show.AJex sokl 52 tickets. Sue sold 10 more than AIe:Il. Jo sold 10 more
!hanSue. IbNmanytidIetscIid AIe:Il.
Sue.and Jo seI in at?
Mulhple (hoKe
1111111111' 111101' 111'11111111' Solve tach problem.
3. Which point on the numberline
represents a number that isdivisible by
both 2and61
Problem Solving on Tests
Choose the ietiel' of the correct 8nSwet'.
.ãH..ã.._...ããã..ããã_ããã••.••..•..••..._..
c 124 tickets D 186tickets
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...
_ _ 1/13UsIon ...Ul'<ll!tSIOflII
Algebra
Solve Equations
Ob}ec:tiv. Use mental malfl toso/YemulUplicati(:o"l anddivisionequati(:o"ls.
Learn About It
Alvin brought his comic book collection to school to show the class. He gave ncomic
books to each of 4 small groups. Jf he had 12 comic books. how many did each group get?
You can make a model of the information and write an equation.
Total number 01 com", books 12
o I 0 I 0 I 0
( ..~moo, ' \
Solve 4n = 12. ~nmeans4 "V
You can use mental math to soIvillhe equation.
4n = 12
o 3
Solution: Each group gOI 3 comic books.
WhaIf>J_t~
4&<:p.>als 121
"'-.... Try 3. /
Other Examples
A. Use a Oivision Equation.
28+n-7
B. Find the Unknown Oividend.
28+4=7
102
63+7-9
Sincen+7-9.
n_7><9.
Try 63.
Guided Practice Solve each problem.
I. Jonah has 30 comic books. He wants to read them over the ne~t 5 days. If he reads the same number each day. how many will he read a day;'
Solve 5n ,. 30.
Total number ot comoc books 30
0 0 0 0 0
- - - "" "" "" . "" .., - ""
2. Marion gave each of her 7 friends 7 comic bool<.s. How many comic books did she give out?
Solve7X7-n.
• What muhipNcatioo 01
<lvisionfadcan help roo SOlve\hiSI>qWtioo?
• DidICI>&CI< my &OMioo?
Total number of comoc books' "
, , , , , , ,
.- .- .- .- .- .- .- ,- ,- ,- ,- triend friend -
Explain Your Thinking "'How does knowing multiplication and division facts help you solve equatior15 mentally?
Practice and Problem Solving Solve ellCh problem.
a. SI1aron has 36 comic books. She has 4 of each type of comic book. How many diffefef1t types does she have?
Solve 4n - 36.
4. At the comic book convention. Nelson sold comic books for S3 apiece. He sold
$27 worth. Howmany did he sell?
Solve 27 + n .. 3.
o o I 0 o o o o
Make a model 01 the Inlormatlon; write and solve an equation.
5. Seven issues of a certain comic book cost $42. How much does one iSStJe cost?
6. Five friends shared some comic books, Each friend got 8 comic books, How
manydid they share?
•
Chapter 4 Lesson 7 103
, , ,o , ,
Use mental math to solve the equations.
,. 6n .. 48 •• 4,<" 8 •• 9y - 81 " . "-20
". 18 + Y= 6 ". 49+n=7 ... 45+n=5 ... 12 + n = 2
... 8t - 32 " . 18 + s - 9 ". 36+n-6 ". 7t .. 21
>0. 4y= 24 ~. n+4=5 ". 72+,<=8 ". t + 4 = 8
X Algebra. Equations Replace nwith 4. Is the equation true?
Write yesor no.
23.3n_12 2 4 . n + 4 _ 8 2 5 . 8 + n _ 2 26. 6n '" 24
27.20+n-5 26.7n-74 29.n+2-2 3O.nxn-16
Use the tunction rule to lind e/t(:h value 01 y.
". Rule: y. 3,<
• , • , •
,
Rule: ,< • 36+ Y
• , , , ,
,
Solve.
". Savannah organizes her collection of 28 ... Draw a model or use algebra tiles 10
comic books in bags. II she puts n show 6n .. 24. Solve the equation and books in eoch 01 7 bags. how many explain !low your model helped you.
books are in each bag? Explain, ... Kevin has 3 limes as many comic books
". Debbie saves $5 each week for nweeks as Jen. Serena has twice as many comic
Irom her babysilling money. If she books as Jen. If Serena has 6 comic spends $18 of her savings on comic books. how many comic books do the books and has $21e11, how many weeks three friends have in all?
did she save her mooey?
Create and Solve Choose an equation.
". What 117 look back at Problem 36. ... Then write a word problem lor it and What if SerClla had 30 comic books? solve it.
How many comic books would Kevin, 5,< - 35 r + 4 _ 9 12y - 3 Serena. and Jen !lave in all?
". What's Wrong? Jason said that to Write About It Write a fact family lor solve6n= 12. you multiply6and 12, 3n - 18. How can writing a fact family Whal is wrong with Jason's answer?
help you solve this equation?
104 Eotr.l ProcIiceSeepage101,SetE.
Open Response
Dlvlde.lCh-4.~~
<Ii. 432 ... 4
<13. 2.346 ... 6
l
42. 1.134'" 9
<1<1. 9,045'" 7
<IS. Jared collects paintings.11 rooms in his housewh~:ahse H~ I
can put his painlings. He has 121
";,,,,,,. H~moo, ";"';,,, " , J
he pUI in each room? Make a model and explain. IO>.~, ~7)
Math Reasoning
Patterns on a Hundred Chart
You can use a hundred chart to find divisibility panerns.
This pattern shows the numbers that are dMsible by 10.
If you draw a triangle around each numbef that is dMsible by 5. how will that pallem be the same or differem from the pattern for divisibility by 10?
Copy the hundred chart on another sheet of paper.
I. Draw an X on each number in the chart that is divisible by 2. Whal pallern do you notice?
2. If you draw a square around ali the numbers that are divisible by 4 and put a star on the numbers thaI are divisible by 8. what pallerns do you nOlice?
3. Use a different color to draw a horizontal line through the numbers that are divisible by 3.
Next. draw a vertical line through numbers that are divisible by 6. What new patterns do you nOlice?
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"
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" " " .. " ~ " " .. 00
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" " " M " '" " '" " '"
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Chapter 4 Lasson 7 105
.e Chapter ReviewlTest
VOCABULARY
1. Anumberis __ byafl(l{her number it theqUOl:ienthas
no remainder.
2. A of a numbef"divides "'10 lhat nomber with
00...-.
So Ifiii dMdend is a multipleof adivisor. thedMdend andthe
dMsorlre~
CONCEPTS AND SItIW
&tlmete the ql>QlienL a.-1, " 'e&-<e1I
Vocabulary
"'1$ ,... . ~
- ...
"" ~ oC
,.,woIo_
4.598+3 5. 18.320 -+ 9 •. 173.462 + 4 1.21.568 -+ 7
"2,01'+6 11. 9"8.207
g. 672.461 + 7 12. 7)2,906
10. 16.715 -+ 5 13. 7)49,079 Tell eaeh number 10 see whether lila dlvlalble
by 2, 3. 4, 5, 6. 9, Qr 10.r..->n •.w.W-GiSl
14.315 IS. 600 1•. 720
U. . mental malh 10 solve each eql,l,t1on. a.-1. lCQ-10Sl
11.8b-54 llil.16+c-' 2O.c+7-7
17. 317
21.9b-,8 22. 72+n-24 23. 6yã 54
PROBLEM SOLVING
Name theoper.uon(s) you used to sot....
the ptotMm. ,...3,PI'~')