither is 27038
• 10. Sutra 14,  By One Less than the One Before is useful for multiplying by nines.  For example to find 777 × 999 we reduce the 777 by 1 to get 776 and then use All from 9 and the last from 10 on 777.  This gives 777 × 999 = 776/223.
• 11. Sutra 15,  The Product of the Sum was illustrated in the Fun with Figures book for checking calculations using digit sums: we find the product of the digit sums in a multiplication sum to see if it is the same as the digit sum of the answer.  Another example is Pythagoras’ Theorem: the square on the hypotenuse is the sum of the squares on the other sides.
• 12. Sutra 16,  All the Multipliers is useful for finding a number of arrangements of objects. For example the number of ways of arranging the three letters A, B, C is 3×2×1 = 6 ways.
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