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Integers
Definition

Positive integer – a number
greater than zero.
0 1 2 3 4 5 6
Definition

Negative number – a number
less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Place the following integers in
order from least to greatest:
297
-56
39
-125
78
0
Place the following integers in
order from least to greatest:
297
-125
-56
-56
39
0
-125
39
78
78
0
297
Definition

Opposite Numbers OR Additive
Inverse – numbers that are the
same distance from zero in the
opposite direction
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Definition

Integers – all whole numbers and
their opposites on the number line,
including zero.
7
opposite
-7
Definition

Absolute Value – The distance a
number is from zero on the
number line
The absolute value of
9 or of –9 is 9.
Negative Numbers Are Used
to Measure Temperature
Negative Numbers Are Used to
Measure Below Sea Level
30
20
10
0
-10
-20
-30
-40
-50
Negative Numbers Are Used to
Show Debt
Let’s say your parents bought a car but
had to get a loan from the bank for
$5,000.
When counting all their money they add
in -$5,000 to show they still owe the
bank.
Hint

If you don’t see a negative
or positive sign in front of
a number, it is ALWAYS
positive.
+9
Integer Addition Rules

Rule #1 – When adding two integers
with the same sign, ADD the numbers
and keep the sign.
9 + 5 = 14
-9 + -5 = -14
Solve the Following Problems:
-3 + -5 =
4 + 7 =
 (+3) + (+4) =
 -6 + -7 =
5 + 9 =
 -9 + -9 =

Check Your Answers:
-3 + -5 =
-8
+11
4 + 7 =
+7
 (+3) + (+4) =
-13
 -6 + -7 =
14
5 + 9 =
-18
 -9 + -9 =

Solve the following:
1.
2.
3.
4.
8 + 13 =
–22 + -11 =
55 + 17 =
–14 + -35 =
Check Your Answers
1.
2.
3.
4.
8 + 13 =
–22 + -11 =
55 + 17 =
–14 + -35 =
+21
-33
+72
-49
Integer Addition Rules

Rule #2 – When adding two integers
with different signs, find the difference
(SUBTRACT) and take the sign of the
larger number.
-9 + +5 =
9 - 5 = 4 Answer = - 4
Larger absolute value:
Solve These Problems
3 + -5 = 5 – 3 = 2 -2
 -4 + 7 =
7 – 4 = 3 +3
 (+3) + (-4) =
4 – 3 = 1 -1
7 – 6 = 1 +1
 -6 + 7 =
 5 + -9 =
-4
9–5=4
0
9–9=0
 -9 + 9 =

Solve the following:
1.
2.
3.
4.
–12 + 22 =
–20 + 5 =
14 + (-7) =
–70 + 15 =
Check Your Answers
1.
2.
3.
4.
–12 + 22 =
–20 + 5 =
14 + (-7) =
–70 + 15 =
+10
-15
+7
-55
One Way to Add Integers Is
With a Number Line
When the number is positive,
count to the right.
When the number is negative,
count to the left.
-
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
Answer: +3 + -5 =
-2
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
Answer: +6 + -4 =
+2
-
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
Answer: +3 + -7 = -4
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
+
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
Answer: -3 + +7 = +4
+
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive one.
Change the sign and add.
“Keep, change, change.”
is the same as
2 – (-7)
2 + (+7)
2 + 7 = 9
Here are some more examples.
12 – (-8)
-3 – (-11)
12 + (+8)
-3 + (+11)
12 + 8 = 20
-3 + 11 = 8
Solve the following:
1. 8 – (-12) =
2. 22 – (-30) =
3. – 17 – (-3) =
4. –52 – 5 =
Check Your Answers
1. 8 – (-12) = 8 + 12 =
+20
2. 22 – (-30) = 22 + 30 = +52
3. – 17 – (-3) = -17 + 3 =
-14
4. –52 – 5 = -52 + (-5) =
-57
Integer Multiplication Rules

Rule #1
When multiplying two integers with the same sign,
the product is always positive.

Rule #2
When multiplying two integers with different signs,
the product is always negative.

Rule #3
If the number of negative signs is even,
the product is always positive.

Rule #4
If the number of negative signs is odd,
the product is always negative.
Solve the following:
1. +8 x (-12) =
2. -20 x +30 =
3. – 17 x (-3) =
4. +50 x +5 =
Check Your Answers:
1. +8 x (-12) = -96
2. -20 x +30 = -600
3. – 17 x (-3) = +51
4. +50 x +5 = +250
Integer Division Rules

Rule #1
When dividing two integers with the same sign,
the quotient is always positive.

Rule #2
When dividing two integers with different signs,
the quotient is always negative.
Solve the following:
1. (-36) ÷ 4 =
2. 200 ÷ -5 =
3. – 18 ÷ (-9) =
4. +50 ÷ +5 =
Check Your Work:
1. (-36) ÷ 4 = -9
2. 200 ÷ -5 = -40
3. – 18 ÷ (-9) = +2
4. +50 ÷ +5 = +10
Evaluate the following:
1. -45 + 10
3² - 2
2. 7 + -4(9 – 4) =
3. -50 ÷ 5² + (3 - 6) =
Check Your Work:
1. -45 + 10
3² - 2
-35 = -5
7
2. 7 + -4(9 – 4) =
3. -50 ÷ 5² + (3 - 7) =
-13
-6
Evaluate the following if n = -2 :
1. -5 (2n – 2)²
2. -48
n-6
Check Your Work:
1. -5 (2n – 2)²
2. -48
n-6
-180
6
Aren’t integers
interesting?