2. Measuremetlt At amuseum. a short film starts every45 minutes. OnSaturday the fll"Sl. film start:s at 10:00AM. What time does the fifth mcMe Slaft?
I. N~ boughl 8 $UIITIJIS and gave away 3 stamps.Then she bought 4 more stamps andsold 2 $Ulmps. After buying 3 morestamps.. NJoa had 47 stamps.
How many stampsdid Nina start with?
SOlve elK:h problem.
3. Howmany IJI will balance ~ .1> ?
4tiM!!T'1ImD ! an@rnm~
Choosethe letterof the correet answer. i ; ttlCOITedIn._Isnot he~.c:hoose NH. i
;
i;
l j
i i
,;...~ i i
...j
._~;.~;.;:.;j,;;,.;---
di1J __1I.Usl<n .... _
Compare, Order,
and Round Decimals
Objective Com,:>are, order.lindfOUnddoldnIaIs,
Learn About It
Which of the numbers at the right is greater?
Compare 0.5 lind0.25.
Different Ways to Compare 0.5 and 0.25
Way 0 You ClIn use1I number line.
0.5 is to the rightof 0.25. $0 0.5>0,25. 00 0.25
I
0.' 0.75 , .0
Way 0 You ClIn compllre digits.
STEP 1 Align the decimal points. STEP 2 Staft from the left. Compare the digitS until they are different.
0.50 0.25
Solution: 0.5 is greater than 0.25.
Order 4, 4.32, and 4.317 from greatesllo least.
0.50
0.25 Since 5 > 2, 0.5 > 0.25.
You can use what youknow to order three or more decimals.
'01£.,0 Align the oeeimal ~n... Start !Iom the left.
points. Write zeros 0 Compare the digits.
if necessary.
~u... Continue
o comparing.
'.000
4.320 4.317
4.000 0 4.320 4.317
4.320 2
4.317 ,
4.000 is the least number.
4.320 > 4.317
So. 4.320 > 4.317> 4,000.
Solution: Ordered!rom greatest toleast. the numbers are 4.32. 4.317. 4.
20
Round 0.607 to the nearest hundredth.
Different Ways to Round 0.607 to the Nearest Hundredth
Way 0 You can use a number line. , I I , I '
0.607 is closer to 0.61 lhan to 0.60. "~ "~ 0.607t O.al
WayO You can use rules for rounding decimals.
STEP 1 IdenlWy the place STEP 2 Look al the digit10 STEP 3 If that digit is 5or you want10round 10. its right. greater. increase lhe
rour.dingãplace digit by t.
0.6.0.7 0.007 II thaI digit islessthan 5.
I I 00placenotdig~.changeThen drop allthe roundingã
rounding ~ce digntolhe right
digitsto the right.
0.6Q7
I
0.6t
7 >5. SO change 0 10 I.
Solution: 0.607 rounded to the nearest hundredth is 0.61.
Other Examples
A. Round 10 Ihe Nearest Tenth
0~18
' - t < 5 0.418rounds to 0.4.
Guided Practice
B. Round 10 the Nearesl Whole Number
.,,,
' - 7Osgreate<!han 5. 2 798 roundS 10 3.
~'.i\l YOurself
Order the numbers tram greatesllo least, Compare. Write >, <, or =for each • •
1.0.45.0.88 2. 0.6 • 0.006 3.4.153.4.2
• [);d I 819'l!le decimalpoints?
• WhooI "'81h& digits _em?
• Whal isIt>e digillO the right
01the r<Uldingplace?
4. 0.0825; 0.56; 0.8 $. 1.3; 1.52; 2.08
Round to the pla<:e of the underlined digit.
8. 0.0.e,5 7. 0.512 8.0.1!5 9. ;1.957
Explain Your Thinking" How does aligning the decimal points help)lOu compare decimals?
Chapter 1 Lesson 7 21
Practice and Problem Solving
Compare. Write >, <.or '" lor each e.
10.0.09.0.tl 14. 17 e 16.882
11. 0.945 • 0.941
u. 2.454 e 2.462
12. 0.3.0.300 16. 3.631 e 3.7
13. 0.023 • 0.23 17. 9.9 e 10.1
Order the numbers trom greateatlo least.
18. 4:0.425: 4.25 21. 0.34: 0.4: 3
111. 0.6: 0.68: 68 22. 3.55: 3.472: 4.14
20. 2.544: 2.545: 25.43 23. 0.72: 7.2: 7
Round to the plsee olt~underlined dl9it.
24. 0.157 28. 3219
25. fi..459 26. 7.5a8
30. 6.163
27. 28.126 31. 27.3-S.3
X Algebra. Properties Compare. Write>,<. or '" lor eaeh e,given
a'" 0.895. b = 0.75. e = 0.075, and d = 0.1.
32. be c 33.aed 34.ced
Find a digit that will maket~Inequality true.
30. 0._5 > 0.37 3$. 2.396 <2.39_
..~.
311. Australia has 2.5 persons per square kilometer. Mongolia has 1.7 persons per square kilometer. and Namibia lias2.2 persons per square kilometer. Order the countries from least to most crowded.
41. Robin weighs a bunch of green grapes and a bunch or red grapes on a digilal scale. The green grapes weigh 120.308 grams and the red grapes weigh
120.381 grams. Which bunch of grapes weighs less? Explain.
40. Represent Suppose a 10 x 10 grid represents the number 1. Use 10 x to grids to represent the numbers t.24 and 1.05. Explain how you can use the grids to compare the two numbers.
42. Many libraries use the Dewey Decimal System to classify and order books.
Books are shelved from lowest numbers to highesl numbers. Three books are numbered 1.97t.l.978.and 1,97.
Which book should be first on theshelf?
Mixed Review and Test Prep Open Response
Round each number to the place indicated by the underlined digit. PI-1, 1..om<Jns3.-.J~
Multiple Choice
49. Which sel of numbers is ordered from least to greatest?(0\. I, ~7l 43. 2.040..567
~. 12.3.08
47. 4.Z82,5
44. 0.fi75 46. 15.ZS9
48. 48.~
A 0,378; 0.42: 0,424 B 306.905: 36.999; 306.91
c 3.098; 3.089; 3.088 o 3t.333: 31.033: 3.t33
Social Studies Connection
Roman Numerals
Our numbel" system is just one way to write numbers. The Romans created a number system usillg symbols called Roman numerals.
To read Roman numerals, follow Ihese rules:
• Add Ihe numerals from left to right.
VI=5+1=6 Xl=10+1=t1
XX-l0+10-20 DC-500+100-600
• If a numeral has a value that is less than Ihe numeral Of) its right. subtract those numerals. Then continue to add.
XIV = 10 + (5 - 1) = 14
eXI.v" 100 + (50 - 10) + 5" 145 What is each number below?
I (I)
y(5)
IX (10)
L (50)
C (100)
D (500)
1. 11 2. XII 3. LXXIX 4. OXLlIl 5. oxevlI
6. Explain the similarities and differences between our decimal system and Roman numerals.
Chapter 1 Lesson 7 23
~ Chapter Review/Test
VOCABULARY
1. In the number lOS. the5 tells how many times 10is used as thefactor. 1\ is called the ----'
:l. Inthe number lOS. the 10 is caled the----,
3. A numberwritten WI __shows thevalue of each digit.
CONCEPTS AND SKIUS
Wrftt e..::11 number in standard form.~HI..",-<HI.
~5.,Pll-.4-.SI
Vocabulary
.... u,,-_
.. ..-
-- ... -
.. two milion, lour hundred Ihree Ihous8nd.seYeflty-sa
5. (4 X 10.000,000) + (7 X 1,OOO,OOO) +(9 x 10,000) +(1 X 1,000) +(S x 100)
•. two hundred twoand tweI1ly-twohundredUis
UMuponent, to write each number in .~~ncledform. '--'""2-3.",-~
7.70.900.200.408 8.1,003.080.300 •• 38 10.3.002 Round eaeh number to theplace of tile underlined digit.
~ l,pp,~~4.pp_10-13.I . - ,1,pp. 20-23)
11. 12.043 12.12£.9.53 13.12.6,925 14.37.62:8 15. 37§.255 Order the numbers Irom greatest to lent.-'-4.PI>- to-l3, ' - 7 .PI'~
1•. 37.483: 37.493: 39.473
18. 459.32I.C)02; 49,321,001: 458.399.999 PROBLEM SOLVING
FInd • pattern to soIwthe problem.
,,-"",-Ie-,.
20. Thelilelllbelship of the localstamp QOIedon' club iilOeasedsteadily in pasl
years. In2OCI3. !herewere 21 mernbeB:
in 2004. 29members: in 2005. 37
members. Howmany members is it ~keIy
to have in 2008?
24 Chapter 1 Chapter AaviewlTest
17.0.02: 0.021: 0.201
1•. 5.034.966: 5.350.955: 5.034.965
Show You Undentand ExplainthediHerence in YltIoeof each digil:in !henumber 1.111.111.
Extra Practice
Set A A.-=n 1.pp.~
Write each number in word form, short word form, and expanded form.
1. 16.362 4. 148.300
Set B A.-=n2. Pl>.I5-7l
2. 279.018
e. 567,255
3. 36,109 6. 100.002
Use exponents to write eaeh number In expanded form.
1.7,094
Set C ~3.pp, 8-{ll
2.43,729 3.309,309 4. 673,209
Write each number In standard form.
1. six huJldred lifty-three million. seventy-five thousand. one hundred forty-nine
2. (3 x 10") + (2 x lOS) + (9 x 10') + (6 x ltr') + (5 x 10') + (5 X 10') + (6 x 1(0) Write each number in short word form.
3. 34.503.598
Set D n.-:n.,pp 10-131
4.81,094.389.002 $.430.398,278.021
Order the numbers from greatest to least.
1. 84.392; 804.381: 84.492
Round each number.
3.108.27310 the nearest ten thousand Set E n.-:ns.PP 101-151
Write each de<:imal in words.
2.2.394.309: 239.410: 2,395.301
4.489,560,711 to the nearest million
1.0.069 2. 1.14 3.0.056 4.0.049 s.2.901 8.0.03
Set F ~1. W.2l.l-23)
Order the n..,mber, from lea$! to 9reate$!.
1.0.149.0.073.0.72 2. 10,002.0.103.1.03 3. 0.009. 0.15, 0.8 Ro..,nd to the place 01 the ..,nderlined digit.
5ãZãt2 6.8,5;:19 7.32.aog
I ExIraPracticeat edIIplace.comlmap I Chapter 1 Extra Practice 25
,
• _ fill.1/5Us100l .... _ _
Expressions and Addition Properties
Objective R88<1. wrile, and 9V8Iua18~$ coruaining variables and applyadd~ionproperties.
Learn About It
Steve has 4 more ride tickets than Lily has, Since you do not krlOW h-owmany tickets Lily has, you can use II variable, a leller such as x or n, to stand lor the number of tickets Lily has.
You can compare the numbe!" 01 tickets Steve has wilh the numberof tidets Lily has by using a mathematical expression thaI uses a variable.
Mathematical expressions that use variables are called algebraic expressions.
Write an expression.
Vocabulary
v8rlabl8 expreuiof>
What If Uly has1ticket? What If Uly has10tickets? What IfUly has ntlckets?
Then 1 + 4 shows how Then 10 + 4 shows how Therl n+ 4 shows how many tickets Steve has. many tickets Steve has. many tickets Steve has.
The expression means The expression means The expression means
4 more than t. 4 more than 10. 4 more than n.
Another Example
Write an Algebraic Expression In Worda Translate n - 3into words.
, - 3
J t ' -
some numoo< subtract lhr88 The expression n - 3 means to subtract three lrom some number,
28
~ Or ....rPo"I~18AnoWôtO
~ Often therei~ more than ::::: one WIJ-'1 to write IJ-n ... IJ-lge~rlJ-ic cxprellllion in
wo.-Jll. OTher f'O'l'lli~le WI>.'(ll
~ IncluJe,
~ " thrt:o!eM thlJ-n6OmO
~ numbor
~ "ta~ethree IJ-wa'lfrom
CO" 6OmO num~er
<C"" "I>. number minu!! three
-~~ C Extratoelp at etI\Iplace.comlmap
Algebraic expressiolls allow you to replace variables with different numbers.
To evaluate an expression, substitute a number for the variable.
Matt has2 fewer tickets than lily.
Wrila Ina expression lor the number ollickets Mall has.
"-2
t
"'-"""berQllid<etslilyhes
Substitute a number lot n.
It Lily has 5 tidlets,
then n - 2 becomes5 - 2.
Simplify.
Solution: If Lily has 5 tickets, then Mall has 3 tickets
The addition properties you know for wltole numbers also apply to expressions with variables.
There are three properties that make adding easier.
Addition Properties
Commuta~v"Property Associative Property Identity Property
WI>eoyou add two numbers Whenyou add numbersor Whenyou add 010anlKTlberor orvariables. you cancharlQe variables, yoo can \l"OUpthem variable. theresult is the same theorderw~houtchangW"IQ indillertl<"lt ways without numbet. variable. or sun.
""- changing the ....-n.
Example: Example: Example:
a+7=7+" (y+4)+2=y+(4+2) "+0=0+,,=,,
Guided Practice
Write an algebraic expression for each word phrase.
Translate each algebraIc expression Into words.
Then evaluate when n,. 4.
1. some number plus6 2. Siess than a number
MkYOUfle/f
• 00the words <loscribe an addition ..xpression0(a SYbtr!OClionexpression?
• Wha1 ...;If(ls(kI1 uselor
tilevariables?
3. n + g ... 1t - n ,. 14 + n $. n - 4
hpl..in 'tour Thinking'" Is the Commutative Propertytrue forsublt'aClion? Why or why not? Use Exercise2 (oc4) to expla;n your anWJ8l".
Chapter 2 Lesson 1 29
Practice and Problem Solving
Write an algebraic e~pfe6Sionfor each word phrase.
,. subtract 10 from a number •• 9 plus a number •• 3 more than a number
". take t5 from a number ". add 5 to a number ". 6 isdecreasedbya number
TranSlate eaeh algebraie e~pressioninto words.
". "+8 ". 8+e 1$. x-12 ". 12 - x ". ,+ 0
". , - 5 ". 5+y 2O.h+9 ". 16 - I ". '-y
Evaluate each e~presslonwhen a = 15.Then write >, <,or =to compare the e~pressions.
23.3+ge9+3
u. a-14e2O-a
24.3+0ea-2
2(1. (a+ 4) + 6ea+ (4 + 6)
B $6 + n 0$6 - n
Solve.
27. At 310 feeL the Millennium Force roller coaster once was the tallest coaster in the WQrld. Write an e~pression to show the height of the current record holder.
EJcplain what the variable represents, 29. Draw a diagram and write an e~pression
to show tIow many are in the group.
A group of friends went on the roller coaster.
• first car: 3 friends
• second car: 4 frief1ds
• third car: ? friends
How many are in the group if2friends are in the third car?
rOpen Response
Write >,<, or =tocompare.!G<lIdo~I
31. $3.06 e 3 dollars + 1dime
32. SO.55 e 1quarte.- + 1 nickel 33. 2 dollars e 8 quarters
30
28. To ride on the Millennium Force.
passengers must be 31 least 48 inches lall, AI is taller lhan that. Write all expression to show how tall AI is.
EJcplain what the variable represents.
30. What's Wrong? Alma wrote the associative property this way.
U tl U 1I If II llll]
9 - (!:i - 3) =(9 -!:i) - 3
EJcplain how you know what Alma did wrong.
Multiple Choice
34. Ben has S6less than Emily. Ifn
stands for Emily's money. which
e~pressionshows Ben's money?
p,.2,L.-.. 1)
An +S6
en - S6
&IraPr.\cIictseePaoe45,SetA.
00<ằ6343 1. 0.0006723: 0.0010257: 0.0004925
2. 0.0089437: 0.0089586: 0.0089564 0000086 YOtl carl round, compare, and order these very small rlumbers lhe same way you round, compare. and order Olher decimals.
Then order from greatest10least
Round each number to the nearest millionth.
,. 0.0ססoo78: 0.0ססoo72: O.
~.: : •• 0.0004624: 0.000480: O.
, -'
,-
• • •
! ~ ~ ¥~ ! ~
~ ¥I !
• j Ij Jj Ii I
I • I J , l
, • , , , • , • • ,
, • , , • • • ,
Number Sense Miniature Numbers
Engineers design larger structures likeroller
coosters, butlhey also design e.>clfemely small things. too.
A nanogui\(lris aOOutlhe sire011 blood
cell, It measures 10micmrneleffi long, One micromeler is 1 millionth of a meter. The width of each striflg on the guitar is about 50 nanometers,whicf1 is 50 bilhooths of a meter; about thesireof 100atomslThe rlumbers are shownin thep1ace-value chartbelow
Number Sense Brain Teaser .
Digit Prices
The price, in cents, of a souvenir pencil at an amusement park is a two-digit number.
The ones digit is 3 less than the tens digit The sum of the digits is 15. How much does a souvenir pencil cost?
••
••
••
••
••
••
••
••
••
••
••
••
••
••
•
Use only the di9itS 0.1, and 9to write a decimal in billionths. Use each digit atleaSl once.
Your decimal should be lhe least possible decimal that rounds up to the nearest millionth.
Education Place
Chod<0'JteduplKe.comfmllp lor more I)ra;n teasers,
Chapter 2 Lesson 1 31
• _ _ lI1lLlston ....~
Estimate Sums and Differences
Obiective Estimal8 sumsand ditkl,,,no&S,
Learn About It
vO~,:~ary I
rnun:...J
One flume ride is 3.610 feet long. Another flume ride is 1.315 leetlon9ã About how many leet differem are these lengths? An estimate is a number close 10 an exact amount Nl estimate tellsabouthow much or about how many.
You can round to estimate sums or differences.
Different Ways to round
WayO Rounding to the greatest place gives an estimate.
WayO Rounding to a tesser place is more precise. This gives
a better estimate.
3,610 1.315 - 0 -
'.000 - 1.000 '.000 Solution: Thedifference is about3,00QfL
3,610 3,600
1.315 - - 1.300
'.:lOO
Solution: The difference is about2,XlOfL
Way E) Rounding both numbers up and down gives an estimated range of answers.
Round down '.000 + 1,000 ..-
'.000
3.610
+ 1,315 - 0 -
Round up '.000 + 2,000 6.000
Solution: The sum of 3,610 and 1.315 is between 4.000 and 6.000.
Other Examples
A. Front-End Estimation Use the front digits. 3,458
+1,555 '.000
+ t ,000 '.000
3,458 + t ,555 .. 4,000
32
e. Clustering
54 + 49 + 41 + 62 + 39 +46 -?
The numbers dusteraround 50.
The,e a,e 6 numbers.
Use multiplication to astimate tha wm, 6)(50-300
54 +49 + 41 + 62 + 39 +46" 300
Guided Practice
Estimate. Tell which IT1(!thod you used.
1. 746
+ 746
2. 30.909 18,850
,. 7.749
1,654
.. ~Yourself
• DidIusethe J<lOO<ling
--
• DidIa(I(Ior subtract thefQUnded I'OJIl"Itiers
~-
Explain YourThinking" If you are estimating a sum and you roond both numbers up. will your sum begreater than orless than the actual sum? Explain,
Practice and Problem Solving
Estimate. Tell which method you used.
•• 595 •• 826 •• 7.502 , . 3.199
+ 820 ~ 371 + 2,875 + 2,539
•• 2.8003.392 •• + 9.8398,000 ". 3,5672,249 ". 9.0031,654
". 29,678 - 12,854 ". $29 + $54 ". 3,498 + 2.909 + 2,701
Solve.
1~. In one hoor, 1.076 riders rode a ooaster.
In the next hoor. 1,423 riders rode the coaster. About hOW" many riders rode the coaster in those two hoors?
17. Analy:r.e Each hour 1,834 people can ride one roller coaster, On another coaster, 1,645 people ride per hour.
Estimate the difference in the number of riders per hour.
10. Some coasters can go more than 100 miles pel' hom. The new Xcoaster 90es 76 miles perhour. About how much less thallloo miles pel' hour is that?
18. Create and Solve Write two problems about roller coasters: one that requires an exact answer and olle that requires an estimate. Solve your problems and give to a partner to solve.
Open Response
Write the value 01 the underlined di9it.
P\ " l.-=<> 1)
10. 2.!l1,475 21.907.311
20. 3~072
22. 112.tll
" . " " ' " _ , $164 00food. and$38 onsowenirs. VJIlat<id<." $45 00is l
• ~~."" ~ti=" ,r "'" ."~"' J
she spent?10>.2, l.-=<>21 Explain.
Chapter 2 Lesson 2 33
Add and Subtract
Whole Numbers
Objective Addand subltaetwhole numbers wiIh up10fMtdigits
Learn About It
On Monday 6.395 people rode on a roller coaster.
On Tuesday 2,768 people rode. How many people
rode tileroller coaster on tllOse two days?
Find 6,395 + 2,7611.
Acidtheones.
Regroup 10 ones as 1 len wher.eve,possible,
13 OI1ell - 1ten 3ones
,
6,395 +2,768
,
Add the hundreds.
RegfOUp 10 huoo,lIds as l11lousand whenlMIr possible,
11 hundreds - 1!tIoosard 1t>..ndnld
, "
6, 3 9 5 +2,768 , 63
Solution: The total is 9.163 people.
You should check your work.
~n.o Add the lens.
o Regroup 10 lens as 1 hundred wheneverpossible.
16 tens - 1 hundred 6 lerlS
"
6.395 +2,768 63
~tb Add lh"thousands.
o
, "
6,395 +2.768 9. 163
Use estimation to check.
6.395 l-!!!!!!O€> 6.000 + 2,768 lrou_,y +3,000 9.000 The sum isclose to 9,000.
Solution: The total is 9.163 people.
34
Use subtradion 10 check.
Addition and Subtraction are oppositel)( inverse operations. Opposite or inverse opera~onsare operations that uod<l and check each Olher.
Sum 9.163
- Addend - 2,768
Other Addend 6.395
How many more riders were there on Monday than on Tuesday?
You can draw a model to show the information.
Nowyou can use the model to solve the problem.
Find 6,39S - 2,168.
I Monday' 6.39S r>ders
Tuesday 2.768rders I l)!lerenoe? nder1;
. '" Subtract the ones. ..nã.. Sublract the lens.
0 Since 8> 5. you must regroup 0
I ten as 10 ones.
" "
6.3'- 6.3'-
-2,768, -2,768
"
. '" Subtract the hundreds. ..11;.. Subtract the thousands.
0 Slnce 7> 3, regroup I thousand 0
as 10 hundreds.
• l' 'j • t' 'j
•. , •••
-2,768 - 2,768
627 3. 627
Add to check.
Solution: The diflereflce is3.621 riden;.
You can also use a calculator to check.
~ ..!J -!.J -!.J ~ .!J 2J -!J -!.J .:EJ I
The difference is 3.627.
Another Example Zeros in Subtraction 30,058 - 11,814 - n
3.627 +2.168 6.395
] b 2 1 I
2 II II'~
~D.¢.58
17,874
12.184
_ Youcannot subtract 7 tens trom 5 tens. Thln~
There are no hundreds or thousands to regroup. ~--' 300"""'df80Sequats299
so reMme 3 len lhousands h~ pIvs 10 !enS
Chapter 2 lesson 3 35
Guided Practice
Add or sublracl. Check lhal your answer Is reasonable.
•• 457 , . 6.701 ,. 54.187
+ 285 + 3,495 + 12,579
•• 829 , . 3,402 •• 42.317
- 287 - 1,689 - 19,675
7. 7.814 + 543 8. 34.516 + 478 + 2.347 II. 867 - 328
,,~k loutJelf
• Do I r>ee<:l1Oregroup?
• wtl&resl>ouIdIWI~B
~.. -
...t>ers?
Explain Your Thinking" When subtracting. how do you regroup tens wllen there is a zero in the hundreds place?
Practice and Problem Solving
Add or sublracl. Check that your answer Is reasonable.
". 746 ". 952 ". 643 ". 587
+ 459 + 374 + 199 +96
... 746 " . 752 ". 500 H. 3.958
- 199 -97 -354 - 498
". + 3.985 439 ". 58.5839,407 >0. 67.109 15.407 ". + 4.782 561
22. 567 + 4.986 + 6.998 23. 5.050 - 3.328 24. 7.685 - 3.858
X Algebra. Eltpressions Find each sum or difference when
n = 1,000,000 and s = 499.
2s.n+9 26. n + 9.000 27. n + 9,000,000 26. 1,000 - s
1Q Data Use the table to solve Problems 29-32.
211. Howml.lCh longer isShockWave'" than Flashback?
30. Amile is5280 fOOL If you ride Titan twtce.
how much more orless than 2 miles have
you ridden?
31. Hem much higher isMr. Freeze'" than Aashback?
32. What is the range of heights of these roller coasters?
36
Roller Length Height
Coaster (in feet) (in feet)
Flashback 1.876 125
Mr. Freeze'" 1,480 236 Shock Wave'"' 3.500 116
Titan 5.312 255
••
-- .-
- - - - - - - - -
Ell Ell ill •• •• ••
" • -
-. •
• •• "
•
Count back 3 hours from 1:30 P....
When it is 1:30 P.M. ;n Ponland. Maine. it is 10:30 A.M, in Ponland. Oregon.
1:30 P.M. 12:30 P.M. 11:30A.M. 10:30 A.M.
Social Studies Connection Time Zones
Identify each missing time.
Each time you cross into a new time zone wtlile traveling from east to west you need to set your watch 1 hour earlier. Ponland. Oregon is located three time zones west of Ponland. Maine.
It is 1:30 P.M. in Ponland. Maine. What time is it in Ponland. Oregon?
1. 3:10 P,M. in Atlanta. Georgia is ... in Houston. Texas.
2. 1:15 P.M. in Oallas. Texas is in Las Vegas. Nevada.
3. 9:00 A.M. in Denver. Colorado is ... in New Yorl<. City. New York.
4. 8:30 ...M. in Seattle. Washington is in JaCksonville. Florida.
WEn LVCi)READf R tdup!a<e.''''''''''"P
Check your understanding of Lessons 1-3.
Evaluate each expression for n = 8.~ 11
1. n + 14 2. 12 - n 3. n - n
Estimate each sum or difference. [LioSOO'l21
4. 432 +675 5. 9.240 - 582 6. 647 +290 + 36 Add or subtract. Check your answer.(I.Malro3)
7. 548 + 397 8.1.462-841 II. 3.290 + 1.876 10. 7.005 - 1.527
I Extra PraclJCe al edujIlace.comImllll I Chapter 2 Lesson 3 37
Add and Subtract Greater Numbers
ObjactJ" UN ... _Ill,l*'lCliI _ _.
...1iorI.Of_o"*"'VII> MId _ _ lraCl \If-''''-''
Le<lrn About II
When you add or subtract greater numbers. you need to choose the most appropriate method lor solving the problem You can use mentalll1llth. pencil and paper, estimation. II calculator. orIIcomputer.
One amusement parll; hlld 2,349.783visitoBin one year. Aoolher pIf1t had 2.185.326 visitors. How many visitors did both perkstogether hI'Ye thaIyear?
Add. 2,349,783 -+ 2,185,326 _ n
I
Estimate before youNd. Round 10tl'le Wllilln, place.
The St.-nIhotAd beIIbou:.,000.000.
ThenccmpIete !he . '"i(liL
2.3<19,783 - 2.000,000
-+ 2.185.326 - -+ 2,000,000
",000,000
.1t. Add Ihe digitsin the .1£<> Add !he <igitsin ....
e thousands period. 0 rroilliOh, p£ace.
"" ""
2.349.783 2,349,783
+2,185,326 +&185,326
_-'-- ':..:'C':' :':O:9=====_'~,~'~3 5, 109
• 1b Add 1he6gitsin!he
0--2,3"9.783, , +2,185,326
'"~
Solution: The lOtaI number of visitOl'S is 4.535.109.
Another Example
You c:an UM II ClI!culalor 10lind the differ_nell in attendance .t the two~rk•.
Subtract. 2.349.783 - 2.185,326
.!.J .!.J ..!J ..!J 2J ..!J ..!J ..:J .!.J ..!.J .!.J .!.J ..!J .!.J .!.J ~ I I b ~ 'I 5 1 I
38
Add or subtract. Tell whleh method you u$ed.
Guided Practice
1. 247.625
+ 53.218
2. 746.000 - 156.923
3. 2.386.940 t,OOO,OOO
MkYourseff
• DidIregroupinI!le co<re<:l places?
• DidId>oose a
mettlodlllatmal<es
sense?
bplain Your Thinking" Whell is a computer a good choice for adding greater numbers? Whefl is it not a good choice? Explain.
Practice and Problem Solving
Add or subtract. Tell whleh method you u$ed.
4. 612.956
+ 423,890
,. 2.345.976 - 254,500
e. 617.700 + 82,430
7. 5.321.908 + 4,600,000
8. 234.809 - 150.000 9. 7.210.658 - 6,800.321 10. 547.987 - 476.000
11. 475.000 + 125.000 12. 400.000 - 73.300 13. 1.754.867 - 1235.800
Mental Math. E.timation • PaP"< and Peneil • Cak:ulato<
Roller Total Number of Rldel"$
Coaster Since Opened (to 2002)
Flight of Fear 2,768.065
The Beast 32.904.365
The Racer 39.963.282
Top Gun 9.239.507
Use the table for Problems 14-16.
14. How many fewer than 40.000.000 riders have been on the most popular ride lisled in the lable?
1'. All together. have these four roller coasters had 1 billion riders? How can you tell?
16. How many mom than 2.750.000 riders have been on Flight of Fear? Show how you got the answer
Mixed Review and Test Prep
A 36.640 • ".360 I
c 47.740 D 463.~
Chapter 2 lesson 4 39
Multlple Choice ~
23. In oneweek 213.360 pwple.rode I
on a rOlief coaSlef. How much less than 250.000 riders is that?
P>.2.t.-..4)
2o.9x2 22.7X6 18.5x2
Open Response
Multiply.~41
17. 2 x 4
la.4x4
Addition and
Subtraction Equations
Vocabulary
eoq..atlon
Objective Use mental malh 10so/Ve acldilionand soblractioneqoalion$.
You can make a model 01 the Information.
Use the madelto write an equation.
Learn About It
'*"<;rw r3fl~ts: n I Dilfeffl'nOe' :) At a rafting ride at the wate!" pari<..the blue rafts have three more seats than the yellow rafts The blue rafts have 7 seats. How many seals do the yellow rafts have?
I
... An equalion is a mathematical statement indicating that the quanlities0< expressions on either skle ot the equal sign (~)ha...e the same value.
• Write the equa~on in words. _ 'f'llloow rallseats +difference bI..e rall sealS
• Replace Itle wordswith values _ n +
l jvariables 'rom the model.
• SolveItle equation using mantal math. _ n +3 7 Replace the variable nwittl4. 4 +3 _ 7
3 ,
Solution; The yellow rafts have 4 seats.
Another Example
Write the equa~on shown by the model. Use mental math to solve the equation.
You can write an addj~on
equation.
46_n+18 n - 28
What number plus 18 equals 46? Try 28.
You can write asubtraction equation.
46-0_18 0-28 46 minus whal number equals t8?Try28
40