4. Sue Ann putall the snowdomesin Ia)us in a carton. Sheput 8 soowdomes in a
layer. Howmany layersin!hecarton did shemakewith her snowdomes?
5. Since Sue Ann posted her snowdomes on liefWebsite, she has$Old half ofher collection. AbotJt tloY\t ITllJdl mooey has
... _,
.. Robert spentS19 on 3 snowdomes. He bought TheWindy City.Remember!he
Alamo. and one other. Which OIher snowdome did he buy? Explain thesteps
)'OIl look 10find your answer.
. . . .'.Slll. . .
N... o. Numbt1" ""'.
Sllo.doones .- S."
ThI~Cify " • •
Reo, ..., .Ihe AIl>mo • • ,
r _ _
• ."
Golden Gale BridOB , , ,
S-IheE_iJlIdM .. . ..
Chapter 4 Lesson 3 91
- . - _ 1112 Uoteo ...1,1""'...
Divisibility
Obfeclive Determine - .2. 3. 4. 5, 6, 9,or10 Is • faclOr01 • IlUmber.
Vocabulary
dlYlSlble 1""'0<
Learn About It
A number is divisible byanother number when the quotient is a wtlole number and there is no remainder. Any laclor of a given number divides into that number with no remainder.
Alexanãder has collected 2,032 picture postcards from around the world. He wants to organize the collection into 3-ring
binders, and he wants each page filled.
with no cards left over. Should he use pages that can contain 3 cards each or4 cards each?
Is 2,032 divisible by 3or 47
Decide whelher 2,032 is divisible by3.
If 2,032isclvisible by3, then the sumoj the digits 012,032iseqllllllO arnukiple 013.
2+0+3+2-7 7 is not a multipleof 3.
2,032 is nol divisibleby3, so Alexander cannot use 3-eard pages.
Solulion: Alexander should use pages Ihat can contain 4cards each.
Another Example Divisibility by Zero
There are no numbers divisible byo.
115 + 0- n,lhennx 0-5.
There is no vallie for n lt1at makes n x 0 - 5 true.
This means that the equivalent division senleOC(l, 5+ 0 - n, has no solution.
92
Decide whether• 2,032is divisible by 4.
11 2,032 is divisible by 4, then the lasl 2 d;g;ts make up a multiple 01 4.
The lasl 2 digits are 3 ar>d 2, ar>d 32 is a
mUltipleof 4.
2,032 is divisible by 4, so Alexander can use 4-eard pages.
Use divisibility rules to decide which 01 the numbers at right is divisible by2, 3. 4. 5. 6. 9.and 10.
725 240 536 360 382 590 Eliminate the numbers that are not divisible by 2, 3, 4. 5, 6, 9.and 10.
.'" Check for divisibHiry .'" Check for divisi~liry .'" Check 'or divisibility
0 by 2. The ...mber 0 by 5. The ...mber e by 10. The number must end with O. 2. must end with 0or 5. must end in O.
4.6,or8.,.,. ... '" .. . ... ... '" '" '"All althe remaining360 ".
360 30' 5" numbers are
divisible by to.
.'" Check for divisi~lity loU", Check lor divisibility .'" Chad<. for divisibility
0 by 4.The lasttwo 0 by 3.The sum 0' the 0 by 6. The number digits make up a digits must be divisible mustbedivisible
number divisible by 4. by 3. byboth 2 and 3.
,,, 360 - Both aro divisiblo, .. '" by 3. Both are divisiblo, .. 360
" ,.
Check lor divisibility by 9.Tha sum of the /' Think
"
.'" 0 digits must hedivisible by 9. 2+4+0_6
'-...3+6+0_9/
... '"
Solution: The number 360is divisible by 2. 3, 4, 5, 6, 9. and 10.
Guided Practice
Tell whelller each number Is divisible by 2, 3,4. 5, 6, 9,or 10.
1. 325
5. 315
2. 540 6. 990
3. 393 7. 323
4. 632
8. 3.012
• DidIchool< the fnaJ digitslor divisibilityb)l2. 4. 5.and 101
• Did Ichool<lordivisibilityb)I
3.6,and 9?
Explain Your Thinking'" If a numbel' is divisible by 9. must it be divisible by 3? Explain why or why not.
Chapter 4 Lesson 4 93
Practice and Problem Solving
Tell whether each number Is divisible by 2, 3, 4, 5, 6, 9, or 10.
II. 110 14.7,100
10. 29
1$. 1.278
11. 177
1$. 1.123
12. 531 17. 6.765
13. 455 18. 1.107
X Algebra. Expressions Find a value of nthat makes the expression divisible by 2, 3, and 5.
111. 18n
23.9n+3
20.n+7
24.n-5
21. 10n .2$. 5n
22.2O+n
2$.2n-4
Stamp Sets
[!J Data The table below shOws the number of stamps In variOUS stamp sets. Use the table lor Problems 27-30.
27. Dwayne botJght a set of stamps whose numbef of stamps is divisible by 2. 3. 5.
6,9. and 10. Which set is it?
Mexico
Country Numbe, Per Set 28. One set of stamps is divisible only by 5.
Which set is it? How can you tell?
N. Berta puts all the stamps from a set in an album. She puts 9 stamps on each page because that is the greatest
numbef bywhich the number of stamps is divisible. Which set did Berta use?
30. Shelly bought one of each seL Use divisibility nIles to see if 2. 3. 4. 5. 6. 9.
or 10 stamps will fit on a page so that the same number of stamps are on each page.
31. Is a multiple of 2 always a mulliple of 4? Is a multiple of 4 always a multiple of 2? Explain why or why flOt.
Write About It Tony says thaI if a numbef is divisible by 3 and 9, rt must also be divisibleby 6. Using examples, explain whetherOf not his rule worlls.
Brazil
United States
, ..
""
""
94 E>.traPno::tice SeepIlgIe 107. Se1 C.
Algebraic Thinking Finding Patterns
ImI You can use your calculator to find division patterns.
Enter 1 followed by as many zeros as your display will show.
Nowdivide by 9. Drop the numbers after the decimal point.
1OOOOOOOO+9-11111111
Repeat Sleps 1 and 2 bul enler a 2 first in Step 1.
2OOOOOOOO + 9 - 22222222
What do you predict you will see when you divide 3OOOOOOOO by91 Try ~. What pattern do you nolice? Use the panern 10 predict what you will see when you divkle 8OOOOOOOO by 9.
Use the same steps as above but this time divide by 99.
Howis tile pattern the same? Howis it different?
Tell whether each number Is divisible by2. 3, 4. 5, 6, 9, or 10. (\.eoot:<l4l Estimate each quotient. Then divide...1-21
Check your understanding of Lessons 1-4.
4. 7.294 + 3 3.523+6
2. 8.256 + 7 1.634+8
~. 332 e. 540 7. 945
Solve. Name the operatlon(s) you used.(\.eoot:<l31
$. Aunt Karen bought one set of 236 stamps and another set of 149stamps. She gave the same number of stamps to each of her5 nieces. Howmany stamps did each girl get?
I Extra Practice at eduplace.comlmap I Chapter 4 Lesson 4 95
Obtectiv8 Determinew!Ien 10 P<Jl ~rO$ln IhequoIiIw>1.
Zeros in the Quotient
""
5!2.ill
-25 1
IllS _ Multiply, 3' 5 - lS Subtrect 15 151
o The,...is no remall"loe,.
.'" E) &'"'~"~-ãI0Mde lhe ones.
,~,
Think 5"5 ones
?ten Think 5)1 ten
There are JlOI enough IBM 10 divide,
SO _ Write 0inthe lens 5}2515 place to show that -251 theqvotienl has0
01 tens.
~tlto Bring <IOwn lhe lImS.
a Divide thetens.
There ereJlOIenough
thOusandStodivide.
111undf(ldS Think 5)25hundreds
sJ25i5 , Muhjply 5 5
- 25.- Subtract 25 25 o Compare, 0< 5
",.r.., o De<;;dethefirstwhe'"digiIQlltIeto ~
QlIOI>ent.ThendiVide.
?lhousaods Think 5)2 thousaods
Learn About It
Solve 2,515 + 5 = n.
Ram6n has 2,515 marbles. He has bought 5 plastic boxes for storing his marbles, 1/ Ram6n puts Ihe same number of marbles ill each box, tlow many marbles will be in each box?
Solution: There will be 503 marbles in each of the 5 boxes.
ChlfCk.
Mu~iply.
503 X 5 = 2.515 Other Examples
A. Zero In The Oivldend B. More Than One Zero 2.265 R3
4)9,063
- '110 _ Bl'Ing down the zero from _ 8 the hundredS place.
-"26 23 -23 3
700 R4 7)4,904
-"0 0 _
-0
'"
-0 ,
The resutt is O. but there are more places \0 drvide.
Wl'Ite 0 in tile lluotien~
because0 tens 7 0 tens. Then oontmue.
96
Guided Practice Divide and check.
,. 7)284 2. 4J3.602 3. 8)34.421
f\';\c. YoUrself
• Where00 Iwritethe tirSl digit?
• HowdoI kr>owwilen too dMsiCItl;sdooe?
... 301+5 ~. 2.801 + 3 &. 240.120 + 6 Explain Your Thinking" In Exercise 5. what would happen il
you did not bring down the zero?
Practice and Problem Solving Divide and check.
,. 7)568 • 3]624 ,. 2]801 ". 815.632
". 4)3.603 u. 5]43.004 ". 6)300.056 , •. 21121.481
". 613 + 3 " 5.522 + 6 H. 8208 + 6 " 16.006 + 5
". 70200 + 9 ". 63,564 + 7 ". 627.153 + 3 " 457.267 + 9
". 1.06Z4
". 2."
". O.Oas
24. Fill in the missing numbers in the division.
B 200 trays o 230 trays 5.26
6)••. 16.
-00
- ..0100
-12
00 -00
o
A 25 trays c 205 trays Multiple Choice
33. Amarble collector has 1230 marbles. If she displays them in trays thm hold 6 marbles each.
how many trays does she need?
lChã~, l,..,.,51 Solve.
23. Acompany made 52.250 of one kind of marble in 5 days. ElICh day. it made the same numbel" of marbles. How many marbles are made earn day?
25. A loy show ran for two days. TIckets cost
$3. On thefirst day. ticket sales were
$3213.On the secDfld day. sales were
$2.949. How many lickets were sold?
25. Acollector of antique marbles paid
$1.000lor4 marbles.What is the average price paid per marble?
Mixed Review and Test Prep Open Respon$4il
Round each numberto the underlined place.(C1>. 1.~4_71
28. 2.45.324.936.316
30. 221.809.302 32. 712,805
ExtraPracbce See P3ge107.Set0 Chapter 4 Lesson 5 97
Objective Use!JU"SS aOOctIedc tosoIwa probMlm.
This Is what you know:
• Glen has 24 sets 01 salt and pepper shakers .
• The number offood sets is 3 limes the number of character sets.
o The numberat animal sets is divisibleby 2 and 3.
Problem-Solving Strategy
Guess and Check
Problem Glen collects 3 different kinds of salt and pepper shakers. The number of his sets with food is3 limes lIle number that ShOW characters.
The number of sets that show animals is divisible by 2 and 3. Glen has 24 sets. How many of each kind does he have?
You (lan use a Guess-and-Check s!ralegy to solve the problem.
Usewhat you know.
Organize your guesses in a table
Ch.racters Food Animals
(C) (F) (A) COrrltd?
3timesC-F
A is divisible by 2 and 3.
F+C+A-24
Continue guessing and checking until you koow you have the correct answer.
SOlution: Glen has 3 character, 12 animal.