1. Fast calculation methods

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

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

4. Multiplication

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

6. Multiplying by 11  Example: Find the result of 35*11 Solution 35 11 * 385 +

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

8. Other multiplication methods  Find the result of: 57*53 Solution 53 * 57 * 1 + * 3021

9. Squaring  Square the number: 53 Solution 53 ^2 2809 + ^2

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

11. Division

12. Division by 5  Find the result of: 147/5 Solution 147/5= 147/(10/2)= (147*2)/10= 294/10= 29.4

13. Average of 3 numbers  Find the average of: 89,91,95 Solution: (89+91+95)/3= (89+91+93+2)/3 (89+91+93)/3+2/3= 91.66

14. 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

15. 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

16. 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 x n mod 7 and x 0 =1

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