గుణకారం చేయకుండానే గుణించండి II సింపుల్ ట్రిక్ II Multiplications II Dr.V N Raju Sir 

It is useful to maths students not others becasuse *it has so many rules (conditions).* *Ex1.* 12 x 13 = 156 (correct) *Ex2.* 22 x 23 = 256 (incorrect) Why? First digit of each number is 2 in ex2. *Condition:* First digit of each number must be 1.

These two numbers (12, 27) near to 20. So *base = 20* *12 x 27* = 12 12-20 27 27-20 = 12 -8 27 +7 = 20(12 + 7) -8x7 = 20(19) - 56 = 380 - 56 *= 324* (OR) *12 x 27* = 12 12-20 27 27-20 = 12 -8 27 +7 = 20(27 - 8) -8x7 = 20(19) - 56 = 380 - 56 *= 324*

*23 x 23* = 2(23+3) 3x3 = 2(26) 9 *= 529* *26 * 26* = 2(26+6) 6x6 = 2(32) 36 = 64 36 = (64+3) 6 *= 676* *23 x 26* = 2(23+6) 3x6 = 2(29) 18 = 58 18 = (58+1) 8 *=598*

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*25 x 24* = 2(25+4) 5x4 = 2(29) 20 = 58 20 = (58+2) 0 *= 600* These two numbers (25, 24) near to 20. So *base = 20* *25 x 24* = 25 25-20 24 24-20 = 25 5 24 4 = 20(25+4) + 5x4 = 20(29) + 20 = 580 + 20 *= 600* (OR) *25 x 24* = 25 25-20 24 24-20 = 25 5 24 4 = 20(24+5) + 5x4 = 20(29) + 20 = 580 + 20 *= 600*