Fast calculation methods Addition Add 137 95 Solution

Fast calculation methods

Addition Add 137, 95 Solution: 137+95= p (137 -5)+100= 132+100= 232

addition Add 97+95+98+94+93 Solution 97+95+98+94+93= (100 -3)+(100 -5)+(100 -2)+(100 -6)+(1007)= (500 -23)=477 p

Multiplication

Multiplying by 5 Example: Find the result of 324*5 Solution: 324*5= p 324*(10/2)= (324/2)*10 =1620

Multiplying by 11 Example: Find the result of 35*11 Solution p 35 * 11 385 +

Other multiplication methods Find the result of: 49*51 Solution 49*51= (50 -1)*(50+1)= (50^2)-(1^2)= 2500 -1= 2499 p

Other multiplication methods Find the result of: 57*53 Solution p 53 * * + 57 1 3021 *

Squaring Square the number: 53 Solution p 53 ^2 + ^2 2809

Squaring Square the number: 46 Solution p 46 10 -6 5^2 - ^2 2116

Division

Division by 5 Find the result of: 147/5 Solution 147/5= 147/(10/2)= (147*2)/10= 294/10= 29. 4 p

Average of 3 numbers Find the average of: 89, 91, 95 Solution: (89+91+95)/3= p (89+91+93+2)/3 (89+91+93)/3+2/3= 91. 66

Division by 7 1/7=0. 142857 p 2/7=0. 285714 p 3/7=0. 428571 p 4/7=0. 571428 p 5/7=0. 714285 p 6/7=0. 857142 p

Division by 7(continued) From the previous slide: p Each fraction has the same floating point numbers with the same sequence but with different fraction beginning. p The next slide arranges the fraction p

Arranging fraction 1/7=0. 142857 p 3/7=0. 428571 p 2/7=0. 285714 p 6/7=0. 857142 p 4/7=0. 571428 p 5/7=0. 714285 p The numerator {1, 3, 2, 6, 4, 5} is the same with the sequence generated from the modular equation 3 xn mod 7 and x 0=1 p

Example Find the result of 102/7 Solution: 102/7= (98+4)/7= 14+(4/7)= 14. 5671428 p