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Interactive Study Guide for Students: Pre-Algebra
Chapter 2: Integers
Section 1: Integers and Absolute Value
Compare and Order Integers
A _______________ _____________ is a number less than zero.
Negative numbers, zero, and positive numbers (every number
__________ on the number line) is an _____________.
To graph integers, locate the points named by the integers on a
number line. The number that corresponds to a point is called the
_____________ of that point.
A mathematical sentence containing < or > is called an
_________________. It compares numbers and quantities.
Examples
Write an integer for each
situation:
1. 500 feet below sea level
2. a temperature increase of
12 degrees
3. a loss of $250
Use the integers graphed on
the number line below:
.
-5 -3 -1
4
4. Write two inequalities
involving -3 and 4.
5. Replace
make -5
sentence.
Absolute Value
On the number line, notice that 5 and -5 are on opposite sides of 0,
and have the same distance from the origin, 0. This is called the
_______________ ___________ , or the distance from 0. Basically, it
means to take the positive of the number. The symbol is this:
______________
Example: |5| = 5 and |-5| = 5
It works kind of like parenthesis (), because you complete any
operations inside the absolute value signs _________, then take the
_______________ of that number.
with < or > to
-1 a true
6. The final round scores of
the top ten finishers of a golf
tournament were -4,-15,1,+1,+2,+5,0,+3,-10, and -2.
Order the scores from least to
greatest.
Evaluate each expression 7.|8|=
8.|9|+|-7|=
9.|-4|-|-3|=
10. Evaluate |x|-3 if x=-5.
Interactive Study Guide for Students: Pre-Algebra
Chapter 2: Integers
Section 2: Adding Integers
Add Integers
Examples
When you add integers that have the same sign, the answer will also
have that ____________. To add integers with the same sign, add
their absolute values, then give the result the ________ __________.
Find each sum
A _____________ _________ can also help you understand how to
add integers with _______________ sign.
2. -4 + (-5) =
To add integers with ________________ signs, subtract their absolute
______________, and give the result the same sign as the integer
with the greatest ____________ value.
4. 2 + (-3) =
1. -2 + (-3) =
3. 7 + (-4) =
5. -8 + 3 =
6. 10 + (-4) =
7. During the night, the
average temperature on the
moon is -140C. By noon, the
average temperature has
risen 252C. What is the
average temperature on the
moon at noon?
Add More Than Two Integers
Two numbers with the same _______________ value but different
signs are called ________________.
8. 9 + (-3) + (-9) =
Example:
9. -4 + 6 + (-3) + 9 =
4 and -4 are opposites
An integer and its opposite are also called _______________
_______________.
Interactive Study Guide for Students: Pre-Algebra
Chapter 2: Integers
Section 3: Subtracting Integers
Subtracting Integers
Examples
When you subtract integers, it is the same thing as adding its
________________ inverse.
Example: 6 – 8 = 6 + (-8)
Find each difference
1. 8 – 13 =
2. -4 – 10 =
What happens when you subtract a negative integer?
Subtracting an Integer
Adding its Additive Inverse
2 – 2 = _____
2 + (-2) = ____
2 – 1 = ____
2 + (-1) = ____
2 – 0 = ____
2 + 0 = _____
2 – (-1) = _____
2 + 1 = _____
3. 7 – (-3) =
4. -2 – (-4) =
5. In Utah in 1999, the lowest
temperature was -69 and the
highest was 117. Find the
range, or difference for that
year.
Evaluate Expressions
You can use the rule for subtracting integers to ____________
expressions.
Evaluate:
6. x – (-6) if x = 12
7. s – t if s=-9 and t=-3
8. a – b + c if a=15, b=5, and
c=-8
Interactive Study Guide for Students: Pre-Algebra
Chapter 2: Integers
Section 4: Multiplying Integers
Multiplying Integers
Examples
Multiplication is repeated ____________, So, 3(-7) means that -7 is
used three times.
3(-7) = -7 + (-7) + (-7) = -21 Also 3(-7) = -7(3)
Find each product
1. 5(-6) =
2. -4(10) =
The product of two integers with different signs is _____________.
4(-3) = -12
-4(3) = -12
The product of two integers with the same sign is ______________.
4(3) = 12
-4(-3) = 12
(+)(+) = +
(+)(-) = -
(-)(+) = -
Multiplying
Positive
(+)
(-)(-) = +
3. -6(-12) =
4. -4(-5)(-2) =
Negative ()
Positive (+)
A glacier was receding at a
rate of 300 feet per day.
What is the glacier’s
movement in 5 days?
Negative (-)
Algebraic Expressions
You can use the rules for multiplying integers to simplify and evaluate
___________________ expressions.
Simplify:
5. -4(9x)
6. -2x(3y)
7. Evaluate 4ab if a=3 and b=5
Interactive Study Guide for Students: Pre-Algebra
Chapter 2: Integers
Section 5: Dividing Integers
Divide Integers
Examples
The easiest way to divide ____________ is to divide the numbers
(without the signs) like you would normally do. Then think of the
signs of the numbers, follow these rules:












(the –‘s cancel)
The quotient of two integers with different signs is _____________.
12
 4
3
 12
 4
3
The quotient of two integers with the same sign is ______________.
12
4
3
 12
4
3
Dividing
Find each quotient:
1.
 32

8
2.
75

5
3.
 36

3
4.
48

6
ab
Positive
(+)
Negative ()
5. Evaluate
if a  6
and b  8  4
Positive (+)
Negative (-)
Average (Mean)
Division is used in statistics to find the ________________ or
__________ of a set of data. To find the mean of a set of numbers,
find the _____ of the numbers and then _______________ by the
number of items in the set.
6. Rachel had test scores of
84, 90, 89 and 93. Find the
average (mean) of her test
scores.
7.Find the average (mean) of:
-2, 8, 5, -9, -12, and -2
Interactive Study Guide for Students: Pre-Algebra
Chapter 2: Integers
Section 6: The Coordinate System
Graph Points
Examples
If you wanted to find a position on the earth, you could use a GPS
(G___________ P___________ S____________). A GPS uses Latitude
(north and south of the equator) and Longitude (east and west of the
prime meridian). This is one kind of a __________________ system
used in real life. It’s like a great big x-axis and y-axis on the world.
Recall that a point graphed on the coordinate system has an __coordinate and a ___-coordinate. Both the x-coordinate and the ycoordinate can be ___________ and _____________.
( , )
( , )
Write the ordered pair that
names each point.
1. A
2. B
3. C
Graph and label each point,
and name the quadrant.
4, D(2, 4)
5. E(-3, -2)
6. F(4, 0)
( , )
( , )
The x-axis and the y-axis divide the coordinate plane into 4
_________________. The axes and points on the axes are not located
in any of the quadrants.
Graph Algebraic Relationships
You can use the coordinate graph to show _______________
between ____ number.
The sum of two numbers is 5.
If x represents the first
number and y represents the
second number, make a table
of possible values for x and y
then graph the order pairs to
the left.
x+y=5
x
y