Fast calculation methods

Addition Add 137,95Solution:137+95=

(137-5)+100=132+100=232

addition Add 97+95+98+94+93Solution97+95+98+94+93=(100-3)+(100-5)+(100-2)+(100-6)+(100-7)= (500-23)=477

Multiplication

Multiplying by 5 Example:Find the result of 324*5Solution:324*5=

324*(10/2)= (324/2)*10 =1620

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

35

11*

385

+

Other multiplication methods Find the result of: 49*51Solution49*51=(50-1)*(50+1)=(50^2)-(1^2)=2500-1=2499

Other multiplication methods Find the result of: 57*53Solution

53

*

57*

1+*

3021

Squaring Square the number: 53Solution

53

^2

2809

+ ^2

Squaring Square the number: 46Solution

46

5^2

2116

- ^2

10-6

Division

Division by 5 Find the result of: 147/5Solution147/5=147/(10/2)=(147*2)/10=294/10=29.4

Average of 3 numbers Find the average of: 89,91,95Solution:(89+91+95)/3=

(89+91+93+2)/3

(89+91+93)/3+2/3=

91.66

Division by 7 1/7=0.142857 2/7=0.285714 3/7=0.428571 4/7=0.571428 5/7=0.714285 6/7=0.857142

Division by 7(continued) From the previous slide: Each fraction has the same floating point

numbers with the same sequence but with different fraction beginning.

The next slide arranges the fraction

Arranging fraction 1/7=0.142857 3/7=0.428571 2/7=0.285714 6/7=0.857142 4/7=0.571428 5/7=0.714285 The numerator {1,3,2,6,4,5} is the same

with the sequence generated from the modular equation 3 xn mod 7 and x0=1

Example Find the result of 102/7Solution:102/7=(98+4)/7=14+(4/7)=14.5671428