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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 S anskrit) Ancient scholars used these Sutras(formulas) to make mathematical calculations

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vedic mathematics sutra1
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.
terminology
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
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
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 11
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
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
Cool Trick #2

Example 7 x 8

7 3

  • 2

3 x2=6(right part)

8-3 or 7-2=5(left part)

56

cool trick 21
Cool Trick #2

Example 98 x 76

  • 2
  • 24

2 x 24=48(Right part)

76-2 or 98-24=76(Left Part)

7648

cool trick 22
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

  • -7
  • 4

Right part= 100+(-28)=72

Left Part= (107-4 or 96+7)-1=102

10272

multiplication by 9 99 999 cool trick 3
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 * 99Left part: 66

Right part:33

6633

cool trick 3
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
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
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 41
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

square of any number cool trick 5
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
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

cool trick 51
Cool Trick #5

Proof

a is any number

100(a-(100-a))+(100-a)^2

200a-10000+10000-200a +a^2

a^2

paravartya yojayet
ParavartyaYojayet
  • 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
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