snowdomes for $50. If only 8 can ship ....
boa.how many boxeswill he... "yo?
Solve. ..-1,llll- IIlHOlI
25. Toni liasI coIeclion of 2' angel fljJUrines.
She has 5 limes the m~berofaystal angels as hand-painted ones. How many 01 each kind does shehaYe?
106 Chapler 4 Chapler Reviewfrest
Show You Understand Ifa number isdMsibIe by 6. what other numbers isit dMsible by?
...
Extra Practice
Set A~ 1.pp.eHll
Estimatethe quotient.
1.9}355
50 42,426 +- 8
Set B a.-2.pp. . . .
Oi~.
2.4}118
•. 290.000+- 9
3.7}2.906 1.322.164+8
of. 6}5,280
8. 375.166 ... 4
I. 6)547
5. 160+7
2. 9}6.642
•• 6,444'" 4
3. 5)70.655 1. 57,699 +- 9
•• 8)490.826 .. 684.996 +- 7
. , - - , - - _ •..•. _---
Set Ca.-. pp...,..
Tell whet... each numbef I. diYlaibleby 2. 3, 4, S, 6, 9, or 10•
1.114
,. ""
• 725 .. 1,080
• 'S<
.. 4.096 10. 1.188
1. 8)810 5.413+4
2. 5)7,050
.. 15.514 ... 3 1.60,432 +- 6
•. 9)630.728 .. 738264 +- 7
Set E "'-'1.PI). .Q2-.0li
Solve each problem.
I. Laura has collected 81 stamps. If
9 stamps rlt on one pageof her alborn.
howmanypages 'Nill sheneed?
2. Thereare 54 people waiting in line for I rollercoaster ride. 11eoch car holds
6 people. howmany cars will be needed?
3.5x-25 1.4x_48
•. 54-ak '.w+3-9
s.72-9p '.21+-z-1
e. 109 - 110 10. 42b - 84 Chapter 4 E~'ra Practice 107
•
"" ...
... -
-'-
lllS3-c..:.(1
... _.- -
1932-10 101Oacross
--
INVESTIGATION
Amelia Eartlart's first solo flight across the Atlanlic lasted about 15 hours. She flew abou12,025 miles. Find her average speed
in miles per hour. Prepare a report on one of the other fliers on the lime line.
Use Data
IllfTlllQuImbJ-1911
... - _.-piIoI'-""
.e Use What You Know
Use lhls page to review and remember what you need to know lor this chapter.
VOCABULARY
Choose the best word to complete each sentence.
1. Ifone number can beevenly divided by another.
the first number is _ _ by the second number.
2. To check divisiOll, _ _ the divisorby thequotient 3. The numberto be divided in division is called the _ _.
•. The _ _ is the number by which another number is to bedivided.
CONCEPTS AND SKILLS Multiply.
Vocabulary
dividend divisible dM....
multiply multiple
$. 4 X 71 9. 131X5
$.8x34 lo.10X13
7.7x216
11. 911 x6
8.9x147 12.3X222 Tell whether each number Is divisible by 2. 3, 4. S, 6, 9. or 10.
". <3, ". 3.000 ". 735
". 690 ". sa2 ". 600
Divide. Then check.
". 2m 20. 9)724 ". 6}468
" . 75 + 8 23.127+5 ". 549+7
25. Explain or demonstrate why there are no numbers divisible by O.
• _ _ . . - 1/14LhIenMolU"O...laoid
Divide by Multiples of 10, 100, and 1,000
Obje<:tive u.. palt...lSand mental mathtod!Wle bymultiples 01 10. 100. and 1,000,
Learn About It
In 1998. John Glenn was the oldest astronaut to orbit Eanh, As the first American to orbit Earth in t962. part of his orbit was 99 miles above Earth. It is about 240.000 miles to the Moon, About how many times farther would a trip to the MOOfl bethan the height of Glenn's orbit?
Estimate. 240,000 + 99" 240,000 + 100 Find 240,000 + 100.
240.000 • , • 240.000
240.000 • " • 24.000
240,000 • '00 = 2,400
240.000 • '.000 • 2<0
SOlution: The distance to the Moon is aboul2,400 times farther.
Other Examples A. Use Basic Facts Find 16,000 + 8.
16 + 8 - 2 160 + 8"20 1.600 + 8 _ 200 16.000 + 8 - 2,000
B. Use MuUiple$ Of 10 Find 28,000 + 7,000.
28+7 _4
280+70 _4
2,800 + 700 _ 4 28,000 + 7.000 - 4
C. Use Compatible Numbers Estimate 26,000 +400.
28+4-7:
28.000 + 400 .. 70 24+4_6:
24.000 + 400 .. 60
The qUOlient is between 60and 70.
Guided Practice
Divide. Use p.atterns, basic facts, or multiples of 10.
1.800+4 D. 80]6,400
2. 6.000 + 20
$. 900)36,000
3. 4.000 + 500
e. 4.000)200,000
M\t Yourself
• Which bas'cdivision
!actshould Iusa?
• DidI w,ihllOO comlC1 numl>e<01 Zllros?
110
Explain YourThinking iii'- What patlent do you notice in the quotients when you divide multiples of 10 by multiples of 101
~~
Practice and Problem Solving
Divide, Use patterns, basic lacts, or multiples 0110.
,. 280 -+ 7 8. 540 +- 90 V. 18,000..;. 600
". 4,800";' 800 ... 24.000 ..;. 8.000 12. 32.000 ..;. 40
... 180,000 +- 2,000 ... 56,000 +- 8,000 .. . 36,000 +- 600
... 80)64,000 n . 300)900,000 ... 1.000)700,000
... 700}140,ooo " . 5O}25,ooo 21.4,000}120.ooo Use compatible numbers and mulliples0110
to estimate each quotient.
n. 7,240";' 80
" 8.500 +- 40 24. 624.000 +- 900
". 23,900 +- 46 ". 623.000 +- 270 27. 938,000 +- 526
1Q Data Use the table 10$Olve Problems 28-32.
28. How long did one orbit last?
29, About Iww many miles did Glenn travel each minute in orbit?
3(1. At what time did John Glenn's flight end?
31. What was the dilference between Glef1O's closest and farthest points from Earth during his orbits?
32. Create and Solve Use the data in the table to write and solve yourown problem.
Mixed Review and Test Prep
9:47.... (EST)
Numb9rol_ 3
TIme ;., Ofbil 90 mi...1eS
TotslOfbilloogth 80,966 mikls OrlJilaltitudM 99-1$3mila$
Right"",,,lion 400U<s55minlMS
Multiple Choice
38. The distance from Earth to the Moon is about 240,000 miles. The Ulyssesspacecraft can travel about 30,000miles in one hour. How long would it take Ulysses to travel 240,000 miles? p-..~L.-.o 1) Open Response
Fill In each blank. (l3nldt4)
33, 3.000 centimeters ,., • meters 34. 8.000 milliliters ,., • liters 3$. 56,000 grams = • kilograms 36. 227.000 meters '" • kilometers 37. 49,000millimeters . . . meters
A 8 hours B 80 hours
c 800 hours D 8,000 hours Chapter 5 Lesson 1 111
• _ _1115~"'0i""""
Two-Digit Divisors
Objectiv" DMOOby alW<>-QgiIdMsorand9stimata to pIaôlthefirstdigit In th9quolief'l1.
...~. FO<1t..umic
Q U " , " , '
Learn About It
From 1841 to 1866. more Ihan a half million people moved wes\. The Oregon Trail was a popular roule for wagon trains 10lake. A wagon train lefllndependern:e and arrived in Fort
Laramie 45 days later. About how many miles did the wagon train travel daily?
Find 685 +45.
<urrl<
UHoT,\
~t~ US(! an estimate to predict Ille
o first digit in the qootient. Test your prediction by dividing.
WhatoompatilNnumberswit I>8Ipyou pIaôlttlefirst digit?
" -
45)685 _ 50)500 ...
1
45)685 Muttoply, 1 45 45 - 45 _ Sub1lact 68 45 23
n ~"'23' 45
~T~ Sring doWn the ones.o;vide and
o rOCQrd the remainde,.
WhatoompatilN ~"'." ' "
I>8IpyoupIaôllh9I\&l(tdigil?
451235 _ 5O~ . /
15 Rl0 45)685
- 451
235 Mul~pIy.5 45 225 - 225 __ Subtract 235 225 10
10 Coml>a<9.10ã 45
Solullon: The wagon lrain traveled aboUt 15 miles daily.
Another Ex:ample
2e<0$ In tile O",otlenl Find 852 + 42.
E.tlmete
112
2QRt2 42)852
-84 12 -0 12
Check.
Muttipl)' the quotiemby1t>e lIiV;sorand add the remair>der.
(15 x 45) +10 - 685
The res.ull equalsthedividend.
solhequotient is oo<rOC!.
Guided Practice
Divide. Check your answer.
1.11Y89 3. 19}798
..~\lYourSelf
• Whal bask:fac1can I
USfI toestimatethe firsl dlgjt01the
,..-
<1.91+27 is. 68 ... 31 6. 663 ... 82
Explain Your Thinking'" In bercise 6. how did you know where to place the lirst digit in the quotient?
Practice and Problem Solving
Divide. Check your answer.
,. 2OJ87 •• 26)84 8. 31)93
". 32)74 ". 43J86 12. 21J66
". 31}93O ,.. 15}724 liS. 41)825
". 111568 ". 611860 18. 421682
". 47 -+- 22 ". 86 -+- 44 21.99+32
". 390'" 75 ". 544'" 32 2<1. 378 -+- 62
Solve.
2S. A famity spent $260 for oxen to pull their wagoo along the Oregon Trail. If each ox CQst $65. how many oxen dOd they buy?
27. A wagoo train left Missouri on April 15. It anived in Oregon 138 days later.
On what dale did it arrive?
Mixed Review and Test Prep
26. A family saved the same amount each month lor two years to get $792 they needed for oxen and supplies for their trip west. How much did they save each month?
28. What II? Suppose the family in Problem 26 only had 18months to save lhe money they needed. How much money would they need 10save each mooth?
Open Respon!Se -
Evatuate each expression. Write>.<.or
=for each e. p,.2, '-->"11:0., 3, '-->"111 28. (24 - 8) x (82 - 82) e n - 13
30. (9 x 8) x 1 e (4 x 5) x 2 31. 32x6e240-+- 10
-
E.<traPrilCllCeSee woet33. Set 8,
32. A wagon train with 90 wagons uses 8 wagons for supplies. The remaining wagons CQntain 574 travelers with the same number of people in each wagon. How many
propl,"" '" "'h ••goo? """',". J
p.5,'-->"12)
ChapterS Lessoo2 113
ThiS Is what you know:
• One fourth of the lolal number of signers were from Massachusetts and Pennsylvania.
• Four fewe, signers wer. from Massachusetts than from Pennsylvania.
• Nine signers were from Pennsylvania,
Problem-Solving Strategy
Work Backward
Obje<:li". SolveproblemS by wo<1OOg_ard.
Problem One fourth of the total number of signers of the Declaration 01 Independence were from Pennsylvania and MassacllusellS. There were 4 fewer signers from Massachusetts than from Pennsylvania. If lhere were 9 signers from
Pennsylvania. how many signers were there in all?
You can use Work Backward to solve Ihe problem.
You can draw a model.
Think PAã9;
MA_9_4:
f'A+MA_9+(9_4j
PA+MA_14 Total ...mber of SIgners
Start atthe end of the problem with facls YO'J kllOW
andwork backward through the problem, PA .. 9
• Firld the number 01 signers from Massachusens. 9 - 4 .. 5 MA .. 5
• Firld the number 01 sigl'l6rs from
Massachusetts and Pennsylvania. 9 +5 _ 14
• Find the total number of signers. 14 x 4 _ 56
SOlution: There were 56 signers 01 the Declarationof Independence,
Look backat the problem.
Does the answer seem reasonabje and make sense?
114
Guided Practice
UNthe Ask Yourself que.llon. to help you lIOIve eitCh problem.
1. Tlona:s JefJenon.theItWd Ples1delll ofthetnted Stat4 ...ill office fer 8 yeaf$. Hebegan his Ieml2S yeaI$
after hedraftedthe 0eclal1lIioo. of Independencein 1n6. During 'MIat ye<nwas ThomasJefferson President?
S Shouldyou star1 with!he
numbef~ yea...he was in oIliceO(!he yea,he drafted !he Declaration01 Independence?
2. Most delegates signed the Dedaration of Independence 1 month and
1day alter the ContinentalCongress flfSl. met10 discuss it.nlCy began diSC' S5ãlIg it3 days before adoptingit on.July4. 1T76.When was it signed?
Independent Practice
Wort! bltCkwardto ~ MitChproblem..
3. To fn:l out howold John Adamswas
when hesigned theOecIaf'ation of Independence, dMde the sum of24 and theyear he5igrled il by45. How old was John Adams. our 5eCOOd Presiderlt in 1n6whell he signed?
5. Of all the signers of the Declaration 01 Independence. Carter Braxton had the most childrefl. He had twice as many children as Arthur Middleton.
who had 3 times as many as Ben Franklin. Ffanklin had 3 children.
How manydid Braxton have?
A'" Yourself
~:. WIgl r.cadot II.-?
~ Did IpI.en!tieOfNI.tb..10 ... at
~ MCtI.lepbJ ",•••",. model?
~ • Did IlIta"twIltll_ lIMned
~ from !tie endot!tle .. tl m?
• W1'IIcll CIfI'"'MIkMIMdidI _
10 UN?
• Did I _ b&ckwatdUlrough the lac.. In the problem?
~ Old I.olveth.problem?
4. Ben Franklin was theoldest signer of the Oedarationof nIependence.To fll1d his agewhen hesigned itdivide the product of50and Franklin's agewhen he diedby 60. Franklin died atage 84.
How old was he when he signed?
e. Samuel Adams. cousin 01 John Adams.
was a delegate 10 the Continental Congress for 7 years. He became Massachuseus' governor 13yeBlli after Ihat His 3 years as l,IOYefI1Ofended in
1797.Whendid Samuel Adams begin
wort.; ill the Continental Congress?
District 12 Middle School Students
G,'" Number ofStudents
S '"
, '"
, '"
' - ,
' - ""
Mixed Problem Solving
Solve. Show your work.
Tell what strategv you used.
7. Ofthe 56 signers of the Declaration of Independence. ooly William Ellery was a lawyer and a merchant. Of therest. 39 were either lawyers or merchants. There were 9 more lawyers than mercl1anlS. The product of the numbers 01 these careers is 360. How mall)' lawyers were there?