._---~---
I
15. Write a fraction to tell how much althe pizza has been eaten. Theil write an equivalent fraction.
Learning Vocabulary
Equivalent means "the same value" or
"equal 10."
Walch for these words In Ihls unIt. Write their dcfinitions in your journal.
••110
One quarter in this problem means t.
So to ftnd one quaner of an amount. you
multiply by t or divide by4. Find t x 100,
419 __..-VIIIUsleoMolUolOeo.laoid
Ratios
Objective RM<!.wt~". and~~ifyratO>$. C ocabUJa,y~m.'''110
LeClrn About It
Olga finds 7wooden langram piecesin a bo~.Two shapes are quadrilaterals and 5 are triangles. Oneway10 compare the number of quadrilaterals with the number of triangles is towrite a ratio,
The terms of a ratio are the numbers you are comparing.
You can write a ratio in fraction form. with the firsttenn
a~ the bar and the second teml below the bar.
Whst Is the ratio of quadrilaterals to triangles?
'!ITI1", Iden~fythe terms of the ratio.
o . - ~~ ~
2 quadrilaterals Thellrst term ks 2
5 triangles The seoond telm is 5.
'!IT£.<, Wrrte the ra~o of quadrilaterals
o to triangles.
The ratio can be written 3ways.
Word form: 2to 5 Ratio Iorm 2:5 Fraction form: ~
To read all three forms.
say."2 to 5."
Solution: The ratio of quadrilaterals to triangles is 2 to 5. 2:5. or~.
Guided Practice fI,S\r. YOUt"Jelf
Write each rstlo three different ways.
1. 5 cars106 trucks 3. 2 balls to 3 bats
s. 7 squares to 2 triaJlgles
2. 16 cats to 3 dogs 4. 4 caps to 5 coots 6. 9 paints to 4 brushes
• Didtwrite!he tamlS in!hecomlClOôl&f?
• Didtwrite each letio (h'Mdill&""'t ways?
Explain Your Thinking'" In Ellercise 6. if you write the ratio of brushes to paints. would you write 4:9 instead of 9:4?
484
Practice and Problem Solving
Use Ihe trlangtes, squares, and circles below 10 write each ratio three different ways.
,. squares to triangles 8.circles to squares
•• circles to triangles ". squares to circles
". triangles to squares u. triangles to circles
". circles to all figures .. . triangles to squares and circles
...
parallelograms 3
Numbe<ol Each Shape Tangram
Pieces
1Iil Data Use the table and the completed tangram to answer Problems 15-19.
16. Olivia emptied a box of wooden tangram piecesonto the desk. She counted the number of each shape and organized her findings in a lable. What is the ratio of triangles to squares?
16. A tangram is made from 5 triangles.
1 square. and 1 parallelogram. Ifall the pieces are the right size, how many complete tangrams can be made from the shapes Olivia has?
17. Write the ratio of the number of yellow pieces to the number of purple pieces.
18. Write lhe ratio of lhe number of purple pieces to the number of yellow pieces Write About It Explainwhy the answers to Problems 17 aOO 18 are not the same.
Mixed Review and Test Prep Open Response
Write two equivalent fractions. Use muillplicatlon and division.20. . 6 21. 20((h,g. '--'"' III
, ,
.22. 14 23. 20
24. Write the ratio of triangles to figures that are not triangles.
Explain.fCh- 18.lMo<>"11l
...
Chapter 18 Lesson 1 485
• _ _ . . - 2120Uslen0I'Id U..."d
Equivalent Ratios
Objective Use multiplication DOO<liIIIsiontoInc! equivalDm ratios.
Vocabulary
"'lUIVDlent rDtia Dimples! Iorm
- J
Learn About It
Melinda wants to paint her liule sister's dollhouse.
She has chosen a color that requires 4 parts of red for f!'iery 12 parts of yellow. The ratio of red 10 yellow is ,~.
If Melinda uses 8 parts of red. how many parts of yellow will she need? If Melinda uses 2 parts of red, how many parts of yellow will she need?
You can find an equivalent ratio for t~ thm has 8 as its first term. Then you can find an C<luivalent ratio for t~ that has 2 as its first term.
Different Ways to Find Equivalent Ratios
WayO Multiply each term by WaVe Oivicle each term by the
the Dame number. same number.
~ ~ ~ ~
Think: " • • ~• " • • ~" Think: " • • ~• " • • • •
'0Y '0Y '0Y '0Y
Solution: If Melinda uses8 units of red. she will need 24 units of yellow.
If Melinda uses 2 units of red. she will need 6 units of yellow.
.. Aratio is in simplestform when the GCF of the terms is 1.To write a ratio in simplest form. divide each term by its greatest common factor (GCF).
Write ~~'ln slmplestlorm.
12.. ~"' 1. .
'0Y
The simplest form of ~~ isl
486
Think 1 2 - M x 3 t6_~X2X2 2x 2, or 4, Os theGCF.
ExtraHelpateduplace.comlmap
Complete the equivalent ratio:i = f.
~H'... Write the ratio in
o simplest 10rm.
A!>-.
.i , • 1. , '0Y'
Solution: ~ '" ~.
Guided Practice
"'llã... Multiplyby a number
o so 9 is the new
second term.
",'"",,, Multiply each term
o by the same number.
A!>-.
1. , • .! .
'0Y'
.,osk YOlJlself
Write lour equivalent ratios lor each.
1. e: , 2. 8 to 12 3. 6:15
• DidIJnIIti~0<
divk!ebOIh t&rRlSb)'
tt>esame nulW:ler?
Explain Your Thinking "How would you write 6:15 in
simplest form? How did you gel your answer?
Practice and Problem Solving Write lour equivalent ratios for ellCh.
$.3 , e.5t06 7.1:5 8.10104
Write each ratio in simplest form.
"
11. 40 12.6:18 13.24t042 14.12:60
II. 10:16
"
1S. 36
10. , 3
16. 28:32
X Algebra. Equations Complete each set of equivalent ratios.
1 . 8 . 159
17''4=12 1e' 24 ="6 111'25=. 20.~=~
Multiple Choice
27. Complele the equivalent ratio:
'" .
N '" 6ã p.. 18.'"-"':II
r
Mixed Review and Test Prep Open Response
Multiply.(Ch. '3, ~ ~
". 0.09 x 08 a. 3.2 x 0.6
". 0.21 x 0,9 ". 8.34 x 4.7 ,. 0.002 x 0.6 ". 0.03 x 003
E.<\nlPracllCtSee page 503. Set 8
. 4
• 5
080
Chapter 18 Lesson 2 487
Rates
Objective Comparetwoquantitie$wilh _,antun~s.
Learn About It
Vocabulary
, ..
unll ,ale
.-~,
A rate isII ratio thaI compares numbeffi expressed in different units. A rale in which the SOCQnd term is 1is called II unit rate.
A loy factory pmduces 120 robots in 5 days. At this rale. how many robots will it produce in 20 days?
Different Ways to Solve Problems With Rates
Way 0 Use equivalent ratios.
120rOOol$ • rotx>ts 5<ằ($ • 20~
Waye Find the unll rate and multiply.
488
'!t1l!... Multiplyby the numberofdays.
o
Aretelha.! s/lON$dislanCe peruniI01limB iscalled speed.
Aslash.I. isoIIenu.cllol' theWOfdPfJ'.
'J,1t",o Divide \0 find the unit rate in robots
o per day. Per means "for each."
'~:;:S ~ ...,':"
'BY
The rale is 24 robots per day.
The rate is 55 miles per hour. or 55 mVh.
Solution; The faCIOI)' will produce 480 robots in 20 days.
Other Examples A. Speedas a Unit Rale
Acar travels 220 miles in 4 hours, Find the unit rate in m;les per hour.
--===0--
B. Use Speed to Find Time
Howlong will it take to travel 450 km at a rate 01 90kmlh?
It will take5hours.
Guided Practice
C. Rates With Money
A worker receives $75 for 6 hours of work.
Whalis lhe rate of pay per hour?
The rate is512.50 per hour
~~\l YourSelf
Find the unit rate.
I. 30 toys in 10 days
3. 60 meters in 5 seconds ,.100 miles in 4 hours
2. $20in 4 hours
4. $1,000 in 5 days
6. 50 km in 5 hours
• DidIWf~9the ooas?
• IsfTI)Ianswer
",asonable?
Explain Your thinking'" How can you use dillision to find any unit rale?
Practice and Problem Solving Find the unit rate.
7. 80 miles in 16 min 10. 160 pages in 8 days
8. 72 II in 9 secoods 11. $100 in 5 hours
II. 108 melers in 18 min 12. $56 in 7 hours
Complete the unit rate.
13. 400 mi:16 gal = • mi:l gal
.,. $6:2 OZ ., $.:1 OZ
14. 84$:12 copies = • ¢:1 copy 16. 437 mi:23 gal" • mi:l gal 17. 1,394 people:34 square miles = • people:l square l11ile
18. 288 photos:12 rolls of film - • phOIOS:l roll of film Find the distance traveled In Ihe given amount of time.
Ill. 5 hours al 50milh 20. 2.5 hours at 40 km/h 21. 12 seconds at 16 ftls 22. 0.5 hour al30 mifh 23. 7 days at 25 mi/day 24. 3 min al9 m/min
Chapter 18 Lesson 3 489
Find the lenglh 01 time lor each trip.
25. 200 mi at 50 milh 26. 75 km at 25 kmfh 27. 1.5001\ at 30IUs 28. 225 mi at 45 milh N. 252 ft at 12 fUsee 30. 175 m at 35 mfmin
X Algebra. Variables
Use the rate of 140 toy robots produced In 5 days to complete each rate.
31. nrobots in 8 days 34. 420 robots in ndays
32. nrobots in 2 days 35. 350 robots in ndays
33. nrobots in 0.5 day 3tI. 490 robots in ndays
1Q Data Use the advertisement lor Problems 37-40.
37. To the nearest cent. what is the unit price of an action figure?
38. 'Mlictl has a greater price per game.
the Action Games packageorthe Soltware 5-Game package? 'Mlat is the difference between the two unit prices?
39. 'Mlictl package of building blocks has a greater price per block, the 75-block pack or the 125-block bucket? To the nearest cent. what is the difference between the two unit prices?
40. You Decide Suppose you playa game in which you need at least 50 Can-Do Canned Zoo animals. How would you buy the animals? To the nearest cent.
what is the unit rate per animal?
~~4ãGatrIt padcage htk ot4
598 516.15
~~7s.ato<lpad< S-G~~ pad~ge
515.89 5124.15
US-Block budOl
S2J.50
Batrel of 1Z ....imal.511.50 ~'~'r=::l,~i~
Batrel 0130~nimal.
526.15
41. What's Wrong? Hal's car travels 450 miles on 15 gallons of gas. Hal
calculated that he would need 63.000 gallons for a 2.100-mile trip. 'Mlat did Hal do wrong?
490
U UULlULlLlUl
Hal
450m~15 6<'1 E 4so.15. 30 30mi per",,,lion
2.100~30~b?>,OCO b?>,OCO",,,I for2.100mi
Numberol • beats at rest Numberol • beatsahe'
~.-
TIl8 /Msiestp/ac9tolindyour
pulseIs onII>esid901yourned<.
Time
Math Challenge Heart Smart
~T£.<> Ma~ethe following table,
o r----,--::-r-:----,--,---,--,----r-,---,
1 0 1 1 1 1
second. minute hour day week
~T£.<> Ta~e)'OUrpulse for 10 seconds. Based on
o )'OUr to-second heart rate. fill in the first row Of YOU'table.
~TI'''' LeI's exercise!Do as many jumping jad<.s
o asyou can in 1minute.
~T£.<> Ta~e)'OUr pulselor 10 seconds. Based on
o )'OUr 10ãsecond heart rate after exercising.
fill in the second rCHI of )'OUr table.
Com~ete tile following activity in order to determine )'OUr hearl rate lor a minute. an hour. a day. and a wee~
Check your understanding lor Leasons 1-3.
Write each ratio three different ways.~I) • • • •
1. circles to rectangles 2. rectangles 10 circles
3. pentagons 10 circles 4. pentagons 10 other shapes Write four equivalent ratio. lor each.n.-::n2l
5. , 7' 6.81010 1.6:2 8.12t09
Complete the unit rate. '--'"31
II. 252 mi:9 gal'" • mi:1 9al 10. $3,48:6 cans" $.:1 can
Chapter 18 Lesson 3 491
• _ _ 2121 UslenMdUolOOo.laoid
Proportions
Objective LearnwhatII PfOI)OrtionislIor<lhOw10tndcross~,
Vocabulary
propottlon
Crollproduct
Learn About It
, "
to Solve 9 = 81
Martin and Tina are playing a word game. In Martin's group of tiles, theratio of vowel tiles to his total tiles is 5 to 9. This is the same as the ratio of \/OWCltiles to the total tiles in the game. The game has a tolal of 81 tiles. How many vowel tiles does the game have?
To solve the problem. you can write a proportion. A proportion is a statement that two ratios are equivalent
Martin's vowel UMl1I _ 5 n _ vowelutes inthe game Marlin's total tiles _ '9" 8t _ tOlalUlas inthe game
, "
Solve lor n. "9""8i'"
Different Ways