Calculate Quickly! Created by Inna Shapiro ©2008

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

Problem 1 (257, )+( )

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

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

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

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

Answer 26*25-25*24+24*23-23*22+22*21- 21* *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

Problem 4 Calculate: …

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

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

Answer (74 * 147 – 73)/(73 * ) = (73 * – 73)/(73 * ) = (73 * )/(73 * ) = 1

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

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

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

Answer 423,134 * 846,267 – 423,133 = 423,133 * 846, , ,133 * 846, ,267 – 423,133 = 423,133 * 846, , ,133 * 846, ,134 = 423,133 * 846, ,134 = 1

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

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

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.

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)

Problem 10 Simplify to an irreducible fraction without calculating the exact numerical value: ( )/( )

Answer ( )/( )= ( )/( )= ( )/( )= (9*4)/(23*4)=9/23