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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