Integers like 2 and -2 are called opposites because they are the same
distance from0, but on opposite sides. Complete the grap'hic organizer
about opposites.
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: additive inverse : ÿ
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Essential Question, i i! ÿ;
WHAT happens when you:
add, subtract, multiply, and
divide integers?
Two integers that are opposites are also called additive inverses. The
Additive Inverse Property states that the sum of any numberand its
additive inverse is zero. You can model 2 4- (-2) on a number line.
Start at zero,
I
= , I I I ÿ I f I 1
--4 -3 --2 --I
0
I
2
3
4
Move 2 units to the right to show 2.
Then move 2 units to the left to show -2.
So, 2 4- (-2)=i 01.
....... ]
The temperature outside is -5°. Name the temperature that
,
f
....
would make the sum of the two temperatures 0°. i ._ÿ
o
.=
0
E
3
Which ÿ Mathematical Processes did you use?
Shade the circle(s) that applies.
C) Apply Math to the Real World.
! C) use a Problem-Solving Model.
Q Select Tools and Techniques.
(ÿ Organize Ideas.
C) Analyze Relationships.
Q Justify Arguments.
(ÿ Use Multiple Representations.
con nectED.mcgraw-hill.com
Lesso. 1 Add Integers 203
' ÿI
To add integers with the same sign, add their absolute values.
The sum is:
• positive if both integers are positive.
• negative if both integers are negative.
Examples 3 + 4 = 7
, Determine--3 + (--2).
The model shows
Start at O. Move 3 units down
0
to show -3.
? 2
From there, move 2 units down
-3
to show -2.
.m .
--2
that the sum of
-]
2 negative integers
-2
is negative.
-3
--4
-5
-6
So,-3 + (-2) = -5.
2,. Determine --26 + (--17).
--26 + (-- 17) = --43
Both integers are negative, so the sum
is negative.
--4 + (--3) + (-5) = -7 + (--5)
= -12
Add -4 and (-3)•
Add.
.,
0ÿ" H'? Do these problems to find out.
b. --10 + (--4)
d. -8 + (-10) + (-7)
204 Chapter30l
Integers
0
To add integers with different signs, subtract their abso ute values.
The sum is:
Words
f
t
• positive if the positive integer's absolute value is greater.
• negative if the negative integer's absolute value is greater.
/
\
I
Models
I
[
//
(
........
,1
0 1 2 3 4 5 6
5. Determine--3 q- 2.
/ÿ. Determine 5 + (-3).
I
--3
Iÿ
I
,
•
0
I
i
1
I
I
2 "3
ÿ
.i
5
i
I
ÿ4
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4
I
#-ÿ
I
5
--3
'
I
ÿl
--3 i
ÿ #
I
-2
I
#
11
!
0
So, --3 + 2 = --1.
So, 5 + (-3) = 2.
Q
+2
Ii
Determine 2 + (-15) + (-2).
2 + (--15) + (--2) = 2 + (--2) + (--15)
Commutative Property (#)
----[2 + (--2)] + (--15)
Associative Property (+)
=0+(-15)
Additive Inverse Property
= -15
Additive Identity Property
i
i'
-1
Iÿ,7. Do these problems to find out.
e. 6+(--7)
f. -15 + 19
g. 10 + (-!2)
h. -13+18
i. (-14) +ÿ
5-
-7
m
a, +
-
Lesson 1 Add Integers 205
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"1
Tutor
7, A roller coaster starts aÿointA, it goesÿt, down
- 3 ÿ- n f_ÿ, and then upÿ ÿo point B. Write anÿ
sentence to find the height at point B in relation to point A.
Then find the sum and explain its meaning.
4.ÿ-(ÿ {ÿ¢ 5ÿio ÿ-ÿ : 36 4: (-32)
20 + 16 : 36
[
. Lÿoint B is 4feet hÿlÿerthan p0ÿint Zi)
[
..........
I
Add. Use a number line. (Examples I-6)
. -6 + (-8): _ÿd
.....
.
--3+10:
.._.7
....
i
.
9
©
--9 + (--5) + (--6) : -- ,Sÿ- (ÿ
-8 + (-4) + 12 =
%/
- S ÿ3 r<
5. Sofia owes her
brother$25. She ivÿher brother the
rI ÿ' $18 sheÿeamed dog-sitting. Write an additiÿon exprÿÿ
to describe this situation. Then find the sum and explain
its meaning, (E×amfle7)
....
_.ÿ.ÿ-_ -}- [(ÿ//" -7
........
Rate Yourself!
8
How co,ÿ-ÿiÿeÿ- awÿ 7otÿ aOootÿ.
Explainhow
; Building
onthe Essential Question
aÿa!.a!.iÿ iÿ{-eÿevs? ChecE ÿrhe boÿ
you know whether a sum is positive, negative; or zero
without actually adding
.........................................
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@
...............
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-a
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o
Find out online. Use the
Self-Check Quiz.
Check
c:
206 Chapter3 Operations with Integers
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it
AÿaJyze Reÿatiorÿhÿpÿ Lena deposits and withdraws money from a
12o
bank account. The table shows her transactions for March. Write anadditi__ o.n
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expression to describe her transactions. Then find the sum and explain
its meaning.
ÿ c_,
%b
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.l
I
deposit $300
withdraw $50
withdraw $75
deposit $225
-"
ProblellÿS Higher-OrderThinking
o
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131. Oreate Describe two situations inwhich opposite quantities combine to
make zero.
14. Analyze Explain why you add to find the sum of two negative integers, but
subtract to find the sum of a positive and a negative integer. Use a number
line or counters in your explanation.
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!i!
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Analyze Simplify.
7.-9+m+(-6) 7ÿ,ÿ-(.5-cI
18. Create Write an expression that cab represented by the number
oÿ
line below.
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--5 --4--3 --2 --I 012345
208 ÿeeÿ ÿ-ÿoIre pÿ8€ÿ:ÿ? Download more Extra Practice at connectED.mcgraw-hill,com.
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