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Integers
Unit I, Lesson 2
Online Algebra
VHS@PWCS
Integers and the number line.
Integers are defined as whole numbers
and their opposites.
 They include the positive numbers, zero and
negative numbers.
Zero on the number line is called the
origin.
-5
-4
-3
-2
-1
Negative numbers are to the left of
zero and get smaller the farther
they are from 0
0
1
2
3
4
5
Positive numbers are to the right
of zero and get larger the farther
away they are from zero.
Comparing Integers.
Using the number line below compare the
following integers, using < or >. Click for the
answer and an explanation.
2.
-5 < -3

-5 is to the left of -3 so it is less than -3
-2 < 3

Negative numbers are always less than
positive numbers.
3.
-2 > -5
1.
-5 ? -3
-2 ? 3
-2 ? -5
1.
2.
3.

-5
-4
-3
-2
Smaller Numbers
-1
-2 is to the right of -5 so it is larger than -5.
0
1
2
3
4
Larger numbers
5
Integers and Absolute Value
 Absolute Value is the distance a number is from
zero.
 Because it is distance it is never a negative
number!
 |-3| means the absolute value of -3.

-5
-4
Since -3 is 3 spaces from zero:
 |-3| = 3
-3
-2
-1
0
1
2
3
4
5
Simplify each expression.
-5
1. |-8|
1. 8
2. |6|
2. 6
3. |-4|
3. 4
4. |0|
4. 0
-4
-3
-2
-1
0
1
2
3
4
5
Opposites
 The opposite of a number is a number
that is on the opposite side of the origin,
but with the same absolute value.
 Examples:
the opposite of 5 is -5
The opposite of -8 is 8
Adding Integers with the same
sign.
To add integers with the same sign:
1. Add
2. Keep the sign
Examples:
-5 + -9 = -(5 + 9)
= -14
-11 + -25 = -(11 = 25)
= - 36
Try these on your own!
Click for the answer.
1. -18+ -12
1. - 30
2. -21 + -16
2. - 37
3. -125 + -631
3. - 756
4. -18 + -14 + -63
4. - 95
5. -22 + -21+ -5
5. - 48
Adding Integers With Different
Signs.
To add numbers with different signs (-9 + 15)
1. Subtract the absolute values of each number.
2. Keep the sign of the number with the largest absolute
value.
Example: - 9 + 15:
1. Subtract 15 – 9 = 6
2. Keep the sign of the “larger”


Since 15 has the larger absolute value and is positive, the
answer is positive.
SO – 9 + 15 = 6
Try these on your own!
Click for the answer.
1. -11 + 8
1.

2. 24 + - 16
3. 13 + (-12)

Sometimes you will see
expressions written this way. The
parentheses just separate the
operation and the integer.
-11 + 8 = -3
2.
24 + -16 = 8

3.
4.
24 – 16 = 9, and 24 is
the “larger”
13 + (-12) = 1

4. 12 + - 45
11 – 8 = 3 and 11 is
the “larger”
13 – 12 = 1 and 13 is
the “larger”
12 + - 45 = - 33

45 – 12 = 33 and 45
is the “larger”
Subtracting Integers
The algebraic definition of subtraction is:
a–b=a+-b
Essentially this means that subtraction is
the same as adding the opposite.
So by definition:
9 – 11 = -9 + -11
We changed the subtraction to addition
and the 11 to it’s opposite – 11.
Subtracting Integers
We will use the definition of subtraction to subtract
integers. It’s just easier that way. And it
makes a lot of things in algebra easier.
To Subtract Integers:
1. Leave the first number alone
2. Change the subtraction to addition
3. Change the number after the subtraction to it’s
opposite.
4. Follow the rules for adding integers.
Subtracting Integers
-18 – 28
1. Leave the first number alone
-18 - 28
2. Change the subtraction to addition
-18 - 28
-18 + 28
3. Change the number after the subtraction to it’s opposite.
-18 + 28
-18 + - 28
4. Follow the rules for adding integers.
-18 + -28 = -46
Try these on your own!
Click for the answer.
1. -15 – (-18)

Again, the parentheses
just separate the
operation and the integer.
2. 25 - 18
3. -11 – 16
4. 17 – (- 24)
1. -15 – (-18) = -15 + 18
=3
2. 25 – 18 = 25 + -18
=7
3. -11 – 16 = -11 + -16
= -27
4. 17 – (-24) = 17 + 24
= 41
Multiplying Integers
The rules for multiplying integers are the following:
 (positive) x (positive) = positive
 (negative) x (negative) = positive
 (positive) x (negative) = negative
 (negative) x (positive) = negative
So: -7(-4) = 28
7(4) = 28
- 7(4) = -28
7(-4) = -28
Dividing integers
The rules for dividing integers are the
same as the rules for multiplying
integers:
Positive/positive = positive
Negative/negative = positive
Positive/negative = negative
Negative/positive = negative
Try these on your own!
Click for the answer.
1. -8(-9)
1. -8(-9) = 72
2. -16/-4
2. -16/-4 = 4
3. 6(-8)
3. 6(-8) = -48
4. 45/-5
4. 45/-5 = -9
5.
-12/3
5.
-12/3 = -4
Review
Wow we went over a lot in this lesson.
 Absolute value
 Opposites
 Adding, subtracting, multiplying and
dividing integers.
Check out the video from United Streaming
for another view point
Homework
Text book
 Page 23: 13 – 28
 Page 27: 7 - 16