Vedic Mathematics : Vedic Mathematics
Topics : Topics Vedic Mathematics- Brief Introduction Sutras with Examples
Introduction : Introduction Vedic mathematics is the system of Mental Calculation consisting of 16 sutras(ways/formulae's). This sutras can be applied to each and every topics in mathematics (including arithmetic, algebra, geometry, trigonometry, conics, astronomy, calculus etc). It was presented by Hindu scholar and mathematician, Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja. Tirthaji invented this sutras while studying Vedas in the early years of 20th century.
By one more than the previous one (Ekadhikena Purvena) : By one more than the previous one (Ekadhikena Purvena) Used to calculate square of a number ending with 5 . Example 35 2 Step I: square last digit (5 2 = 25 ) Step II: one more than the previous one Add 1 to the previous number(1+3=4) and multiply them 3 * 4 = 12 Step III: Concatenate the above steps as Step II and Step I ( 1225 ) 35 2 = 1225
PowerPoint Presentation : 95 2 10 5 2 (9*10) (5*5) (10*11) (5*5) 90 25 110 25 = 9025 =11025 For Practice: 45 2 75 2 135 2
All from nine and the last from ten (Nikhilam Navataścaramam Daśataḥ) : All from nine and the last from ten ( Nikhilam Navataścaramam Daśataḥ ) When a number is to be subtracted from huge power of 10, Subtract last digit from 10 and rest digits from 9. Examples 10000 -2345 7655 For Practice: # 1000 – 45 # 10,00,00,000- 66 Subtract last digit(5) from 10 a nd rest of digits from 9 10,00,000 10,00,000 - 81 = -0,00,081 9,99,919
Vertically and crosswise (multiplications) Urdhva Tiryaghyam Sutra : Vertically and crosswise (multiplications) U rdhva Tiryaghyam Sutra Multiplication of 2 digits numbers (ax+b)(cx+d) = acx² + x(ad+bc) + bd 42 * 53 Step I: (Vertically) 2 * 3 = 6 Step II: (Crosswise) (4*3) + (5*2)= 22 {Carry forward 2} Step III : (Vertically) 4*5 = 20 Step IV: Add Carry forward (2) with Step III number (20) = 22 20 2 2 6 = 22 2 6 5 6 * 73 35 5 7 1 8 = 35 5 8 8 = 40 8 8 Step I: 6 * 3 = 18 (Carry Forward 1) Step II : (5*3) + (6*7) = 57 (Carry Forward 5) Step III : 5*7= 35 Step IV : Add Carry forwards one by one from right side.
PowerPoint Presentation : Multiplication of 3 digit number ( ax+by+c ) * ( px+qy+r )= x 2 ( ap ) + xy ( aq+bp ) + ( arx + bqy 2 + cpx ) + y( br + cq ) + cr For Practice : # 43 * 97 # 76 * 64 # 542 * 968 # 753 * 746 1 4 5 * 2 6 3 2 1 4 3 7 4 2 1 5 = 2 1 4 3 7 4 3 5 = 2 1 4 4 1 3 5 = 2 1 8 1 3 5 = 3 8 1 3 5 Step I: 5* 3= 15 (Carry Forward 1 ) Step II: (4*3 + 5*6 = 42) (Carry Forward 4 ) Step III: (1*3 + 4*6 + 5*2 = 37) (Carry Forward 3 ) Step IV: (1*6 + 4*2 = 14) (Carry Forward 1 ) Step V: 1*2= 2 Step VI: Add carry forwards 1 by 1 from right side.
Special Multiplications (Used if numbers are closer to Power of 10) : Special Multiplications (Used if numbers are closer to Power of 10) Example (Less than Powers of 10): 7 -3 * 8 -2 5 6 = 56 Step I: 7 is 3 deficient (-3) from nearest 10 power. Step II: 8 is 2 deficient (-2) from nearest 10 power Step III: Multiply deficient's (-3 * -2= 6 ). Step IV: Cross Addition [(7+ (-2) ) OR (8+(-3))] = 5 99 -1 *91 -9 90 09 = 9009 Step I: 99 is 1 deficient (-1) from nearest 10 power(100). Step II: 91 is 9 deficient (-9) from nearest 10 power(100). Step III: Multiply deficient's -1 * -9= 9 =09 (As power 100 used) Step IV: Cross Addition [(99+ (-9) ) OR (91+(- 1 ))] = 90 Step I: 92 is 8 deficient (-8) from nearest 10 power(100). Step II: 75 is 25 deficient (-25) from nearest 10 power(100). Step III: Multiply deficient's -8 * -25= 200 . (Carry Forward 2 as power 100 used) Step IV: Cross Addition [(92+ (-25) ) OR (75+(- 8 ))] = 67 Step V: Add the Carry Forward to Step IV. 92 -8 *75 -25 67 2 0 0 = 6900
PowerPoint Presentation : Examples (More than Powers of 10): 13 +3 * 12 +2 15 6 = 156 Step I: 13 is 3 excessive(+3) than nearest 10 power (10). Step II: 12 is 2 excessive(+2) than nearest 10 power(10). Step III: Multiply excessive(+3 * +2= 6 ). Step IV: Cross Addition [(13+ (+2) ) OR (12+(+3))] = 15 113 +13 * 102 + 2 115 26 = 1 1526 Step I: 113 is 13 excessive(+13) than nearest 10 power (100). Step II: 102 is 2 excessive(+2) than nearest 10 power(100). Step III: Multiply excessive(+13 * +2= 26 ). Step IV: Cross Addition [(113+ (+2) ) OR (102+(+13))] = 115 114 +14 * 108 + 8 122 1 1 2 = 12312 Step I: 114 is 14 excessive(+14) than nearest 10 power (100). Step II: 108 is 8 excessive(+8) than nearest 10 power(100). Step III: Multiply excessive +14 * +8= 112 . (Carry Forward 1 as power 100 is used). Step IV: Cross Addition [(114+ (+8) ) OR (108+(+14))] = 123 Step V: Add the Carry Forward to Step IV.
PowerPoint Presentation : Examples (Mix Numbers): 7 -3 * 12 +2 9 -6 (9-1) (10+-6) 84 Step I: 7 is 3 deficient (-3) from nearest 10 power(10). Step II: 12 is 2 excessive (+2) from nearest 10 power(10). Step III: Multiply deficient's & excessive(-3 * +2= -6 ). Step IV: Cross Addition [(7+ (+2) ) OR (12+(-3))] = 9 Step V: As 10 power used, Add 10 to Step III Step VI: Subtract 1 from Step IV. 97 -3 * 112 +12 109 -36 (109-1) (100+-36) 108 64 Step I: 97 is 3 deficient (-3) from nearest 10 power(100). Step II: 112 is 12 excessive (+12) from nearest 10 power(100). Step III: Multiply deficient's & excessive(-3 * +12= -36 ). Step IV: Cross Addition [(97+ (+12) ) OR (112+(-3))] = 109 Step V: As 100 power used, Add 100 to Step III Step VI: Subtract 1 from Step IV.
PowerPoint Presentation : 88 -12 * 112 +12 100 - 1 44 (100-1-1) (100+-44) 98 56 Step I: 88 is 12 deficient (-12) from nearest 10 power(100). Step II: 112 is 12 excessive (+12) from nearest 10 power(100). Step III: Multiply deficient's & excessive(-12 * +12= -144 ). Carry Forward 1. Step IV: Cross Addition [(88+ (+12) ) OR (112+(-12))] = 100 Step V: As 100 power used, Add 100 to Step III Step VI: Subtract 1 from Step IV, again subtract carry forward(1). (-44).
PowerPoint Presentation : Next part of presentation will have simple ways of calculating Square of a number ( a 2 ) Cube of a number ( a 3 ) Square root of a perfect square ( √a ) Cube root of perfect cube ( 3 √a ) Other special techniques.