Vedic Mathematics Sutra

Sid Mehta

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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.

The Sutras

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

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

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

Cool Trick #1

• Proof(a5)(a5) where a is some positive integer

(10a+5)(10a+5)=100a^2+100a+25=100a(a+1)+25

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

Cool Trick #2

Example 7 x 8 7 38 2 3 x2=6(right part)8-3 or 7-2=5(left part)56

Cool Trick #2

Example 98 x 7698 299 242 x 24=48(Right part)76-2 or 98-24=76(Left Part)7648

Cool Trick #2

If one number is greater than base and the other is less Right Part: Base + product of both deficitsLeft part: Cross Subtraction -1Example 107*96107 -7108 4Right part= 100+(-28)=72Left Part= (107-4 or 96+7)-1=10210272

Multiplication by 9,99,999(Cool Trick #3)

Only when working base and multiplier are the sameStep 1Left part: multiplicand -1Right part: the deficiency of multiplicand

Example 67 * 99Left part: 66Right part:336633

Cool Trick #3

Proofn is a number in which all digits are 9a is some number n*a=answerLeft part is a-1Right part is (n+1)-aCombining the parts: (n+1)*(a-1)+(n+1)-a=an

When the sum of final digits is the base and previous parts are same(Cool Trick#4)

Step 1Left part: Multiply the previous part by one more than itselfRight part: Multiply the last digits(sum is the base)

Cool Trick #4

Example: 36 x 34Left part: (3+1)(3)=12Right Part: (6*4)=241224

Example: 260 x 240Left part: (2+1)(2)=6Right part: (60*40)=240062400

Cool Trick #4

Proofa and b are both numbers(ab)(a10-b) or (10a+b)(10a+10-b)100a^2+100a-10ab +10ab +10b-b^2100a(a+1)+10b-b^2

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)

Cool Trick #5

Square of 96Right part: deficiency=100-96=4. 4^2=16Left part: 96-deficiency=96-4=929216

Square of 9992Right part: deficiency=1000-9992=8.8^2=64Left part: 9992-8=9984998464

Cool Trick #5

Proofa is any number100(a-(100-a))+(100-a)^2200a-10000+10000-200a +a^2a^2

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

Indian Multiplication

Step 1: The right hand digits are both multipliedStep 2: Apply inside-outside principle (plus carry)Step 3: The left hand digits are multiplied plus carryExample 56 x 177x6=42 but you only put 27x5 + 6x1=41+4=45 but only put 55 x 1= 5+4=9952