2. Calculate Quickly! Created by Inna Shapiro ©2008

3. Rules Without using your calculator or any other device (your parents included), calculate:

4. Problem 1 (257,368+2573)+(42632-573)

5. Answer =(257,368+42,632)+(2,573 –573)= =300,000+2,000=302,000 (257,368+2,573)+(42,632-573)= =257,368+2,573+42,632-573=

6. Problem 2 354*73+23*25+354*27+77*25

7. Answer 354*73+ 354*27+23*25+77*25= 354*(73+27)+25*(23+77)= 354*100+25*100= 35,400+2,500= 37,900 354*73+23*25+354*27+77*25=

8. Problem 3 Calculate: 26*25-25*24+24*23-23*22+ +22*21-21*20+20*19-19*18+ +18*17-17*16+16*15-15*14

9. Answer 26*25-25*24+24*23-23*22+22*21- 21*20+ +20*19-19*18+18*17-17*16+16*15-15*14= =25*(26-24)+23*(24-22)+21*(22-20)+ +19*(20-18)+17*(18-16)+15*(16-14)= =25*2+23*2+21*2+19*2+17*2+15*2= =(25+15)*2+(23+17)*2+(21+19)*2= =40*2+40*2+40*2=240

10. Problem 4 Calculate: 1-3+5-7+…+93-95+97-99

11. Answer 1-3+5-7+…+93-95+97-99= =(1-3)+(5-7)+…(93-95)+(97-99)= =(-2)*25=-50

12. Problem 5 Calculate: (74 * 147 – 73)/(73 * 147 + 74)

13. Answer (74 * 147 – 73)/(73 * 147 + 74) = (73 * 147 + – 73)/(73 * 147 + 74) = (73 * 147 + 74)/(73 * 147 + 74) = 1

14. Problem 6 Calculate: (244 * 395 – 151)/(244 + 395 * 243)

15. Answer (244 * 395 – 151)/(244 + 395 * 243)= (243 * 395 + – 151)/(244 + 395 * 243)= (243 * 395 + 244)/(244 + 395 * 243) = 1

16. Problem 7 Calculate: 423,134 * 846,267 – 423,133 423,133 * 846,267 + 423,134

17. Answer 423,134 * 846,267 – 423,133 = 423,133 * 846,267 + 423,134 423,133 * 846,267 + 846,267 – 423,133 = 423,133 * 846,267 + 423,134 423,133 * 846,267 + 432,134 = 423,133 * 846,267 + 423,134 = 1

18. Problem 8 Without calculating the numerical values, show, which of the two fractions is greater than the other one: 23/37 or 115/187 ?

19. Answer To compare 23/37 and 115/187 let us overwrite the first fraction 23/37=(23*5)/(37*5)=115/185 We can easily compare now 115/185 > 115/187 => 23/37 > 115/187

20. Problem 9 Compare the two expressions: 1/2 + 2/3 + 4/5 and 5/6 +7/8 + 8/9. Do so without adding the fractions or calculating the numerical values by hand.

21. Answer 2/3 = 4/6 < 5/6 1/2 = 4/8 < 7/8 4/5 = 8/10 < 8/9 => (1/2 + 2/3 + 4/5) < (5/6 +7/8 + 8/9)

22. Problem 10 Simplify to an irreducible fraction without calculating the exact numerical value: (1+2+3+4+5+6+7+8)/(8+9+10+11+12+13+14+15)

23. Answer (1+2+3+4+5+6+7+8)/(8+9+10+11+12+13+14+15)= (1+8+2+7+3+6+4+5)/(8+15+9+14+10+13+11+12)= (9+9+9+9)/(23+23+23+23)= (9*4)/(23*4)=9/23