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Fast calculation methods

Fast calculation methods. Addition. Add 137,95 Solution: 137+95= (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)+(100-7)= (500-23)=477. Multiplication. Multiplying by 5. Example: Find the result of 324*5 Solution:

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Fast calculation methods

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  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 + ^2 2809

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

  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 xn mod 7 and x0=1

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

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