Vedic Mathematics Sutra Sid Mehta Hey Sid how

Vedic Mathematics Sutra Sid Mehta

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

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, 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)=[3 x(3+1)]25=1225 Example: Square of 105 (105)=[10 x(10+1)]25=11025

Cool Trick #1 • Proof (a 5) where a is some positive integer (10 a+5)=100 a^2+100 a+25 =100 a(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 3 8 2 3 x 2=6(right part) 8 -3 or 7 -2=5(left part) 56

Cool Trick #2 Example 98 x 76 98 2 76 24 2 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 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

Multiplication by 9, 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

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

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)

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

Cool Trick #4 Proof a and b are both numbers (ab)(a 10 -b) or (10 a+b)(10 a+10 -b) 100 a^2+100 a-10 ab +10 b-b^2 100 a(a+1)+10 b-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 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=998464

Cool Trick #5 Proof a is any number 100(a-(100 -a))+(100 -a)^2 200 a-10000+10000 -200 a +a^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 multiplied Step 2: Apply inside-outside principle (plus carry) Step 3: The left hand digits are multiplied plus carry Example 56 x 17 7 x 6=42 but you only put 2 7 x 5 + 6 x 1=41+4=45 but only put 5 5 x 1= 5+4=9 952