Calculate Quickly!

Created by Inna Shapiro ©2008

Rules

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

Problem 1

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

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=

Problem 2

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

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=

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+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 + 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 + 395 – 151)/(244 + 395 * 243)=

(243 * 395 + 244)/(244 + 395 * 243) = 1

Problem 7

Calculate:423,134 * 846,267 – 423,133423,133 * 846,267 + 423,134

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

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 115/187let us overwrite the first fraction

23/37=(23*5)/(37*5)=115/185We 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 < 5/61/2 = 4/8 < 7/84/5 = 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)

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