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- .t'-l:'.i.tne: ·- - - - ----- Rational # 's and Operations - Integers and Absolute Value 1-Vrite a n integer for each situation. ' a profit of $9 Dat~ : ____, PreA!gebra ! Evaluate each expression. I 1101 io l Order the integers. I I -~ From least to greatest {O, 1, -3} -3 0 , 7 inches more than normal I j- 51 s From greatest to least {-5, -1 , -9, 10} A bank withdrawal of $50 -9, -5, -so -I IO From least to greatest {-2, 3, -8, 7, -7} 2 feet below sea level -1- 21 - 2. ! .i -2. l- 71-5 53°C below zero ~ -53 An elevator goes up 12 floors Id- Hig~erOrderThinkirg ·,. The number of yards a football team moves on the field can be represented by using the expression jsl 4j . Ho~ many yards does the football team move? H.o-.'T. PROBLEMS +I- In golf, scores are often written in relationship to par, the average score for a round at a certain course. Write an integer to represent a ·~~score that is 7 under par. - fWhich integer represents the temperature . shown on the thermometer? @ B -11°F -10°F C D 11°F 10°F REASON I NDUCTIVELY If = 3 , what is the value of x? lxl 3 ol.. - 3 One of these things is not like the other ... Identify the expression that is not equal to the other three. Explain your reasoning. .. ~~~· f~!f~· 1 -i· 2:!_!C; . . 1 A recipe calls for 2 4 cups of flour to make a t .. ~~----.w.'.~ ('.$) f~:j You have been asked to change a fraction to .a K:"" 3,,, decimal using long division. 1,.·,' --~~ batch of cookies. How frrnny batches of cookies can be made if you have 15 %cups of flour? • A fraction whose denominator is a factor of 9 will have one repeating digit. 1 EX: 3 = 0.33 • A fraction whose denominator is a factor of 99 will have two repeating digits. EX: ® Beth bought 22 trading cards, of which 20 were sports cards. What decimal shows what portion of the cards were sports cards? - / 1 - = 0.0303 33 If this pattern continues, then how many repeating digits will a fraction whose denominator is 9,999 have? Give an example that supports your answer. ., ! . 0 Oc I ooo I ~ - Na~e: ~ Dat e: - ---- - -Sheet # 03-02 Properties of Addi tion . PreAlgebra " = = = = = == = = = = " ":t it::'Z\>.l:".\ ;~l~;{~ ·Determine which equation illustrates the \,~,-:.iil State whether the example given illustrates the ~:'.'!i>b~ commutative property and justify your L'if.':'8&.tt;'~ associative property (A), or commutative ~ answer. property (C). Rational #'s and Operations - ;i::::. ~---~J.1 .. .. .. A (a+b)+ c = a +(b+ c) C a+O=a @ (a+b)+c=c+(a+b) D a+(-a)=O C. (a) x+9=9+x A (b) 100+ (52.+45)=(100+52)+45 c (c) c_ (d) Determine which equation illustrates the "' associative property and justify your answer. {) (a+b)+c=a+(b+c) B (a+ b )+ c = c +(a+ b) C D C. X. + ( y + 3 .) = X. + ( 3 + y ) (e) (6.+3)+4 =4+(6+3) Explain the difference between the Commutative and Associative Properties. a+O = a a+ (-a)= 0 A property is a statement that is true for any number. You may wonder if any of the prope1ties apply to subtraction or division. If you can find a counterexample, an example that shows that a conjecture is false, the property does not apply. 89 + 45 = 45 + 89 FFgl:· "Ol!.'=-~"" . l<!'.fif{~ Explain how you can use the commutative . mverses . property an d a dd'it1ve to h e1p you evaluate the following mental math problem. State whether the following conjecture is true or false. Iffalse, provide a counterexample. I Subtraction of whole numbers is associative. I -J 3 +- 2/ - 0 IJ - -(d - 3)-1 0 Alana wants to buy a sweater that costs $38, sunglasses that costs $14, a pair of jeans that costs $22, and a T-shirt that costs $16. Which property is illustrated by the following? 6+0=6 Additive identity B Additive Inverse C Associative Property of Addition D Commutative Property of Addition © Which property is illustrated by the following? 6+ (-6) A ® C D =0 Additive identity Additive Inverse Associative Property of Addition Commutative Property of Addition Here is an expression for the total cost. You can rearrange the numbers using the properties of math. Look for sums that are multiples often. On the lines provided, write the property used to write equivalent expressions. 38 + 14 + 22 + 16 Original expression 38 + 22 + 14 + 16 (38 + 22)+ (14+16) 60+30 90 A. Add Simplify Date: - - - - Sheet # 03-03 Ratio!'.'al #'s and Operations - Opposite Quantities PreAlgebra ~;:'." · Your hand starts with a black 7. Find three [~~~~ During a football game, Kevin gained five l~··"-~~ yards on the first play. Then he lost seven different pairs that would complete your hand and result in a value of zero. yards on the second play. How many yards does Kevin need on the next play to get the team back to where they started? Show your work. ;g••• • •• ;g ••• ••• ;g••• . -4 -3 'I.. Write an equation for each diagram. -5 -;) ·--,,·-···--···· -··--··-/.. I I ••• II I .3 I ·2 ,.1 () 1 oie l 2 4- B. ~ Write an equation to model the sum of the situation below: A hydrogen atom has a zero charge because it has one negatively charged electron and one positively charges proton. -1 + l =- O I -4 -6 -1 ···------~-!.. ~ ~ I f I I I A. I 3 4 + -tt =0 ~ l I I I ·2 -3 -4 I 0 ·1 1 2 3 4 -4+4=0 How are these e9.uations alike? 1he ~ .both comb1ru 4 aod +-(-1) ~ 0 Create a real-world story problem that models opposite quantities combining to zero. Ex : I had 6so bu}-/-kt1 J bouj h+ cf 5o (JlltKtJ Jt50-JJ5D =-o How are these equations different? s dl +~ 1 oiede( 1 1 What is it about the diagrams that lead to these similarities and differences? J21a g(am A .Stor-1- cl 0 BoeJ Iv tz19h+(+) ~v\ ~ ~Pi H) ]21a8vc.M B ~t~ ~ C\ On the number line below, the numbers h and k are the same distance from 0. Write an equation to express the value of h + k. ( • h 0 h+-t =- 0 • &..\- o go-es to 9oes b !H ¥t-) Write an addition sentence that corresponds to the arrows below . ) k •I -2 I -1 IE, 0 1 2 i:X-:,~ 3 4 5 6 lOtf ~ +ts) -::::-o 7 8 9 10 ' ·~ Each hole on a golf course is assigned a number of strokes that a player should need to make to complete the hole. If a hole is par-3, th~a player who completes the hole with 5 strokes gets a score of 2 and a player who completes the hole in two strokes gets a score of -1. A player then adds the scores for each hole on the course to find the score for the game. Half way through a game of golf, a player has a score of three under par. Write an integer to represent this situation. Then find the additive inverse of the integer, and tell what it CV'lQ.Q llS . A futeger: --:-3 Additive fuverse: 3 The additive inverse represents how many extra strokes the player can take and still complete the game in the assigned number of strokes. futeger: 3 Additive Inverse: -3 The additive inverse represents how many extra strokes the player can take and still complete the game in the assigned number of strokes. futeger: - 3· © Additive fuverse : 3 The additive inverse represents how many strokes below par the player must remain and still complete"the game in the assigned number of strokes . futeger: 3 Additive fuverse: -3 The additive inverse represents how many strokes below par the player must remain and still complete the game in the assigned number of strokes. Find the opposite of -8. a . -8 b. 1 +8 8 d. 0 0 'Vhich property is shown? 15+(13,+11}= (15+13)+11 Associative Property Commutative Property c. Identity Property d. Distributive Property <P. Tell which property is represented. 454+0 = 454 a. Distributive Property (8 Identity Property c. Associative Property d. Commutative Property Tell which property is represented. p+q =q+p. a. Identity Property b.. Associative Pr.operty @ Commutative Property d. Distributive Property • · Name: Date: Rational #'s and Operations - Adding Rational #'s Exploring "Adding Int egers" with the Integer Game - Sheet # 03-04 PreAlgebra Ms. Bisal's class is playing the integer card game. A few of her students' rounds are shown below. Please fill in all missing spaces. The first player's information has been completed for you. ~ Part A Player 1 and Player 2 added integers with the same sign. Name some similarities and differences in the number lines and the results. +3 < I I I I I I I I I I .... , _____....., I 1I l I I I I I I I > bo4fl 30+ 8 bu+ un~ d\f.f s t3nL .10 .9 .S .7 -6 .5 4 .3 ·2 ·I a 1 2 3 4 5 o i 8 9 10 Model the number sentence on the number line above to check your result. Part B Create a rule for adding integers with the same sign. Describe what happened to the value of the hand. \/Q\u e illt1?eased i_ r:mt~ ~- -3 ~lect-~ -:: -5 E -3 nbscluk valu~ s A-dd Part C Use your rule to find the follOwing 'sums. a. -4 + (-2) 012345$78910 Model the number sentence on the number line above to check • v your result. ~escribe e. -205 + (-123) -20 -32g d. -18 + (-64) b. 5 + 9 what happened to the value of the {land. Yalue c.-4+(-16) - g1 dec(e~ed f. 15 + 7 22 Part A Player 3 and Player 4 added integers with @ different signs. Name some similarities and differences in the number lines and the results. bot~ got )_ · bu+ wt '"1 d1tfe•e11.t s16 C\S Model the number sentence on the number line above to check your result.. Part B Create a rule for adding integers with different signs. ~ Describe what happened to the value of the hand. vo.\ue ·1<)c.ee <0d r4/.M4 ~$Mffl.j§4-l#\\ti!., 3 Select -5 3 +- - 5 - ') Su btro. d- o.\JscAu.k \/ o.l~J ~ Part C Use your rule to find the following sums. < I I I I I I I I I I I 1I I I I I I I I I > -10 -9 .a .7 .s .5 4 ~ ·2 .f 0 1 2 3 4 5 $ 7 8 9 10 ~fodel the number sentence on the number line above to check a. -10+7 -3 c. 6 + (- 3) 3 e. - 12 + 65 53 1our result. Describe what happened to the value of the hand. \16lue d ecr <Llhed. b. 8 + (-16) -B d. 5 + (- 9) -4 f. 105 + (-126) - 2.) Use the number line provided to model the following sums. 5 + (-6) -l+(-4) +- ' 1 A water faucet is turned then ? inches to th~nd 2 inches to th~ again. How far is the 4 water faucet turned? s s ... ... _, 3 2 5 A 3 @ 2 13 14 25 28 _I +J.. 1 '+ ~+2.\ 2.5 ii C i + (- ;) + -2 -3 -S f< ( I I I I I I I I I ·10 .g ..s .7 .Q .5 -1g -1-~ 0 -4+(-3) ~ i 4 .3 o 1 2 3 4 s s 1 a g ro l]i] Use the diagram below to complete each part. -11 II fl I I I I I I - =t- "l. -3 I I > Which of the following story problems describes the sum of 19 + (-l~)~cle all that apply. @ Alfonso's da~im $19 for raking the leaves from the yard on Wednesday. Alfonso ~ $12 at the movie theater on Friday. How much money does Alfonso have left? B Alfonso 9 his brothe;" $19 for raking the leaves while Alfonso was sick. Alfonso's dad ~hirif$12 for doing his chores for the week. How much money does Alfonso have now? Alfonso's grandmothe~hint"$19 for his birthday. ~ 8 worth of candy and ~nother$4 on a new comic book. How much money does Alfonso have left over? Find the sum of 5 + (-7) + (3) A 15 C 9 1 D -5 ® @ Arrow2 --7) Arrow 1 <-l--l-+-+--+-~-1+-+-.jo...-.l--1--J--+--+--l---l--l-+-l--I--+--+ ~ -1D ..g -8 -7 -6 .5 -4 ·3 ·2 ·1 0 1 2 3 4 5 6 7 B 9 10 Part A Label each arrow with the number each arrow represents. Part B Write ari equation that represents the sum of the numbers. Find the $Um. . ' 5 +-(-3) +(- +) ·= -5 Which is a solution of A B i 3 +x = C 4 @ 0.25 171 Danny says O? 3 4 -0.25 +- tLuis says and ~ 171 1- 71 and are the same number. 't I- 71 are different numbers. 171 and J- 7J both equal 0. Akiko says J71 and I- 71 combine to make 0. Who is correct? Mai says :.t Find the sum of 0.75 + (-0.68) A -0.07 0.07 B 1.43 D -1.43 (~ _ +_5 __ .2 .1 0 1 2 3 4 5 6 1 8 9 10 @ (-i) + : i +(-t} + s-~)}t -4 ~ 11 D What is the value of the expression below? 0 ~ 17 28 4 c @ B t-'l = l'l Luis Danny C D Mai Akiko Date: - -- - - - Name: -~--------------~ Rational #'s and Operations - Subtraction Myth Sheet # 03-05 PreAlgebra Exploring the "Subtraction Myth" with the Integer Game - Ms. Bisal's class is playing the integer card game. A few of her students' rounds are shown below. Please fill in all missing spaces. The first player's information has been completed for you. ~ L=:=-~"""-"""'""'"" . ."""~""",""""""'""" D"""i~""'c"""ar-.d""'4""""""....,.,.."""';=·_'" '~"· "'""'~=3:""","""',""""· What is the relationship between subtracting an integer and just adding its inverse? Use the players' rounds to justify your response. -4 +7 I : <I I I I I I I I I I ~ ~ • J .s ~ : I ! ! I j I 1I i I I I I I I I 4 ~ ~ ~ o 1 2 3 4 s a 1 s g m > Model the number sentence on the number line above to check your result. Write - 7 - 4 as an addition expression. Describe what happened to the value of the h and. Which of the following expressions is represented by the number Jin~ below? II I 14111 <I I I I l I I I I I -10 .9· .S .7 .S .5 4 ~ ~ 11 -5-4- 3- 2- 1 0 1 2 3 4 5 I 1I I I I I I I I I > © -4+3 -4+7 A -2 .\ 0 I 2 3 4 5 6 7 8 9 10 B Model the number sentence on the number line above to check your result. ~ ~III 3 + (-7) 0 + (-7) D Write 2 - 4 as an addition expression. . .;,scribe what happened to the value of the hand . .- ~ (a) Write the addition expression that is modeled on the number line below. < I I I I I I I I I I I 1I I I I I I I I I (b) Write the subtraction expression that is modeled on the number line below. > -10 .9 .& ·1 .S .5 4 -3 ·2 ·I 0 I 2 3 4 5 6 7 8 .9 10 Model the number sentence on the number line above to check your result. Describe what happened to the value of the hand. C I I -* -1 r4h% ~Mlffl·fol--ff\141, 4 < I I ,,-...... -10 .9 -8 Select -2 I I I I I I I I .s .7 .s ~ 4 ~ ·2 .\ I0 11 2I 3I 4I 5I sI 7I 8I 9I 10I > !odel the number sentence on the number line above to check · your result. Describe what happened to the value of the hand. I I I I -6 -$ ... -3 - l -1 0 I I I I I 1 l 3 4 I I I I ) 5 6 7 8 l l~ I Lis I Describe what happened to the value of the hand when you add a I Describe what happened to the value of the hand when you positive. subtracted a negative number. I ~~~~~~~~~~~~~~~~~~- ! ~~~~~~~~~~~~~~~~~~When we see double negatives, how can we rewrite them to make our lives simpler? 0 0 -5-(?) = -3 ~ -8 -13.5+13.5 11'\vt<Se I -5 + 2.72 Circle the integer below that will make this number sentence true. -5.~0~ 2 Name the property illustrated by the following. x+(-x) = 0 -5.5 +10.5 10 + (-5) 5 lrwe(se (a) Write an addition sentence to represent the number line below. -~ -4+50 20$ 6) +-3 -1+ 5+-~-20 ~..v+b (-1 -r -20) t{5 +-b) -24 + II -13 +(-13) (b) Write a subtraction sentence to represent the number line below. -s-3 i. - 3 ;. -g I I I I I I I !c:ncl -12-11-10-9-8-7-6-5-4-3-2-1 I I I 21 + (-16) 12. J.:.::!38.7) ..[, lb 12..?,t ~-t I 0 25+(-5)EG2) -2+(-6) +5 1,. - 8 +5 l -3 2.2.. "" 25 + -5+ 2 (2s+-21 -1---s 2. t + -5 PreAlgebra Sheet # 03-06 Apply properties to simplify the expression. Name each property. Apply properties to simplify the expression. Name each property. (-!+%)+~ 1 5 2 6-+5--13 9 3 1t- - 3 +~· Ji ·~ 2-Q .f- - Lt+~ q .~ ({ I ~5/q q 3 @ s A. _Lf_ I <;Ji . Cl Apply properties to simplify the expression. Name eaijcroperty. rrD+ 1- _'!__ 11 8 l§l 5 T J_9_ .f- -5- +- S'b 3 3 7 Jjj_ +-32. s 3 . 12 r C1J Cj er·- 992 5'-' - ~JD 2..1 °~~ Apply properties to simplify the expression. Name each property. BJ @!E}}(-~) 5 J_ +~..§..¥ 5'· · ~ · 5~ ,,,-..... fl+ -:--6±. Apply properties to simplify the expression. Name each property. 'tO 8 5 E&' t -+ 8' 10 0 .!2 + (?:_ - Z) 'Vv 8 +~ s Apply properties to simplify the expression. Name each property. .IL+ 2-f, ~+>;,Q \!__?J . ~+(~-7-) 8 5 8 1' - 9 + 6E!:X>)+ 4-2 + 9 t~~ Apply properties to simplify the expression. Name each property. ~ ! Date: _ _ __ . Name:--------------Rational #'s and Operations - Applying Properties · I f ob\:rt'l 0 (j)t-G + f, +4 +-2@ J j(o f- -2 @ ~ Evaluate -8 + 8 A @ o -16 16 B Which of the following is a way to find tlie value of - 4 + (-6) ? D 8 Marissa simplified the expression shown below as follows. A Find the absolute value of the sum of 4 and 6 B Subtract 4 from 6 and find the absolute value of the difference C Find -4 on the number line and then move 6 units to the right 10 - 25 - 6 + (- 2) -15-6+(-2) Stepl -9+(-2) Step2 -11 Step 3 @ Find -4 on a number line and then move 6 units to the left Which of the following describes Marissa's mistake? i0-25 ,$' In step 1, she should have replaced 10-25with 15, not -15. IO f- -25 ,,:ff' In Step 0 -/5 +-6 @ In Step 2, she should have replaced D 23 28 1 -- © 8 -15-6with-21,not -9. c In Step 3, she should have replaced - 9 + (-2) with - 7, not -11. D ·- 21 - +8 4 A 1, she should have replaced 10- 25with -35, not -15. @318) Evaluate: 25 56 5 - 7 -3_ +_!_·2 '+ ) ~ -3 2 --t-8 %' -~ 8 On the number line shown below, point Q has a value of 8. Q -10 !6 8 10 What number must be added to 8 to get a sum ofO? ~ -8 c 0 -8 -4 -6 B -2 0 2 D -4 4 8 B 1 -45 _,e"' 3 _!_!_ 24 Point A is shown on the number line below. A -4 -3 -2 -1 ;p( 4..!. __p+ +- -1·1-'1- .2.i .21 -83 24 5 0 -2 <:; Which of the following is the additive inverse of the number represented by point A? .t\ -3.5 c:: 3.5 B -2.5 2.5 <ij) • Which subtraction sentence is shown by this model? .,,.-...~.r""\~ 11J' . I --6 . . . 5 I ~ I I· + f -3 -2 -1 .t\ -5 - 1=4 B -5-4=-1 © D 0 I 1 f• 2 -1-4 = -5 -5-(-1)=4 Simplify: - _!_!_ + (-1 ~) 16 8 15 .t\ -If . -15 2.. 16 t- j(Q ~ ·Z 15 )Y 16 - ii f- - 2(o fb 5 HS -2 16 © y - 2.!2 16 - 3:+ ·- · i l:i Date: _____ Pr e Algebra . Name: Rational # 's and Operations - Applications Sheet # 03-07 [ ~·>nlimmptDi§i•tniriffi,MR \o 0 r each of the following problems: ART A Write an expression to describe the situation In a footb all game, Matt gained 10 yards on his first carry. He was tackled for a loss of 12 yards on his second carry. Write a subtraction expression to represent Matt's net yardage after the first two plays. PART B Evaluate the expression from part A . Part C Explain the meaning of the result found in part B as it relates to the situation. 10+-I{_ (I 0 -12 ( Larissa owes her older brother $25 . She gives her brother $18 she earned dog sitting. PART A PARTB The temperature outside is -3°F. An hour later, it drops 6°F and 2 hours later, it rises 4°F. -J 5 f 18 PARTA -=t PARTB ----- PARTC Ms. Bisal is on a television game show! The scoreboard shows she gained 100 points, lost 150 points, lost 350 points, gained 500 points, and then lost 50 points. You need 100 points to win the game. Did Ms. Bisal win? - ?;t-G+t -q -r4 -5 ---'----- Show all work. 100 + -1 S'o+-3.fO -t~o+-so JO o t~oo PARTC std/ owe:; $:} J 5 deq1ees he/tfiV 0 C;oo A pelican starts at 60 feet above sea level. It descends 60 feet to catch a fish. PART A PART A PART B __.0'----- fl aJ sea fevef PARTB 3 +-1 -I ----- ~ - ((;2. PARTC . /05} l · Withdrawal $100 $65 $56.25 $26.30 $20 $98.18 ~ 18 ~ - / 80-13 Tiziana' s bank charges a $5 fee if she has a negative balance. If she has a positive balance they give her a bonus 1 of - - of her balance. What is her final balance after the fee 25 or bonus? Show all work. t I PART B J Deposit Birthday check Babysitting Money New Outfit Movie Date Allowance Valentine Gift Brenda has a balance of -$52 in her account. The bank charged her a fee of $10 for having a negative balance. -52f--/O . The following chart shows Tiziana's withdrawals and deposits for the month of February. PART C PART A o -1 < t -3c;-o +- -m + - 5s-o 50 The platform on a diving board is 3 meters high. A diver dives 4 meters off the platform. GO t -Go + I! I owes bat'IK Jt0l I f 8 ~ . 00 I Bo .13 +21 Ne"° Ba lartu +. i 1./-- . 11- · · ~.~~ Which of the following situations could be '- represented by the equation shown below? A submarine is traveling at a depth of 152 feet below sea level. The submarine was given instructions to rise to 63 feet and then drop 84 feet. Part A: Write an expression that describes this situation. ~ -/52.+G3-I- ~8t -/=I 3 Part B: Simplify the expression. Fl 3 ~ Part D : What does the opposite represenn 4i this situation? /Jee r .leue ·~ A toy superstore is selling a video game for a special price. The store receives shipment on Monday, Wednesday and Friday. The table shows the number of video games shipped to the store and the number sold during the w eek. Use this information to find the number of video games the store has left at the end of the week. Received Mon day Tuesday Wednesday Thursday Friday 15 6 7 19 27 41 28 q/ -15 r 10J ~r 1J A construction worker was 4 feet under the gro)Jnd. He went up l 0 feet. How many feet is the construction worker above ground? @ 6 c -6 D 14 @ 104 D -25 -J-s Doug has 3 swings his first time at bat in a baseball game and another 3 swings his second ®ies at bat, but makes a total of 0 hits. Yvette overdrew her account with a check, making her balance -$10. She deposited $10, bringing her balance to $0. The lowest temperature in Ji-Yeon's town last year was -4 degrees Farenheit (°F), and the lowest temperature this year was also -4 °F, which is a difference of 0°F. . i __________ ______.---.., J +-«> rl"rSJ 12<1 -1' B Create your own real world application problem which involves the combining of negative and positive numbers. -1 f-(0 A running back rushed for 129 yards through 3 quarters. In the 4th quarter the running back lost 5 yards per rush. The running back rushed 5 times in the 4th quarter. How many total yards did the running back have after the 4th quarter? A . 154 C 144 /Jqt-5+-s- Sonya spends 8 hours volunteering for $0 per hour, for a total pay of $0. D @ -14 Manuel is 2 Yi miles away from the end of a bicycle race. He is ridding at a speed of 6 miles per hour, so he will finish in 3 Yi hours. A © Val's Submarine was 400 yards below sea level at 4:00pm. By 8:00 pm it had risen 300 yards. What integer represents how far from sea level Val's submarine was at 8:00pm? A 700 C 100 B -700 -100 A Luke spent 2 Yi dollars on a salad and another6 dollars on a sandwich, so he has 3 Yi dollars left. Which if the following best describes a situation in which the sum of a number and its opposite is equal to O? Sold 23 The temperature one morning was -2 'h degrees Celsius (°C). It increased by 6 °C during the day to reach a high of 3 Yi °C. Jana studied for 2 Yi hours, starting at 6:00 P.M., so she still needs to study for 3 'h more hours. Part C: What is the opposite of the number you received in partB? 11~ /eel ahoue - 2_.!._ +6=3_.!._ 2 2 i . Nam~: Rational #'s and Ope.rations - Distance on a number line drwwet h4 Two players are on the field below. Note their positions. What is the distance between the two players? Date: _ _ _ __ Sheet # 03-08 PreAlgebra What is the distance between -9 and -3? /-q--3) ~ J-q+3J~J-"J ~f£1 Use the number line below to check your answer. ' 1- i " 1<¥"'<YYY=i1 t - q - 8 -1 -" -S' -~ -3 What is the distance between -2 and 5? J -1 For a science project, Richie recorded the temperature when he woke up and when he went to bed for three days in January. His results are shown in the table below. Find the day with the greatest change in temperature. _.,.._.~, ' Montfr' ~~~-:~ '; ·f.;fStart ,. End ,'· '·r Start+ End -s 10+ , ,-- 10°F Monday 15°F 35°F -s -1-2..0 _5op ~5- - ~o- - 25- - 15- - to- - o- s~ .:.S- < ;;· Start ·; 'End · I;'· 01s'ianC:e '· 10- Use the number line below to check your answer. .------lI ~ w- - -s -2 -I 0 I 2. 3 1 5 What is the distance between 5 and -3? J5--3J __, Js+3\~ lBl-" 8 Use the number line below to check your answer. -I ~ -3 -2. -I O s ~---B , o +-s 15 15 f) t 3) I) - 3~ '~ .. -3~ 50 Wednesday - -5°F 5 Tuesday 'K'10- 20°F I 5 -20 20 -s-20 -:zs At 6 A.M. the temperature was-5 °C. In the afternoon, the temperature was 10 °C. What was the change of temperature during the day? / -15 °C Wer1• up S<l DO!l.,1"e I ft' H 0 -5 +-lo 25 A. Is there a relationship between the sum of each pair of integers and the distance between them? If so, explain. No Hes . "01.sfaoct 1s alwa'/> ~ ~~-~~-----;P~O~S-'~-~_e_d_,_fl_e_,c_~~ ~~-~ (absolule value) -5 oc 10 °C 15 oc r . -5 -IO - S" t" - 10 -/\ A valley is 7 5. 5 feet below sea level. A nearby plateau is 125.75 feet above sea level. What is the difference in elevation between the two locations? /:)5. ..,.~ @ 50.25 ft c 133 .3 ft - -:f 5.\o B B. Is there a relationship between the difference of each pair of integers and the distance between them? If so, explain. - 5 I ~ I -2 ~ -s \ ~ l -1- I -=, + 118 .2 ft D 201.25 ft s' 0.2.s Which of the following expressions represents the distance between -12 and -5 on a number line? @ B j-12-(-5)j c j- 12 + (-5)j j-12-5j D j12+5j r - ,. Jgl · 3 ~. l ·.~ Ali caught a fi sh that weighed 9.5 pounds. ' Lisa Li~j caught a fish that weighed 5% pounds. How much FIND THE E RROR "' Demi Lovato is finding -15 - (-1 8). Find her mistake and correct it. rr + / a more did Ali 's fish weigh? 1 - 5. l 5 3. 1 S jbs 18 -3 [[] ~ ~ . f 10 q. ~ - 5. r 5 -1\ Fill in the blank in the sentence below with the correct term. The absoJuk'{a lu e of a number is the distance between the number and zero on a number line. ru or false? When@ is a negative integer, n - n At 6:00am the temperature was -6 °F. By 3:00pm, the temperature has dropped by 8 degrees. -~ Part A -s~;; - cl -8 0 - - 14° F Use what you know about adding and subtracting integers to explain why your answer is correct. Use words and/or numbers to support your explanations. B 4+(-7) : -3 D l-21+7+(-ll) l .. :J. ... -11 q +- 11 dvopp inr 1~ ae5ahve. ' add r Keep. SaMR s~f1s Which of the following is equal to -8? - z. A B 15-7 =-8 -15 - 7 :. -l z. C 15~) -2 -1 0 1 2 3 4 © 5 Which of the following expressions represents the distance between -4 and 5 on the number line? A B J-4+51 l4-5J c ® <25 +- J-5-(-4)J l-4-51 Jake owes his sister $3. She decides to "take away" his debt. That is, he does not have to pay her back. Write a subtraction sentence for this situation. A geologist finds a layer of shale 2 % feet below ground level, represented by the number -2 %, and a layer oflimestone 4_! feet - 8 o { - 2 ~ --1 !~ c G) l~feet 8 B 1~ 8 2 ~ feet feet l3 ~ 1+ n 1 Define integer. Give an example of a number that is an integer and a number that is not an integer. a.L..:t"""' e9 Pe."<JL '- 5 [-Jl , _ 3.3 lI __ __,alo!. t:~e_.!!~=_h~~:;i.l:~. .4:~ f '' _.la~ .l (l~d__:j~ ~1~l-::___ ~ ._,_ f i 8 3E:::E -3+.3 below ground level, represented by the 1 · numb er - 4. What is the distance between 8 these two layers? -=- ~ Which sentence about integers is not always J _ 5 ~ _3 true? Positive - positive = positive B Positive + positive = positive C Negative + negative = negative D Positive - negative = positive A number line is shown below. -3 2.Z. ~ - 15@7) + -4 ( lovus-~1. Which of the following numerical expressions results in a positive number? A - 4 + (- 7) :: - JI 4 + 7 ;: 3 PartB -5 0 -5r5;0 J .- (o -t- -5 What was the temperature at 3:00 pm? =0 . '6 ! opp OS j bVO I = =;z. o .: . ~ 1- ~'t ~ l ==="""-f:x: : :s:,:-=3====a=o=o=e=>=< =·==-~'-2==5=.·-: . :2=== 6 feet Ye 1~/B 1