Vedic Mathematics Session 4

Vedic Mathematics – session 4 : Vedic Mathematics – session 4 By Malay Slide No. 1 TeachOrissa Redefining Education

What will we learn today? : What will we learn today? General rule to simplify multiplication (Urdha-tiryak) Duplex of a number General rule to find square of a number (using Urdha-tiryak) Slide No. 2 TeachOrissa Redefining Education

General rule to simplify multiplication (Urdha-tiryak) : General rule to simplify multiplication (Urdha-tiryak) ax2+bx+c dx2+ex+f ------------- adx4+(ae+bd)x3+(cd+af)x2+(fb+ec)x+cf Slide No. 3 TeachOrissa Redefining Education

Example : Example x3 x2 x 5 8 2 2 3 1 ------------- 10 13 42 3 31 ------------- 13 44 42 Slide No. 4 TeachOrissa Redefining Education

Duplex of a number : Duplex of a number Before seeing the actual process we need to get acquainted with some mental calculation. Lets get introduced to a new term called duplex denoted by D. D = x^2 if the number(x) has one digit     = 2xy if the number (xy) has two digits = 2xz+y^2 if the number (xyz) has three digits and so on. Example: case1: Consider a number 5          Duplex i.e. D for 5 = 5^2=25 Case2: Consider a number 83            Duplex i.e. D for 83 = 2*8*3=48 Case3: Consider a number 482             Duplex i.e. D for 482 = 2*4*2 + 8^2 = 80 Slide No. 5 TeachOrissa Redefining Education

Example contd.. : Example contd.. Case4: Now you tell me the Duplex i.e. D for 4321 Ans: D = 2*4*1 + 2*2*3 = 20 Case5: Now you tell me the Duplex i.e. D for 54368 Ans: D = 2*5*8 + 2*4*6 + 3^2 = 137 Slide No. 6 TeachOrissa Redefining Education

General rule to find square of a number : General rule to find square of a number Ans: First find the D for all possible combination of the digits on the number 432 as we have done in Urdha-Tiryak and add them. That’s all. You got the answer. Demonstration: 432 Taking 1 digit i.e. 4, D = 16 Taking 2 digits i.e. 43, D = 2*4*3 = 24 Taking 3 digits i.e. 432, D = 2*4*2 + 3^2 = 25 Taking 2 digits i.e. 32, D = 2*3*2 = 12 Taking 1 digit i.e. 2, D = 4 Write the above duplex in the following fashion: 164524 221 ---------- 186624 Slide No. 7 TeachOrissa Redefining Education

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