vedic mathematics sutra
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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 - PowerPoint PPT PresentationTRANSCRIPT
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 10,100,1000
• 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