Lesson 6 - Part 2: Rational Numbers

8/8/2019 Lesson 6 - Part 2: Rational Numbers

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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!

Lesson 6 - Part 2: Rational Numbers

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