lesson 6 - part 2: rational numbers
TRANSCRIPT
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DONOW!
Whatisara-onalnumber?Explain,usingexamples.
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Lesson6Part2:
WhatareRa-onalNumbers?
Standard:7.N.1
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ComparingandOrdering
Thereareacoupleofdifferentways:
1.Convertallvaluestodecimals.
2.Convertallvaluestofrac-onswiththesamedenominator.
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Convertthesetodecimals:
1/4,0.9,1/5,1.5,0.6
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FindtheLeastCommonDenominatorto
compare:1/5,3/8,2/9
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UsingtheLeastCommonDenominatorto
CompareRa-onalNumbersThe least common denominator of two or more frac-ons is the LCM of thedenominators.Howcanweusethistocomparefrac-ons?
Youmayonlycomparefrac-ons,bylookingatthenumerator,whenthedenominatorsarethesamevalue.
EXAMPLE:Compare2/3,4/7,and5/11.First,findtheLCMofthedenominators(3,7,and11).
The LCM of 3, 7, and 11 is 231. We now have to find equivalent frac-ons with adenominatorof231.
We can do this by crossmul-plying: 2/3 = X/231, where X is the value of theequivalentfrac-onsdenominator.
(2231)/3=X462/3=154
Therefore,2/3=154/231.
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Usingthesamemethod
IftheLCDis231,whichmeanstheequivalentfrac-onmusthave
adenominatorof231,whataretheequivalentfrac-onsof 4/7
and5/11?
4/7=132/231
WHY?Because4/7=X/231(4231)/7=X924/7=X=132
5/11=105/231
Nowwecaneasilycompare154/231,132/231,and105/231.
154/231 > 132/231 > 105/231 which means, from least to
greatest,theoriginalfrac-onsare5/11,4/7,2/3.
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PRACTICE
Orderthesera-onalnumbersfromleasttogreatest,whilealso
findingtheequivalentdecimalorfrac-onforeachnumber:
1. ,0.375,3/5,3.5,0.72. 0.2,2/8,11/20,2/3,0.333,1.13. 3/8,0.13,27/50,0.8,0.1234. 7/8,0.932,4/5,18/20,6/75. 0.15,1/5,0.23,1.5,15/20,3/2,2/7
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PRACTICESOLUTIONS!1. ,0.375,3/5,3.5,0.7
=0.75
375/1000=3/8=0.375
HOW?!REMEMBER:Always trytosimplifyfrac-ons!
ThisisdonebyfindingtheGCFofthedenominatorandthenumerator
anddividingbothbythatnumber.TheGCFof375and1000is125.375
125=3and1000125=8.Therefore,375/1000=3/8.
3/5=0.6
3.5=3
0.7=7/10
Therefore,fromleasttogreatest,theorderis 0.375,0.6,0.7,0.75,3.5,
whichisthesameas0.375,3/5,0.7,,3.5.
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PRACTICESOLUTIONS!2. 0.2,2/8,11/20,2/3,0.333,1.1
0.2=2/10=1/5
2/8==0.25
11/20=1.05
2/3=0.666
0.333=1/3
1.1=11/10
Therefore,fromleasttogreatest,theorderis0.2,0.25,0.333,0.666,
1.05,1.1,whichisthesameas0.2,2/8,0.333,2/3,11/20,1.1.
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PRACTICESOLUTIONS!4. 7/8,0.932,4/5,18/20,6/7
7/8=0.875
0.932=932/1000=233/250
4/5=0.8
18/20=9/10=0.9
6/7=0.85714286
Therefore, from least to greatest, the order is 0.8, 0.85714286, 0.875,
0.9,0.932,whichisthesameas4/5,6/7,7/8,18/20,0.932.
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PRACTICESOLUTIONS!5. 0.15,1/5,0.23,1.5,15/20,3/2,2/7
0.15=15/100=3/20
1/5=0.2
0.23=23/100
1.5=15/10=1
15/20==0.75
3/2=1=1.5
2/7=0.28571429
Therefore, from least to greatest, the order is 0.15, 0.2, 0.23,
0.28571429, 0.75, 1.5 = 1.5, which is the same as 0.15, 1/5, 0.23, 2/7,
15/20,3/2=1.5.
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3/7,3/20,1/6
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2/8,3/5,4/9,5/12
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3/8,2/13,4/16,4/7,5/9
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LEARNINGLOG7.N.1
0.5,3/8,5/12,4/7,4/9
Carla believes that the only way of placing the
abovenumbersinorder,fromleasttogreatest,
isbyfindingthedecimal.Isshecorrect?Explain.
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LEARNINGLOG7.N.1
Billiebelievesthat0.2,1/8,3/12,16/20,and0.8
are in order from least to greatest. Is she
correct?Explain.
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HOMEWORK
Explainwhyeachofthesenumbersmaybeconsideredra-onal.
1.3 2.12/25 3.0.6 4.8.2216 5.0.3215
LEARNINGLOG
Charliebelievesthatanydecimalnumbermustalsobeara-onal
number.Ishecorrect?Explain!