1-2 Practice A - mathbjaran

Name LESSON

1-2

Date

Class

Practice A Properties of Real Numbers

Find the additive inverse of each number. 1. 5

1 3. __ 2

2. 6.1

5

5 

0

6.1

6.1 

1 __ 2

1 __

0

2

0

Find the multiplicative inverse of each number. 4. 11

5. 3.5

1 ___ 11

11 ⴢ

1

2 6. ___ 3

2 __ 7

3.5 ⴢ

3 ___

2 ⴢ ___

1

2

3

1

Complete each number sentence. Make each statement true. 7. 5  7  2   5  7   5 



2

8.  4  6  3 

4

 6  3 

Identify the property demonstrated by each equation. 9. 7x  x ⴢ 7

10. c  3  5   3c  5c

Commutative

Distributive 12. 0  y   y 

11.  4  y   1  4   y  1 

Associative

Additive Inverse

Use the table for Exercises 11–14. Use properties and mental math to help you find each cost. 13. cost of a T-shirt and a hat

$16.70

The Outfit Outlet

$43.40

14. cost of 2 T-shirts and a pair of jeans

$18.80

15. cost of a pair of jeans at a 20% discount 16. total cost of one of each item

$40.20

Jeans

$23.50

T-shirt

$9.95

Hat

$6.75

Determine if each statement is sometimes, always, or never true. Give an example or property to support your answer. 17. a  b  c  3c

Sometimes; if a  b  c

18. 4x ⴢ 6  6x ⴢ 4

Always; Associative Property

19. z   z   5

Never; Additive Inverse Property

Copyright © by Holt, Rinehart and Winston. All rights reserved.

a207c01-2_pr.indd 11

11

Holt Algebra 2

12/20/05 1:22:57 PM Process Black

*À>V̈ViÊ
0ROPERTIESOF2EAL.UMBERS

,%33/.

£‡Ó

£‡Ó

&INDTHEADDITIVEANDMULTIPLICATIVEINVERSEOFEACHNUMBER    ??  

&INDTHEADDITIVEINVERSEOFEACHNUMBER  

  ?? 

 











 ??






  ?? 









??? 



  

?? 





 ???





D





 

????  



 

 X SABDAXBX

  ??? 

 ???


 ??? 









 MSNDSNDM

$ISTRIBUTIVE

#OMMUTATIVE



^

????? q
W  ?????  W q^ 


S D

  GH SGDH

#OMPLETEEACHNUMBERSENTENCE-AKEEACHSTATEMENTTRUE  SDSDS

 ?? ???

)DENTIFYTHEPROPERTYDEMONSTRATEDBYEACHEQUATION

&INDTHEMULTIPLICATIVEINVERSEOFEACHNUMBER  

*À>V̈ViÊ 0ROPERTIESOF2EAL.UMBERS

,%33/.



 SD

SD

!SSOCIATIVE



-ULTIPLICATIVE)NVERSE



5SEMENTALMATHTOFINDEACHVALUE )DENTIFYTHEPROPERTYDEMONSTRATEDBYEACHEQUATION  XX

 REBATEONACELLPHONE

#OMMUTATIVE



 DSDD

!DDITIVE)NVERSE



 

 COSTOF4 SHIRTSANDAPAIROFJEANS



 COSTOFAPAIROFJEANSATADISCOUNT



 TOTALCOSTOFONEOFEACHITEM

4HE/UTFIT/UTLET

5SETHETABLEFOR%XERCISESn7RITEANEXPRESSIONTOREPRESENT EACHTOTALCOSTANDTHENSIMPLIFYIT



 COSTOFPENSANDNOTEBOOKS

4 SHIRT





(AT



 COSTOFBINDERANDNOTEBOOKS

3OMETIMESIFABC

 XX

!LWAYS!SSOCIATIVE0ROPERTY

 ZSZD

.EVER!DDITIVE)NVERSE0ROPERTY 

T
E



(OLT!LGEBRA

Y

X

#OMMUTATIVE



 ??T ?? S ??  S   

T



$ISTRIBUTIVE





S

D

 M



0ROPERTIESOF!DDITION P

$ISTRIBUTIVE



-ULTIPLICATIVE)NVERSE

#LOSURE0ROPERTY



4HESUMOFANYTWOREALNUMBERS ISAREALNUMBER

AB;2

#OMMUTATIVE0ROPERTY



ABBA

4HEORDERDOESNOTCHANGETHE SUM

&INDTHEADDITIVEINVERSEOFEACHNUMBER

MORETIMES

  

 n



T
E

n

0OSSIBLEANSWEROFIS(ALFOFTHAT OROF IS



!DD  ANDTOFINDTHETOTALCOSTOF

 n



 q 


^

IS OFFIS




qOFFISAGREATERDISCOUNT



#OMMUTATIVE0ROPERTY !DDITIVE)NVERSE #OMMUTATIVE

 CSDC

!DDITIVE)DENTITY

 

(OLT!LGEBRA

?? 

!DDITIVE)DENTITY

 QSQ
D






!SSOCIATIVE0ROPERTY

 RSSR

0OSSIBLEANSWEROFFIS OFF



)DENTIFYTHEPROPERTYOFADDITIONDEMONSTRATEDBYEACHEQUATION

 M NMN



n


r 


 XX

 !LLMERCHANDISEATTHE3KI3HACKISMARKEDDOWN/VERTHE WEEKENDALLSALESQUALIFYFORANADDITIONALOFF0ROVETHATTAKING OFFTHEORIGINALPRICEISNOTTHESAMEASTAKINGADISCOUNT ANDTHENADISCOUNT7HICHISGREATER



  ?? 

^

??  



Copyright © by Holt, Rinehart and Winston. All rights reserved.



  ?? 

 $ESCRIBEHOWTOUSEMENTALMATHTOFINDTHETOTALCOSTFORDINNERIFTHE BILLISANDYOUADDATIP



 

4HEGROUPINGDOESNOTCHANGETHE AB CABC SUM

 'LENNBOUGHTANEWSHIRTONSALEFOROFF4HEORIGINALPRICEOFTHE SHIRTWAS7RITEANEXPRESSIONWITHOUTSUBTRACTIONTOFINDTHE SALEPRICEOFTHESHIRT4HENFINDTHESALEPRICE

AK4up_Ch01.indd 77

NnN 

!SSOCIATIVE0ROPERTY

#OPYRIGHT©BY(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

4HEADDITIVEINVERSEOFISn 4HEADDITIVEINVERSEOFnIS

n 

4HESUMOFANUMBERANDITS OPPOSITEIS

-ULTIPLICATIVE)DENTITYAND !SSOCIATIVE

(OLT!LGEBRA

NNN

!DDITIVE)NVERSE

 -ONALIVESIN&LORIDA3HEDRIVESMILESTO4EXAS(ERCARSTANKHOLDS GALLONSOFGASANDSHEGETSANAVERAGEOFMILESPERGALLONOFGAS )F-ONAFILLSUPHERGASTANKBEFORESHELEAVES HOWMANYMORETIMES WILLSHEHAVETOFILLUPTHETANKTODRIVETO4EXASANDBACKTO&LORIDA







ISTHEADDITIVEIDENTITY

!DDITIVE)DENTITY  ?? M 

3OLVE



"INDER

%XAMPLES

!DDITIVE)DENTITY

)DENTIFYWHICHPROPERTIESMAKEEACHSTATEMENTTRUEFORALLREALVALUESOFK SKD K ???????  ??  KSDK  



,iÌi>V… 0ROPERTIESOF2EAL.UMBERS

£‡Ó 



0EN



#OPYRIGHT©BY(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

,%33/.

 P

0RICE

.OTEBOOK

T
ET
ET
E

&INDTHEMISSINGTERMORTERMSANDSTATETHEPROPERTYILLUSTRATED

Y

)TEM

 COSTOFNOTEBOOKSATDISCOUNT ABINDER ATDISCOUNT ANDPENS

*À>V̈ViÊ

0ROPERTIESOF2EAL.UMBERS

 X

3CHOOL3UPPLY3TORE

T
ET
E



 ABCC

£‡Ó

.EVER T
 EqT
E T
E



*EANS

$ETERMINEIFEACHSTATEMENTISSOMETIMES ALWAYS ORNEVERTRUE 'IVEANEXAMPLEORPROPERTYTOSUPPORTYOURANSWER

#OPYRIGHT©BY(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

 ASBCDSABDSACD

!LWAYS!DDITIVE)NVERSE



5SETHETABLEFOR%XERCISESn5SEPROPERTIESANDMENTALMATHTO HELPYOUFINDEACHCOST  COSTOFA4 SHIRTANDAHAT





#LASSIFYEACHSTATEMENTASSOMETIMES ALWAYS ORNEVERTRUE'IVE EXAMPLESORPROPERTIESTOSUPPORTYOURANSWER

 YSYD

!SSOCIATIVE







$ISTRIBUTIVE



 SYDSYD

,%33/.

 COSTOFITEMSATEACH

 CSDCC

#OPYRIGHT©BY(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

77



(OLT!LGEBRA

Holt Algebra 2

12/27/05 2:48:14 PM