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Vedic Mathematics Sutra

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 Sutra

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  1. Vedic Mathematics Sutra Sid Mehta

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

  3. 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.

  4. The Sutras

  5. 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

  6. 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

  7. 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

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

  9. 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

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

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

  12. 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

  13. 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

  14. 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

  15. 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)

  16. 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

  17. 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

  18. 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)

  19. 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

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

  21. 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

  22. 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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