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Vedic Mathematics Sutra Sid Mehta

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Hey Sid how did you come across this topic? *tell background story*

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Vedic Mathematics Sutra From Vedas(ancient Hindu texts written in Sanskrit) Ancient scholars used these Sutras(formulas) to make mathematical calculations Book is filled Sutras that make arithmetic computation easy and ones that make algebra easy also some other cool little tricks.

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The Sutras

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Terminology Base: every time you see the word base, it is referring to the tenth base so 10,100,1000 Deficiency= base-number Surplus=number-base

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Square of Number Ending in 5(cool trick #1) Step 1: Multiply the figures (except the last 5) by one more than it Step 2: write (square of 5), 25 after it

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Cool Trick #1 Example: Square of 35 (35)(35)=[3x(3+1)]25=1225 Example: Square of 105 (105)(105)=[10x(10+1)]25=11025

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Cool Trick #1 Proof (a5)(a5) where a is some positive integer (10a+5)(10a+5)=100a^2+100a+25 =100a(a+1)+25

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Multiplication-When Numbers are Close to the Base(Cool Trick #2) Step 1: Write numbers and their deficits Step 2: Product has two parts -Right part: product of both deficits -Left part: cross subtraction of either number and other’s deficits

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Cool Trick #2 Example 7 x 8 7 3 82 3 x2=6(right part) 8-3 or 7-2=5(left part) 56

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Cool Trick #2 Example 98 x 76 98 2 7624 2 x 24=48(Right part) 76-2 or 98-24=76(Left Part) 7648

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Cool Trick #2 If one number is greater than base and the other is less Right Part: Base + product of both deficits Left part: Cross Subtraction -1 Example 107*96 107 -7 96 4 Right part= 100+(-28)=72 Left Part= (107-4 or 96+7)-1=102 10272

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Multiplication by 9,99,999(Cool Trick #3) Only when working base and multiplier are the same Step 1 Left part: multiplicand -1 Right part: the deficiency of multiplicand Example 67 * 99 Left part: 66 Right part:33 6633

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Cool Trick #3 Proof n is a number in which all digits are 9 a is some number n*a=answer Left part is a-1 Right part is (n+1)-a Combining the parts: (n+1)*(a-1)+(n+1)-a=an

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When the sum of final digits is the base and previous parts are same(Cool Trick#4) Step 1 Left part: Multiply the previous part by one more than itself Right part: Multiply the last digits(sum is the base)

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Cool Trick #4 Example: 36 x 34 Left part: (3+1)(3)=12 Right Part: (6*4)=24 1224 Example: 260 x 240 Left part: (2+1)(2)=6 Right part: (60*40)=2400 62400

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Cool Trick #4 Proof a and b are both numbers (ab)(a10-b) or (10a+b)(10a+10-b) 100a^2+100a-10ab +10ab +10b-b^2 100a(a+1)+10b-b^2

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Square of Any Number (Cool Trick #5) Step 1: Square the deficiency(Right Part) Step 2: Subtract the number by its deficiency plus carry over(Left Part)

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Cool Trick #5 Square of 96 Right part: deficiency=100-96=4. 4^2=16 Left part: 96-deficiency=96-4=92 9216 Square of 9992 Right part: deficiency=1000-9992=8.8^2=64 Left part: 9992-8=9984 998464

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Cool Trick #5 Proof a is any number 100(a-(100-a))+(100-a)^2 200a-10000+10000-200a +a^2 a^2

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Paravartya Yojayet English Translation: transpose and adjust Mathematical Meaning: In any equation, move a term from one side to another and adjust it by changing its sign x+2=0 becomes x=-2

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Indian Multiplication Step 1: The right hand digits are both multiplied Step 2: Apply inside-outside principle (plus carry) Step 3: The left hand digits are multiplied plus carry Example 56 x 17 7x6=42 but you only put 2 7x5 + 6x1=41+4=45 but only put 5 5 x 1= 5+4=9 952

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