1. 5 yard gain

2. a withdrawal of $40

3. the stock rose 8 points

4. 20 seconds before blastoff

5. a bill for $15

6. a profit of $22

7. 9º below zero

8. 125 feet below sea level

9. a bank deposit of $35

10. sea level

Evaluate.

| –7 | | 15 | | 0 |

– | 5 | – | –3 | | –7 | – | 4 |

| –2 | + |15 | | 9 | – | –4 | – | –101 |

| – 17 | – | 17 | | –13 | + | –3 | | 8 | – | –7 |

Honors Math 7 Summer Work

Integers and Absolute Value

State the integer that best describes each.

Name ____________________________

MIXED INTEGER PRACTICE

Solve WITHOUT A CALCULATOR.

–9 +13 (–7)(–5) 18 – (–6)

–3 – (–7) –9 – 18 303

−−

8(–7) –18 + (–13) –9 x (–5)

–19 + 11 6 – (–15) –54 ÷ (–6)

| –8 | – (–3) –19 + (–7) 408−

| –5 | – |–9 | –19 x | –3 | –10 – (–31)

7 + (–11) 7218−

–14 – (–11)

–9 + 18 14(–7) –12 + (–9)

– 46 ÷ (–2) 8 + (–22) –45 ÷ 9

–9 + (–3) –9(–4) –12 – 19

Order of OperationsSHOW YOUR WORK

Parentheses Exponents Multiplication and Division (in order from left to right) Addition and Subtraction (in order from left to right)

14 +18 ÷ 2 x 18 – 7

15 x 18 + 12 ÷ 3 + 9

8 x 4 + 9 – 9 + 18

11 x 11 – 6 x 17 + 4

2 – 1 + 5 x 4 x 11

16 x 7 x 15 + 11 + 17

10 – 9 x 24 ÷ 8 x 6

10 ÷ 5 + 10 – 9 x 11

3 x 19 x 14 + 18 ÷ 2

10 x 12 – 14 ÷ 2 + 15

14 ÷ 2 – 1 + 3

9 + 15 ÷ 5 x 13

2 x 10 + 10 – 8

24 ÷ 4 + 14 x 2

11 x 10 – 12 ÷ 3

8 ÷ 4 x 2 + 18

18 ÷ 6 + 4 x 15

2 – 20 ÷ 5 x 3

( 6 + 4 )2 + (11 + 10 ÷ 2 )

(9 + 33 – 6 ) ÷ 6 – 32

(10 + 43 – 5 ) ÷ 6 + 52

2 x ( 9 x 5 + 32 ) + 4

( 6 + 3 )2 + ( 9 – 10 ÷ 5 )

(10 + 59 – 32 ) ÷( 24 – 4 )

4 x (12 x 6 – 42 ) + 9

(19 – 8 ) x (10 + 4 ) + 82

PROPERTIES OF ADDITION / MULTIPLICATION

Name of Properties Example

1. Commutative Property of Addition a + b = b + a 2. Commutative Property of Multiplication ab = ba 3. Associative Property of Addition (a + b) + c = a + (b + c) 4. Associative Property of Multiplication (ab)c = a(bc) 5. Distributive Property a(b + c) = ab + ac 6. Identity Property of Addition a + 0 = 0 + a = a 7. Identity Property of Multiplication a •1 = 1 • a = a 8. Inverse Property of Addition a + (–a) = –a + a = 0

9. Inverse Property of Multiplication a • 1a

= 1a

• a = 1

Write the number of the property that describes each of the following.

1. 9 • 5 = 5 • 9 _________ 2. 7 + (4 + 8) = (7 + 4) + 8 _________ 3. 7 + 0 = 7 _________ 4. 5(6 + 4) = 5(6) + 5(4) _________ 5. –4 + 4 = 0 _________

6. 10 ( 110

) = 1 _________

7. –9 • 1 + -9 _________ 8. c + (–c) = 0 _________ 9. 8(6 • 5) = (8 • 6) • 5 _________ 10. xy = yx _________ 11. e + (f + g) = (e + f) + g _________ 12. 4 + (7 + 2) = 4 + (2 + 7) _________ 13. 6(x + 3) = 6x + 6 • 3 _________ 14. 0 + 13 = 13 _________ 15. ½ • 2 = 1 _________

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Two-Step Equations With Decimals Solve each equation. SHOW YOUR WORK.

m

2.8− 4.9 = −7.11

0.4x + 3.9 = 5.78

−10.5 + m

11.57= −2.748

9.2r + 5.514 = 158.234

v

10.44− 2.9 = −4.422

−5.4 − 7.8x = −78.408

k − 2.6

5.2= −0.418

−8.38v + 10.71 = 131.382

-1-

Two-Step Equation Problems

SHOW YOUR WORK

1) 331 students went on a field trip. Six buseswere filled and 7 students traveled in cars.How many students were in each bus?

2) Aliyah had $24 to spend on seven pencils.After buying them she had $10. How muchdid each pencil cost?

3) The sum of three consecutive numbers is 72.What are the smallest of these numbers?

4) The sum of three consecutive even numbersis 48. What are the smallest of thesenumbers?

5) You bought a magazine for $5 and fourerasers. You spent a total of $25. Howmuch did each eraser cost?

6) Maria bought seven boxes. A week laterhalf of all her boxes were destroyed in a fire.There are now only 22 boxes left. With

how many did she start?

7) Sumalee won 40 super bouncy balls playinghorseshoes at her school's game night.Later, she gave two to each of her friends.She only has 8 remaining. How manyfriends does she have?

8) Imani spent half of her weekly allowanceplaying mini-golf. To earn more money herparents let her wash the car for $4. What isher weekly allowance if she ended with$12?

Read Carefully and Solve.SHOWYOURWORK.

1).OjosdelSaladoisthehighestmountaininChile,withapeakatabout6900metersabovesealevel.TheAtacamaTrench,justoffthecoastofPeruandChile,isabout8100metersbelowsealevel(atitslowestpoint).

a. WhatisthedifferenceinelevationsbetweenMountOjosdelSaladoandtheAtacamaTrench?

b. IstheelevationhalfwaybetweenthepeakofMountOjosdelSaladoandtheAtacamaTrenchabovesealevelorbelowsealevel?Explainwithoutcalculatingtheexactvalue.

c. WhatelevationishalfwaybetweenthepeakofMountOjosdelSaladoandtheAtacamaTrench?

2) Aakash,BaoYing,ChrisandDonnaallliveonthesamestreetastheirschool,whichrunsfromeasttowest.

• Aakashlives512blockstothewest.• BaoYinglives414blockstotheeast.• Chrislives234blockstothewest.• Donnalives612blockstotheeast.a. Drawapicturethatrepresentsthepositionsoftheirhousesalongthestreet.

b. Findhowfariseachhousefromeveryotherhouse?

c. Representtherelativepositionofthehousesonanumberline,withtheschoolatzero,pointstothewestrepresentedbynegativenumbers,andpointstotheeastrepresentedbypositivenumbers.

d. Howcanyouseetheanswerstopart(b)onthenumberline?Usingthenumbers(someofwhicharepositiveandsomenegative)thatlabelthepositionsofhousesonthenumberline,representthesedistancesusingsumsordifferences.

3).Onthenumberlineabove,thenumbersaandbarethesamedistancefrom0.Whatisa+b?Explainhowyouknow.

4).Oceanwaterfreezesatabout−2�C.Freshwaterfreezesat0�C.Antifreeze,aliquidusedintheradiatorsofcars,freezesat−64�C.Imaginethatthetemperaturehasdroppedtothefreezingpointforoceanwater.Howmanydegreesmoremustthetemperaturedropfortheantifreezetoturnsolid?

5).Atthebeginningofthemonth,Evanhad$24inhisaccountattheschoolbookstore.

Useavariabletorepresenttheunknownquantityineachtransactionbelowandwriteanequationtorepresentit.Then,representeachtransactiononanumberline.

Whatistheunknownquantityineachcase?

• First,heboughtsomenotebooksandpensthatcost$16.• Next,hedepositedsomemoremoneyandhisaccountbalancewas$28.• Then,heboughtabookforEnglishclassthatcost$34.• Finally,hedepositedexactlyenoughmoneysothathepaidoffhisdebttothebookstore.

ExplainwhyitmakessensetouseanegativenumbertorepresentEvan'saccountbalancewhenheowesmoney.

6).Awaterwelldrillingrighasdugtoaheightof–60feetafteronefulldayofcontinuoususe.

a. Assumingtherigdrilledataconstantrate,whatwastheheightofthedrillafter15hours?

b. Iftherighasbeenrunningconstantlyandiscurrentlyataheightof–143.6feet,forhowlonghastherigbeenrunning?

7).Somepeopledefine3×5as5+5+5,whichhasavalueof15.

a. Ifweusethesamedefinitionformultiplication,whatshouldthevalueof3×(−5)be?

b. Hereisanexampleofthedistributiveproperty:

3×(5+4)=3×5+3×4

Ifthedistributivepropertyworksforbothpositiveandnegativenumbers,whatexpressionwouldbe

equivalentto3×(5+(−5))?

Ifweusethefactthat5+(−5)=0and3×5=15,whatshouldthevalueof3×(−5)be?

c. Wecanmultiplypositivenumbersinanyorder:

3×5=5×3

Usewhatyouknowfromparts(a)and(b).Ifwecanmultiplysignednumbersinanyorder,whatshould

thevalueof(−5)×3be?

Ifthedistributivepropertyworksforbothpositiveandnegativenumbers,whatexpressionwouldbe

equivalentto(−5)×(3+(−3))?

d. Usewhatyouknowfromparts(a),(b),and(c).Whatshouldthevalueof(−5)×(−3)be?

8).ThethreeseventhgradeclassesatSunviewMiddleSchoolcollectedthemostboxtopsforaschool

fundraiser,andsotheywona$600prizetoshareamongthem.Mr.Aceves’classcollected3,760box

tops,Mrs.Baca’sclasscollected2,301,andMr.Canyon’sclasscollected1,855.

a. Whatfractionoftotalboxtopsdideachclasscollect?

b. Howmuchmoneyshouldeachclassreceivetoreflecttheirfractionofthetotal?

9).AnnaenjoysdinneratarestaurantinWashington,D.C.,wherethesalestaxonmealsis10%.Sheleavesa15%tiponthepriceofhermealbeforethesalestaxisadded,andthetaxiscalculatedonthepre-tipamount.Shespendsatotalof$27.50fordinner.Whatisthecostofherdinnerwithouttaxortip?10).Whenworkingonareportforclass,Catrinareadthatawomanovertheageof40canloseapproximately0.06centimetersofheightperyear.

a. Catrina'sauntNancyis40yearsoldandis5feet7inchestall.Assumingherheightdecreasesatthisrateaftertheageof40,abouthowtallwillshebeatage65?(Rememberthat1inch=2.54centimeters.)b. Catrina's90-year-oldgrandmotheris5feet1inchtall.Assuminghergrandmother'sheighthasalsodecreasedatthisrate,abouthowtallwassheatage40?Explainyourreasoning.11).ThetaxifareinGothamCityis$2.40forthefirst12mileandadditionalmileagechargedattherate$0.20foreachadditional0.1mile.Youplantogivethedrivera$2tip.Howmanymilescanyouridefor$10?

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