Calculate Quickly Created by Inna Shapiro 2008 Rules

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

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

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

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

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

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

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=240

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

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

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

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

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

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

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

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

$Problem 8 Without calculating the numerical values, show, which of the two fractions is$

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

$Answer To compare 23/37 and 115/187 let us overwrite the first fraction 23/37=(23*5)/(37*5)=115/185 We$

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)

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

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)

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