=.~~:=~=~ The i
you use 10 find Jerry'l number? i , ,
i ,,
i ,,
j
""5~SI !
...ã..ã..ã_ã_ã_ãã_ã_ã_ã_ã_ã..ã..ã....ã.._ã_ã_ã_ã_ã--ã--1
i, , , i
HandsOn
Relate Fractions, Mixed Numbers, and Decimals
Objective CIlarlQlI <ằcime1S10 lraetior1s 8r'ldrni.&dnurnt>8<S.
andCIWlge rni.&dnumbefsand fractiOns to <lacimaIs,
Work Together
A sUJVey found that 0.2 of the visitors to an art museum stopped at the gift store. A survey five years later finds that ~ of the museum's visitors go to the gift store. Did the two surveys produce the same result?
Work with a partner 10 decide w!lether 0.2 and'}
represent the same number.
"'aterlals
t,3CIion strips
Way 0 Write the decimal as a fracllon in simplest form,
Locate the 'ractions on a number line.
@
" I
, ,
0.2 -10 - '5"
o(i)CDtt
• Are the resu~s the same?
Locate the decimals on a number line.
Waye Write fhe fraction as a decimal. 5"-10, .
•
10" 0.4
"
"
, CD ,
,
• Are the resu~s the same?
246
Now deeIde whether 1.25 and 1i represent the same number.
.'" o
Write the doclmal as a mixed number In sjmplest form.
Write the mixed number as a docimaL
~ ,
1,25-'loo- 1i 1,25- It
. "
1i- 1 '00
,f&-. 1.25
1i -• 1.25
On Your Own
Write eaeh ~Imal as s fraetlon or mixed number in simplest form.
1. 0.8 2. 0.13 3. 0.75 4. 3.6 8. 4.5 s. 7.25
Write each fraction or mixed number as a decimal.
,
7. '5 ,
II. 2S
10. 2 10,
Use Ihe number line 10 complete Exerelses 13-16.
,
A 0.5
,
t B C
, • I
•
, , G
, .
., , ,
13. Write the decimal represented by point A 18. Write the Iraction and the decimal
represented bypoint 0.
14. Write the fraction represented by point C le. Which point represents 1.375? Explain
your answer.
17. What's Wrong? Each nat represents one whole Mamie says lhe shaded par1s of Ihe lIals show that 2,3 - 2 19.,.
Do you agree? Explain your reasoning.
18. When you write a decimal in the form of an equivalent fraction.
why is il important 10 use a denominator that is a power of 10?
HI. How do you know what power of 10 to use as a denominator.
when writing a docimal as anequivalent fraction?
Chapter 9 Lesson 6 247
Compare and Order
Fractions and Decimals
Objective Compareandorder ffaCllonS andd9dmals,
Vocabulary
common denominator
Learn About It
Jeff made a clay animal that isi fool tall. Andrea made a clay animal that isi foot tall. Who made the taller animal?
Two fractions with the same. or like. denominators are said to have a common denominator. Yoo can compare them by comparing the numerators.
5> 3. so i >~. Andrea made the taller animal.
Fractions with different, or unlike. denominators can also becompared.
Compare: and 1.
Different Ways to compare: and:
WayO You can lind equivalent fraellona with a common denominator.
","l"f... Find the lCMofthe '!oTt... Use the common ",111" To compare the
0 denominators ofthe 0 <Uloominatorto fOnd 0 fraC1ioos, compare
fradioos. 8I1uivalenltractions. the r1IJmerators.
Multiples 016: 6, 12. 18.24,30.n. ,e, ,.@--.. Sioce 20;> 15.
~ "
Multiples 018: 8, 16. 24, 32. ,n • • • ,.~ • • • ,. " ';ji;> 20"
'0Y "@Y • •
The LCM of 6 and 8 Os ~4.50. use 5oãe->e>
~4 as the common derlOl11inator.
WayO You can think about Waye You can relate fractions
distance on II number line. to benchmarks.
When the numerators lire the same. the ~is close 10 1 on the oomber Wne, (mellonw~h1he greale' denom;na.lor is
less thanlhe o1her tmelior!. i Oscloser toi lhan ~ Osto'.
~>i
1>i,so~>~. .
Solution: ~ > ~
248
... You can use what you know about comparing fractions to order fractions and decimals.
• Order the fractions.
* < ~ < -¥i. SO the orderfromleaSl to , , . 3 7 3
grea es OS 's' 10'.'
To order lraetlon•.yoo can lind equlvalenl traction •. then compare.
" ,
Order5'"i' and 10from leasl to orealest.
• Use Ihe LCM otthe denominators 10 lind a corrvnon denominalor.
• Find equivalent fractions w~h that common denominal0r,
I
• Order lhe numbers.
1.5>1.45>1,42,
•
801,5>1 20 >1.42.
Theordertrom l/reatest to Ieasl is 1.5.
•
120 .1.42.
To order Ireellonl and decimal •. write them In the ...me lorm.
Order 1.5. 1&>.and 1.42fromgreatesl to least.
• Wr~e!hemi><e<l number as adecimal.
1&>-1+-&;
- 1 +-&
_ 1.45
".@-;
, "
- " . -~
'@/
Work wilh 8 partner.
Complete the ItepI to order declmall and Iraellonl.
. o '"
Write !he1olIowi"ll numbers on a sneet. ,
otpaper: 0.6. I' and 3'
• Guess the orderot the values, from leaSI to grealest.
• Discuss your!/V8SSw~h j'OOr partne,.
Use fraction st,ips to st>ow each01 the th,ee numbers. Line up !he lraction strips SO that lheya~ll" on oneend,
• Order the numbersfromleast 10 greatest
• ts Theorde'the same as)'OUr guesses?
Useequivalent fractions to cI\eckyoura~r.
, , ,
, , ,
1 1 1 1 1 ' 1 " 1 11
I I I I I I I 1
Chapter 9 Lesson 9 249
Compare. Write >, <, or '" for each • • Guided Practice
'. '
1'"9 "9
4.3fã3i ,
5.0.25_ 5
3'"3-12 , ,
6.'"2. , ,5,
• DiOIfinO a common
(IenorrinalOr1
• DiOI writeltwJnul'l'lbars
In "'" sa"", 101m 10 compare !hem?
Explain Your Thinking" How can you compare ~ and 1~
without using a common denominator?
Practice and Problem Solving Compare. Write >,<, or '" lor each _.
3 , 9 , , 3 3 ,
,. 8 - 12 8'10-6 •• 315 - 35 ". 210 - 2"3
, 3 , ,
". 8 - 0.6 12. 0.75 - 4 ". 1.4 _ '"5 ". 4 8 .4,2
Order each 6el of numbef1l Irom least to greatest.
1 7 7 5 17 4
15. 24' 12' '8 16. 2 20.2.75.25.0.9 17. 20' ''8' 15. 0.57 1 11
X Algebra. Equations and Inequalities For each expression, write a whole number lor nthat will make the expression true.
n n 5 n t n
16. 4=0.25 19.0.3=10 20. '8<7 21. "2>10
Solve.
". Some students made clay s<:ulptures.
Juan used~ pound of clay. Arleta used
i pound 01 clay. Maureen used ~
pound of clay. Who used the most clay"
W110 used the least clay"
24. The table at the right shows prices01 train tickets from Eastport to Central City. Durittgtwo weeks. Ma~ makes
8 round trips between the towns. He spends $71. Does he make the same number of trips each week? Explain.
2$. You Decide During the month 01 January.you make the round trip between Eastport and Central City 3 times per week. W11at tickets would you buy? Explain your thinking,
". Penny CUtS three len~thS of ribbons. The
ribbons are 1~ ft ,12 ft and 1.5 It
Show all three of these lengths on a number line. ThOll list the lengths from shortest to longest.
Type of Ticket
""~
Single Trip ... "
Round Trip $t 1.00 lQ-Trip Pass $55.00
WEIeldy Pass "'.00
Month~ Peas~.oo
250 ExtraProctieeSeepage253,SetF.
Mixed Review and Test Prep Open Response
Simplify each of the lollowlng.(Ch.~.lMtOr>61
2:6. 23+(7+4)x5 21. 35 - 3 x (21 - 12) 28. (4X6}+8+4
30, (3 - 1)2 x 9
31, (4 + 6}2 - 82+ 2
32. To make paste, Janlla uses
~ pound of Oour. She also uses 172 pound of salt. Does she use more salt or more flour to make paste? EJ<pla;n.(Ch.9.~9)
Social Studies Connection Mangled Money
Each day the United States Bureau of Engravillg and Printing produces thirty-seven million pieces of paper money. This money has a face value of approximately si. hundred ninety-six million dollars.
If a piece of paper money is tom apart and more than half 01 it remains, the U.S. Treasury Department will issue a check for the face value of the bill. The U.S.
Treasury halldles about thirty thousand cla;ms every year for lorn or mutilated currency, worth O\fer thirty mIllion dollars.
I. Write the four numbers shown atxwe in bold print in standard form,
Write yesor no to Indicate illhe U,S. Treasury would Issue a cheek for that part 01 the dollar bill.
2 3 5 5
2'3 3'8 4'12 !I,TO
Chapter 9 Lesson 9 251
~ Chapter ReviewlTest
VOCABULARY
,. A _ _ is a number greater Ihafl 1 wilh aaetIytwo different factors-itself and 1.
• A _ _ is thegrealeSlwhole oombefthaIis a common
factorof two or more numbers.
3. A Yot1oleI1UTltDIlliIthas moreIhan two faaorsis caIeda~
Vocabulary -~ '" 11,1_",_,
_IGCF'j
. . . COIIIIOMIn
... l\.C..j
-- -~
(ONeEnS AND SKIUS
Write the prime lKtoriution 01 e.m IKlmbef. Use uponenls
" po. .lble.Ifthe number Is prime, write primIr. a.-1-2,pp.224-221}
•. 7 .12 s. 19 7. '" .16 •. 30
Findttle GCF 01 the numbers. ...,..3. PI'-22&-23Q
10. 36,81 11. 18.45 12. 35, n 13. 24. 96
Find ttle LCM olltle number•• _ _ .,PI>-232-23!Il
14. 6.18 15. 20.48 I'. 15.55 17. 12.32
Simplify II possible. Then write each as a declll'\lli.
a.-'Ifu.PI'23&-2'1,l.-cw>&.pp.2"ll-Z_71
" , • " "
18. 3iJ 18. "2 ~.,. 21. 20 22• •
, 7
" 2$.11 21. 1!
23. 10 2... 5 25. 2T06 . " ,
Compare. Wrila>,<. or '" lor eKh • .
... 8.pp. ...2$lj
2L f. i 28. 1 2 . 1~ )(I, ,*.0.12 31. 1~. 0.15 :st. 325. I
PROBLEM SOLVING Sotft...7,pp.2Q-2.t51
33. The lCM oftwo numbers is 200.The GCf is 10.The sumof the numbersis 90. \NhlI1 are the numbers?
252 Chapler 9 Chapter Reviewfresl
Show You Understand Howdoes knowing thatJ < i help
L _ _ . . . _ 7 8 .. "'.._~ . you N...,.. ",..Ii < 9 ..00 ...USKOg
a common denomlnalOr?
Extra Practice
Set A(1Mpl2.w.22'6-227)
Write the prime factorization 01 eaeh number. Use exponents it possible.If the number is prime, write prime.
1.23 2. 41 3.48 •. 50 $. 51
Set B ~3.W,226-231l
Find the greatest common factor ollhe number$.
1. 16,36 6.24.56
2. 27. 54 7. 12.48
3. 48,72 8.39.51
4. 56, 120 9. 15.60
5.99.121 10. 36.54
Set C ll.-="4.w_232-23011
Find the least cOmmon multiple 01 thenumbers.
1.7, 42 8.9.45
2.16.36 7.6.20
3.13.52 s. 20, 30
4.8.28 9. 7,9
$. 12.32 10. 12,40
• Jl . ,
'0
•. ' , Set 0 (I..-..5.pp.236-23Ill
Write each improper fracllon as a mixed number or a whole number. Write each mixed number as an Improper Iracllon.
11 16 12
" 3 2,S 3'6
, , ,
0.5'7 7.7 3 8.3"8
Set E (\.-.:<l5.w,2~~I) Simplify each fraction.
" "
1. :)6 2. 54 ,
,. " 4.~
Set F ~9.pp,248-:/51)
Compare. Write>. <,or '" for each • .
"14-28 , ,
5, '5.0.08,
, ,
2.2"6- 212 6. '4.0.25,
3.52.5 25 ,
" ,
1'12ã12
"
4. '.8.'25 ,
8.'.75.'4"
Chapter 9 ExIra Practice 253
Use Data
5pôr<l '"5~
(... 1""""""',)
e l t l O 1 1 1 2
~Iorleeaumed (per minute) In'UI'IIISbti",
In-line skating is a good way to
keep lit. For a 120-pound
skater, how CSOOs Ihe numoer of calories burned change as he or she goos faster? How does the weight 01 the skater affect calories burned?
Estimate With Fractions
Objective EsfimalG fraetioo sumsanddiIkIrence$.
Learn About It
Dan is 53-k inches tall. His older brother is
72t ;m:t1es tall. About how many more inches would Dan need 10 grow to match his brother's height?
Estimate the differencenf - 531ã
You can use front-end estimation.
","fl!.<> Identify Ihe greatest place
o in each number.
nj ,
- 538
Subtract. Wrrte zeros in the other whole-number places.
72 1 70
-53* c=:> -~
Solution: Dan would need to grow about 20 inches to match his brother's height.
You can also use rounding to estimate with fractions.
, , ,
Estimate Ihe sum i +12+ i'
,
6' 12'
You can round fractions to 0,k. or 1 In order to estimate.
"U.., Decide rteach traction is closeSl1O .'b Round up or down. Then add
0 0,';. or 1. A number line can help 0 the rounded numbers.
you decide. '6+12+i ' , ,
• _ _ 100,,---, ,\ .. _101 n tã_101 I I I
" , + 0'" 11
I , , , , , , , , , , , I .. ,
o ' , • , , ' , • , I !!. 1
" i it • " 'l2 , " " ... mearl$"ls~
apprm:...le/jI Solution: The sum of 5 ,
and 1 is about 11 .
~to.-
256
Guided Practice
Estimate the sum or differenCe. Name the method you used to estimate.
, , 151 + 12.?
" 8-"8 , , ,. . ,
22 t9
0 - 1a~
,. "8 + 12 ••
M\l. YOurself
• IS!helraction cIosoe tOO,i.orl?
• can IuseI""'l-end esbma1lon?
Explain Your Thinking Ill- Explain how you could use rounding to find the difference in Exercise 4 above.
Practice and Problem Solving
Estimate the sum or difference.
Name the method you used to estimate,
1 7 :) 2
!I'4"+lO 6'5+"3
, , , ,
•• "8 - 12 10ã e -1O
• , 14,~-~
". 5-6"
t6~ - ~ ,
n. ". 58 - 46"3
, , 4 1 :) 1
,. 16"8 + 12 12 8'5+"8+4"+"2
9i - 3f ' ,
n. 12. 19""12 + 14"2
... 372 , + 261 , 16, a7! - 24!
...
SOlve.
20, Show why this statement is true:
1i - f .. O. Use a number liJle or draw a picture to explain your reasoning.
Melba is 60f inches tall. When she puts on her new shoes, she grows
3~inches. About how tall is Melba in her new shoes?
22, 3 hours - • seconds
c 3 inches o 5 inches B 2 inches
A 1 inch
Multiple Choice I
26. last year RObin was 50i i~~~~~" I
tall, Now Robin is 54~ inches tall, Which is the best estimate of the change in height? tc/I.10.1.-on 11
-
Mixed Review and Test Prep
23, 300 minutes - • hours
I 24. 1 day = • minutes
ears~.days
rOpen Response Complete. Pa<Io.1
Chapter 10 Lesson I 257
Add With Like Denominators
Obi&ctiv8 Add ffacllons and m1lôld
...tIe,s "'lh li1<9<l9nomlnators,
Learn About It
Deliachooses foods Ihat ""';11 help keep her body healthy. AI the right is her recipe for trail mix.
How much fruit is in the trail mix?
Add. i+l=n