calculate quickly! created by inna shapiro ©2008
TRANSCRIPT
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Calculate Quickly!
Created by Inna Shapiro ©2008
![Page 2: Calculate Quickly! Created by Inna Shapiro ©2008](https://reader036.vdocuments.us/reader036/viewer/2022070305/55148885550346b0158b5bbb/html5/thumbnails/2.jpg)
Rules
Without using your calculator or any other device (your parents included), calculate:
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Problem 1
(257,368+2573)+(42632-573)
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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=
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Problem 2
354*73+23*25+354*27+77*25
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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=
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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
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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
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Problem 4
Calculate:1-3+5-7+…+93-95+97-99
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Answer
1-3+5-7+…+93-95+97-99==(1-3)+(5-7)+…(93-95)+(97-
99)==(-2)*25=-50
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Problem 5
Calculate:(74 * 147 – 73)/(73 * 147 + 74)
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Answer
(74 * 147 – 73)/(73 * 147 + 74) =
(73 * 147 + 147 – 73)/(73 * 147 + 74) =
(73 * 147 + 74)/(73 * 147 + 74) = 1
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Problem 6
Calculate:(244 * 395 – 151)/(244 + 395 * 243)
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Answer
(244 * 395 – 151)/(244 + 395 * 243)=
(243 * 395 + 395 – 151)/(244 + 395 * 243)=
(243 * 395 + 244)/(244 + 395 * 243) = 1
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Problem 7
Calculate:423,134 * 846,267 – 423,133423,133 * 846,267 + 423,134
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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
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Problem 8
Without calculating the numerical values, show, which of the two fractions is greater than the other one:
23/37 or 115/187 ?
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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
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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.
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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)
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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)
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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