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Chapter 2: Integers and
Exponents
Regular Math
Section 2.1: Adding Integers

Integers are the set of whole numbers,
including 0, and their opposites.

The absolute value of a number is its distance
from 0.
Example 1: Using a Number Line to
Add Integers

4 + (-6)
Try this one on your
own…

(-6) + 2

-4
Example 2: Using Absolute Value to
Add Integers

Add…

-3 + (-5)

Try these on your
own…



4 + (-7)


1 + (-2)
(-8) + 5

-3 + 6

-3
(-2) + (-4)


-1
-6
7 + (-1)

6
Example 3: Evaluating Expressions
with Integers

Evaluate b + 12 for b = -5



-5 + 12
7
Try this one on your own…

Evaluate c + 4 for c = -8


-8 + 4
-4
Example 4: Health Application
Monday Morning
Calories
Oatmeal 145
Toast with Jam 62
8 fl oz juice 111
Calories Burned
Walked six laps 110
Swam six laps 40

Katrina wants to check
her calorie count after
breakfast and exercise.
Use information from
the journal entry to find
her total.


145 + 62 + 111 – 110 – 40
168 calories
Try this one on your own…

Katrina opened a bank account. Find her
account balance after the four transactions,
listed below.


Deposits: $200 and $20
Withdrawals: $166 and $38

200 + 20 -166 – 38 = $16
Section 2.2: Subtracting Integers
Example 1: Subtracting Integers

-5 – 5

2 – (-4)

Try these on your
own…

-7 – 4


-11 – (-8)

8 – (-5)


-11
13
-6 – (-3)

-3
Example 2: Evaluating Expressions
with Integers

4 – t for t = -3




-5 – s for s = -7




4 – (-3)
4+3
7
-5 – (-7)
-5 + 7
2
-1 – x for x = 8



-1 – 8
- 1 + (-8)
-9

Try these on your own…

8 – j for j = -6


-9 – y for y = -4


14
-5
n – 6 for n = -2

-8
Example 3: Architecture Application

The roller coaster Desperado has a maximum
height of 209 feet and maximum drop of 225
feet. How far underground does the roller
coaster go?
Try this one on your own…

The top of Sears Tower, in Chicago, is 1454
feet above street level, while the lowest level is
43 feet below street level. How far is it from
the lowest level to the top?


1454 – (-43)
1497 feet
Section 2.3: Multiplying and
Dividing Integers
Example 1: Multiplying and
Dividing Integers

Multiply or Divide.

6(-7)



-5
48


-3
40
-18/2


-24
-8(-5)

18 / -6

-6(4)

-12 (-4)


Try these on your
own…
-45 / 9


-42

-9
-25/-5

5
Example 2: Using the Order of
Operations with Integers

Simplify…

-2(3 - 9)

4(-7 - 2)

-3(16 - 8)
Try these on your own…

Simplify…

3(-6 - 12)


-5(-5 + 2)


-54
15
-2(14 – 5)

-18
Example 3: Plotting Integer
Solutions of Equations.

x
-2x – 1
y
(x,y)
-2
-2(-2) – 1
3
(-2,3)
-1
-2(-1) – 1
1
(-1,1)
0
-2(0) – 1
-1
(0,-1)
1
-2(1) – 1
-3
(1, -3)
2
-2(2) - 1
-5
(2, -5)
Complete a table of
solutions for y = -2x – 1
for x = -2, -1, 0, 1, 2.
Plot the points on a
coordinate plane.
Try this one on your own…

Complete a table of
solutions for y =3x – 1
for x = -2, -1, 0, 1, and
2. Plot the points on a
coordinate grid.
x
3x-1
y
(x,y)
-2
3(-2) – 1
-7
(-2,-7)
-1
3(-1) – 1
-4
(-1,-4)
0
3(0) – 1
-1
(0,-1)
1
3(1) – 1
2
(1,2)
2
3(2) - 1
5
(2,5)
Section 2.4: Solving Equations
Containing Integers

Example 1: Adding and Subtracting to Solve Equations

Solve…

y+8=6

-5 + t = -25

x = -7 + 13
Try these on your own…

x – 3 = -6


-5 + r = 9


r = 14
-6 + 8 = n


x = -3
n=2
Z + 6 = -3

z = -9
Example 2: Multiplying and
Dividing to Solve Equations

Try these on your
own…

Solve…

k / -7 = -1

-51 = 17b
-5x = 35



x = -7
z / -4 = 5

z = -20
Example 3: Problem Solving
Application

Net force is the sum of all forces acting on an
object. Expressed in newtons (N), it tells you
in which direction and how quickly the object
will move. If two dogs are playing tug-of-war,
and the dog on the right pulls with a force of
12 N, what force is the dog on the left exerting
on the rope if the new force is 2N?
Try these on your own…

Sarah heard on the morning news that the
temperature had dropped 26 degrees since
midnight. In the morning, the temperature was
-8 degrees. What was the temperature at
midnight?


-8 = x – 26
x = 18 degrees
Section 2.5: Solving Inequalities
Containing Integers

Solve and Graph…

w + 3 < -1

Try these on your
own…

k + 3 > -2


n – 6 > -5

r – 9 > 12


r > 21
u–5<3


k > -5
u<8
c+6<2

c < -4
Example 2: Multiplying and
Dividing to Solve Inequalities

Solve and Graph…
 2d  12

Try these on your
own…

Solve and Graph.
 3 y  15
y
5
2
7m  21
t
2
5
z
3
1
Section 2.6: Exponents

Power

Exponential Form

Base

Exponent
Example 1: Writing Exponents

Write in exponential
form.




3x3x3x3x3x3
(-2)(-2)(-2)(-2)

Try these on your
own…

4x4x4x4

DxDxDxDxD

(-6)(-6)(-6)

5x5
NxNxNxNxN
12
Example 2: Evaluating Powers

Evaluate…
26
( 8) 2
( 5) 3

Try these on your own…
35
( 3) 5
( 4 ) 4
28
Example 3: Simplifying Expressions
Containing Exponents

Try this one on your
own…
(2  3 )  6(4)
5
2

Simplify…
50  2(3  2 )
3
Example 4: Geometry Application

The number of diagonals of an n-sided figure
is
. Use the formula to find the number
of diagonals for a 5-sided figure.
1 2
(n  3n)
2
Try this one on your own…

Use the formula
to find the number of
diagonals in a 7-sided figure.
1 2
( n  3n)
2
Section 2.7: Properties of Exponents
Example 1: Multiplying Powers with
the Same Base

Multiply. Write the
product as one power.
3 3
5
7
n5  n7
10
25  2
16 16
a a
6 4
4
Try these on your
own…
6 6  63
2
10

4
24 4  24 4
Example 2: Dividing Powers with
the Same Base

Divide. Write the
quotient as one power.
1009
1003
x8
y5

Try these on your
own…
5
7
73
x10
x9
Example 3: Physical Science
Application

There are about 10 molecules in a cubic meter
of air at sea level, but only 10 molecules at a
high altitude (33km). How many times more
molecules are there at sea level than at 33 km?
25
23
Try this one on your own…

A light-year, or the distance light travels in one
year, is almost 10 centimeters. To convert
this number to kilometers, you must divide by
10 . How many kilometers is a light year?
18
5
1018
15

10
103
Section 2.8: Look for a Pattern in
Integer Exponents

Example 1: Using a Pattern to Evaluate
Negative Exponents

Evaluate the powers of 10.
10 3
10  4
10 5
Try these on your own…

Evaluate the powers of 10.
10
10
10
2
1
6
Example 2: Evaluating Negative
Numbers

Evaluate…
( 2)

3
Try this one on your
own…
5
3
(10)
3
Example 3: Evaluating Products and
Quotients of Negative Exponents

Try these on your
own…

Evaluate…
103 10 3
2 5  23
4
5
6
8
6
3 4  35
2
27
Section 2.9: Scientific Notation

Scientific Notation is a method of writing
very large or very small numbers by using
powers of 10.
Example 1: Translating Scientific
Notation to Standard Notation

Write each number in
standard notation.
2.64  10
1.35  10

Try these on your
own…
7
1.35  10
4
2.7  10 3
 5.8  10
6
5
 2.01  10
4
Example 2: Translating Standard
Notation to Scientific Notation

Write 0.000002 in
scientific notation.

Try this one on your
own…

Write 0.00709 in
scientific notation.
7.09  10
3
Example 3: Money Application

Suppose you have a million dollars in pennies.
A penny is 1.55 mm thick. How tall would a
stack of all your pennies by? Write your
answer in scientific notation?
Try this one on your own…

A pencil is 18.7 cm long. If you were to lay
10,000 pencils end to end, how many
millimeters long would they be? Write the
answer in scientific notation.
18.7 10,000
1.87 10
5