The stmg is 2} leetlong. How long is
"'" """
40, VOci boughta )'0-)'0with a stmgthatwas
~ ather height. How long wasthestmg on
Vidu~s yo-yo?
4'. Forthetrick "Tidal W-.ãMaxplaced a lingerunderthe)'0-)'0 stringabout4 inches from lheend 01 its2}-loot lef\gth. Howlong is the rest of thestring?
42. For one job. Ma~ eamed sa for each hour
heworKed. How much did he earn il he worlIed 1~ hours?
4 ()( the40 jobs Max hasYII'Orked so far lhis
year, t 01" themwere IJom repeat costoIl1er$. •
HowIT\3l1)'01 hisjobswere from fleW CU$lomer.i?
41. Cru'. and Solve Writ" your0\IIIl ploblelll thaI uses data lrom thetable.
SolYe your plobiel'L Job'
Evltfll Worked"~ AmountEerned
MaPOpening
" , '"
flog's party
" • '"
Qrw1o ..., , '
'"
_.- 2~ , " .
-- " , '"
Data Usethe ta'-for Problems44-47.
Thetable sI10YiSthe numberof hours MaxwortIed atll8rioos jobs this weekaoo theamoum hewas paid lor each ;otJ.
u. Malsets aside t of his eamings 10put imo savings. Howmuch did he save trom the frve jobsshown in the table?
4S, Ma~ spellt halfor his lime at Rosa's party putliflg on a magic sll(M'. How long was themagicshow?
48. Find themean, median. mode. 8Jld IlInge of theamounts Max earned al his jobsIhi:sweek.
"8
Science Connection How Hot Is It?
If a recipe showa a femperature in 'c, you can convert Ihat lemperature10'Fusln9 this formula: F= ~C" 32.
Here's how to change2OO'C to ãF.
"U", Substitute values
o in the Iormula.
F-~C+32
- (~X 200) + 32
"1f:,,, Then add.
a
F-360+32 F- 392
The temperature 2OO'C is the same as the temperature 392ãF.
Change these lemperatures to 'F.
,. 190'C 2. 150'C 4. 100'C
Multiply. Write your answer In slmplestlorm.~ Ia'ld2\
,.
WHKlV(PRUDER oduplaoee.<omImap
Check your undeBtanding lor Lessons 1-3.
SX~- • '4 ' X"2- • ,
,. .ix~• • •• !X~, , •• I X6, •• 8xl •
Multiply. Write each product In simplest lorm. ~3)
7 3 , 3
7.2e xa 8.1'5X2"2l1.4X5'4
Chapter 12 Lesson 3 319
HandsOn
Model Division
Objective Usemodelsto _ withlracbons,
Work Together
A unilfrtlctlon is a fraction in which the numerator is 1. Yoo can use models to divide a counting number bya unit fraction.
Wor1\ with a partner to find 6 + t.
Vocabulary
unit ffactlon Malerlal.
gridpaper fraC1ioll slrip$
","tl;.oo Draw 6 whole circles.
o Separate each circle into halves.
Dividing 6bytis the same as finding howmany halves are in 6.
CD CD CD CD CD CD
Count to find how many halves are in 6 circles.
oWhatfs6+t?
There are 12 halves in 6 circles. so6 + t -12,
You can use models to divide a fraction by a fraction.
Wor1\ with a partner tofind ~+ ~,
Clwtckyour answar using multiplication.
12x';-_6
320
. o,~ ModelSã•
Find how many 2 mths are in 4 H/ths.
'Whatis~+~?
Clleck.
2X~_~
On Your Own
Match each quesllon with the corred model.
Then complete the division sentence.
1. What is 3 dillided by t?
3+t=-
2. What Is3 divided by~?
3+~-_
3. What is, 3 divided by-1?
3+ 6 - - c I : : : I : : : I : : : I
o 1 2 3
Complete eaeh division end multiplleation to find IIand b.
Use fraetlon strips or grid paper lor help.
4.4+~-a 4X2-b s.5+J-a 5X3-b
7.g+~-a 9x2 .. b
Use your answers Irom E~ereises4-7 to answer E~ereises8-9.
8. What is true about a and bin each e~ercise?
a. To divide a whole number by a unit fraction, by wIlat can you multiply the whole number?
Divide. Check your answers.
3 t 2 1
10'4+4" 11'"3+"3
9 ,
1$'12+ 12
'2.~+k . ,
10. 10 + 10
13.~+~
9 9
. ,
H. 6 + 6
You have learned how to use models to divide Ir&Ctlons.
18. How would you e~plain to another student how to dillide a fraction bya unit fraction?
10. Explain how you found the answers to Exercises 16and 17
Chapter 12 Lesson 4 321
tIIJ __ 212l101<<> .... _ _
Divide Fractions
Objective Use!hereciprocall"di'"detractions.
Vocabulary
reclproul
- - - J
Learn About It
If a fraction is nOl cqualto O.then its reciprocal is obtained by interchanging the numerator and the denominator. For example. the fraction; is the reciprocal of~. If neither anor b is zero. thert the fraction ~ is the reciprocal of~.
Tho . . . .
at,&CIk:<'land its reQprocaIl$always1.
A coneen lasted for 4 hours. The coneen was divided into acts. Each act was different and lasted
~ hour. Howmany acts performed at the COJlCert?
Firtd4 -+- l
",'tb Rewrite the division as a
o multiplication bylhe re<:iproeal of the diviso<.
4+ ~_~>< ~
",'tf,o Look lorcommon faC10l'S
o to cancel.
• n.
-TX2-10 ,
Solution: Ten acts performed.
Che<:kyotlrwork.
10><~_/o;2_2)(2_4 ::....
Other Example5
A. Divide by Counting Number
Find 19 0 + 3.
, "
;0-+-3-;0)(3 -~,
e. Divide Counting Numbers
Find 3 -+- 6.
3-+-6-3><i
-, , -t
c. Divide Fractions
, .
Find i -+- "ii'
~-+-i-~)(~
3><8• 6
-1X5-s ,
_1!
322
Guided Practice M\c. YOUrself
Divide. Write each answer In simplest form. Cl1<N:k.
I I 7 t
,.3+2" 2ã2"+12 3'2"+7
• DiOIn'OJ1IipIy bythe reeip<Qcal 01ltie divisor?
• Did1divideby 00.. 'no,I 1BcIors1O~
4.6 ... 8
Explain Your Thinking" Why does dividing by ! give the same resull as multiplying by21
Practice and Problem Solving
Divide. Write each answer In slmplesl lorm. Cl1<N:k.
1 4 t 2 5 5
1.8+4 8. 5 +8 "'4+3 10. 6 + 12
, . ,
12. '4 ~ 3
11.9+12
13''8+, 2
18.t2+9
14. J'"6
111. '0, ,+"10
1.5.5+15
11.12+ 3,
18.'; ... 2
, ,
21'"10+"5
X Algebra. Functions Complete each lunctlon table.
Write each answer In simplest lorm.
Rule:y.x+8
, " , "
"
• • ,
,
RUIe:y.x+i
• ., "
"
, , • • ,
,
Solve.
24. A balld played lor! hour on stage. Each song lasled I~ hour. How many songs dKl they perfonn?
26. Aband look 3 breaks during a 4~hour COltCert. Each break was ~ hour. How
many minules of breaks were Ihere?
u. One band played 4 audience requests in 15 minutes. What was lhe average length 01 each song Ihey played?
21. Duringa ~-hour aCL the band perfonns 3 songs. Each song is the same length, How long is each song?
32. During a2 hour "leeting. each person spoke lor 6 hour. How many speakers were there? Explain how you gOl your answer. p>- 12.lM.oor>~
211. 984 ... 8 31.102+5 Mixed Review and Test Prep
rOpen Response Divide.(CI>.~. ~2)
28. 674 ... 3 30.742+9
&IraPr.\ctIeeSee page 331. Sel C, Chapter 12 Lesson 5 323
tIP __ mllo1oo ... _
Divide Mixed Numbers
Learn About It
A dance teacher has sctleduled 3~ hours
of practice before the spring recital. Today's practice lasled 1t hours. Whatlraction 01
the practice time is that? You can write each mixed number as an impl"oper fraction to divide.
Divide. 1-l- +3t = n
~,.~ Writs the mixed numbers as
o improperfrae~ons.
1-l-+31-i+~
Vocabulary
mtnd number
~,.~ o Rewrite as a multiplication problemusing the reciprocal of lhe divisor. l
i+~-ix¥
Look for Coml1lOl1 faetOl"s.
m ,
- 2~2~7,
Solution: 1t ... 3i .. ,54
1t hours is ,54of the total practice ~me,
Other Ellamples
~,.~ MUltiply.Be sure the answer
o is in simplest form.
5~1 5
2x,~1-"ii
Che<:k VOUr work.
S , S 1
fiX3z--fi Xi
'"
- 2X1'XI
-!.or,i
A. Dividend is Counting Number Find 9 ... 2i',
9"'2t=t+~
.. tx~ ,
'"
.. , X lJ,
.. t=4
324
8. Divisor is Fraction Find 2t +}.
, 3 , 4
24"+4"=2i x '3
.. ~x~ , ,
'"
- 'i'X'3 , ,
_1_3 ,
C. Dividend is Fraction
, ,
Flnd s + '"3"'
!+ 1~"!+~
-Sx S , , ,
'"
- '8"XS ,
Guided Practice
Rewrlle each dlvl.lon •• , multlpllC:lllon.
Write 'II mixed number. 8lIlmproper Ir.c:llon••
2 2 1 2 1
1'"3+4'5 2,11+1'2 3.8"3+12'2
t,s\('tOUNe/f
• [);dIInYertltI&diY\SQI
to Io<mltI&reclprocaI?
• Dill-, Icanal"".'b'
• DillIwriteII>e(pJOIJenI
",~SlIorm7
Writ. each quotient In .Imp...l form.
Mul1iply 10c:heel<.
" ,
1''4+1'4 .. 4l+2 1o.6+1}
ExplJi;n YourThinking" How Ill'e(he recip...:als 01 unil fractioos and counting numbeni related?
~actice and Problem Solving
Rewrite each each dlYblon ••• muI1Ipl~ion.
3 2 I 3
11.• +1) n.10+3 5 13.. 7'4+4
Wrile each quotientIn almplest kInn.
Multiply to ctlec:k.
" I I 2 1
15.'J+l'2 '''4.+3 11'3'+1"3
22.6+3!
2$."3+ 2"3 , ,
21.3+ 1"2 , , ,
20.4'2+8
, ,
24. 6'2+.
JC Algebra. E~ ...lon. Rewrite ellCh exprnsion 8lI.frac1ion in almplest form. Nonriable eqUJil. O.
27.rl+2 2.. 2+rl No b+a 30. 3rI+3m
CampI. . Write>. <.Of" 'Ofeach e.
31.6f+ 2 t e 6!+2
33. }+!.t+~
".
~.
Chapter 12 lesson 6 325
Choose a Computation Method
[;J Data Use the schedule for Problems35-38.
Beth is studying at a ballet school. The schedule mthe right shows her Monday classes and their times.
35. What fraction of Beth's Monday class schedule does ballet represent?
36. I.ast Monday, Beth was l31e for her Jazz class. She missed tof the class.
How much time is that?
Iklh's Monday Schedule
Class Number of Houn ModefnOa""" 2
.., ..
Charade, StrengthTraimng
".
"!'!'II
~39,
One of Beth's teachers divides each hour of class into thirds, She uses those
si~ sessions to work with different groups. Which class is this?
Measurement Draw a line segment that is 3-ij- inches long. If you divide the line segment into five equal lengths, how long will each piece be? Show it on your line.
3$. Beth's Tuesday schedule
is like Monday's, except ballet class is half as long, and jazz class is twice as long. Does her total time change?
40. Glennis drew a line segment that was 9~ inches long. Then she divided it into line segments that were each 1!
inches long. How many line segments did she make?
e 1t hours
o 6ihours
Open Response
Write the prime factorization. Use exponents if posslble./Ch 9,~:a
41. 36 42, 42
43.56 44.72
L 46. 144
326
Multiple Choice
47. Lance did homework for 2i hours.
He spent the same amOtJnt of lime on each of 3 subjects. How long did he spend on each subject?
p,.12,~61
It i hour
B i hour
Extra Pracllceseepage 331.SetD
Division Scramble
2 players
What You'll Need' twocopies 01 Learning Tool 42 0<2 ll"rM t>oards; 4 sets 01 number cards, numbered t to to
How to Play
o e o o
Shuffle the number cards and place tham on the ta!lje facedown in a stack. Give each player a game board. The goal 01 the game is to create a division example that will hava a greater quotient than your opponent's example has.
In turn each player takes one card from the stack and pfaces that card lace up on his Of
her game board. Once placed, a card cannot be moved.
The game con~nuesuntil each player has four cards showing on his or her game board.
Each player then divides the fractions displayed on the game board The player whose example has the greater quotient wins.
Shuffle the number cards and play again.
This time the player whose ei<8mple has the lesser quotient wins.
Chapter 12 Lesson 6 327
Problem-Solving Decision
Choose the Operation
Obje<:tive A _ 00wto cl1OOS8 ttItI""",atOO ltIatwmhelpyou ... problem.
When solving problems you must cJe.clde which operation lQ use.
Problem The area of the gym floor is 610 square feet Five eighths of the fIoofwill be used as the siage for a "battle of the bandSã COllcel'1. The stage will be separated equally into four sectiofl!>-one for each of the lour bands. How mum space is given to each band?
Find lhe area of lhe gym floor 10 be lOBed as the slage.
Find how much 01 the stage each band will have.
Multiply to find a Iracllon 01 a number.
'" ,, '" • '
Divide to separate a number equally.
'" • '
Solulion: Each band is given 95 1~ square feet of space.
Try These, Solve.
1. look back allhe problem above. Tile remainingi of the gym floor was separated equally into 5 sections for sealing. How large was each section?
3. The drummer needs 29* square feet.
The bassist needs 10~ square feel of space. Howmuch more space does the drummer need? How much space do they need combined?
328
2. Tickets for the concert cost $5.00 at the door. Students could buy tickets in advance for ~ of the doorprice. How much did advance tickets cost?
•. The320 peoplein the audience each cast ooe vote for their favorite band. 11-&
01100 audience voted for Band 1., , -k for Band 2, 16 for Band 3. and "6 for Band 4.
howmarly VOles did each band get?
8. Male sea oilers havebody length. oot including their tail, that is about~ of their
total ~lgth. Suppose a male sea oller is 45 incheslong from the tip of his head to tile tip of his tail About how long is the sea otte(sbody?
15. Rachel's garden has 134 square 1001.She wants to separate the space equally into 6 parts. What will be the size of each part?
II. The full-grown male sea lion is about 20 times heavief than a full-grown male sea otter who weighs 92 lb. About how heavy is a full-grown male sea lion?
Now sotve the problem look back.
Doesyour answer make sense?
Solve. Tell what operation you used.
5. A recipe makes tWO and one half dozen cookies. How many dozen cookies can Sarah make if slle used three times the original recipe?
7. A full-grown male Oller can weigh as much as 92 lb. A full-grown female Oller weighs about~ the weight of a full-grown male. About how much does a full-grown female weigh?
Social Studies Connection United States Congress
TIle United States Congress is made up of the House of Representatives and tlle Senate.
The House of Representatives has 435 members alld tile Senate has 100members.
To pass a bitl. a majority 01 the members (0I1e half of tile members plus 1) of each house must vote to pass the bill.
Problem To pass a bill. how many members of the Senate must vote for the bill?
10. The total length of a grown sea otter (head to tail) is only abouti the length of a sea lion. If a sea olter;s 45 inches 100lg.
about how long is a grown sea lion?
~=::::==W
1. How many members of the House of Representatives are needed for a majority?
2. It takes j of the House of Represef1latives and j of the Senateto vote toOYefride a veto.
How many members of each house is that?
Chapter 12 Lesson 7 329
.e Chapter ReviewlTest