Download Gr8 Integers

Grade 8 Integers!
What You Will Learn


Some definitions related to integers.
Rules for multiplying and dividing
integers.
Are you ready??
Definition

Positive number = 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
Definition

Opposite Numbers = 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 = Integers are all the
whole numbers and all of their
opposites on the negative
number line including zero.
7
opposite
-7
Definition

Absolute Value = The size of a
number with or without the
negative sign.
The absolute value of
9 or of –9 = 9.
Negative Numbers Are Used to
Measure Temperature
Negative Numbers Are Used to
Measure Above and 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 positive.
9 = +9
Integer Multiplication Rules

Rule #1 – If the signs are the same,
pretend the signs aren’t there.
Multiply the numbers and then put a
positive sign in front of your answer.
9 x 5 = +45
(-9) x (-5) = +45
Solve the Problems
-3 x -5 =
4 x 7 =
 (+3) x (+4) =
 -6 x -7 =
5 x 9 =
 -9 x -9 =

Answers
-3 x -5 = +15
+28
4 x 7 =
 (+3) x (+4) = +12
 -6 x -7 = +42
 5 x 9 = +45
 -9 x -9 = +81

Integer Multiplication Rules

Rule #2 – If the signs are different
pretend the signs aren’t there. Multiply
the numbers and put a negative sign
in front of your answer.
-9 x 5 = -45
Solve These Problems
3 x -5 =
 -4 x 7 =
 (+3) x (-4) =
 -6 x 7 =
 5 x -9 =
 -9 x 9 =

Answers
3 x -5 = -15
 -4 x 7 = -28
 (+3) x (-4) = -12
 -6 x 7 = -42
 5 x -9 = -45
 -9 x 9 = -81

One Way to Multiply Integers
Is With a Number Line
When the signs are the same, count
to the right.
When the signs are opposite, count
to the left.
2x3=6
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Multiply Integers
Is With a Number Line
(+3) x (-2) = -6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
What about dividing with
integers?
Integer Division Rule
Dividing by a negative number is the
same as multiplying by a negative
number. Same signs result in a
positive answer and different signs
result in a negative answer.
14 ÷ (-7) is the same as
-14 ÷ (+7)
= -2
Here are some more examples.
16 ÷ (-8)= -2 -33 ÷ (-11)= 3
16 ÷ (+8)= 2 -33 ÷ (+11)= -3
How do we know that “A
negative times (or divided by) a
negative equals a positive” is
true?
The following slides show
two ways to think about it…
Think about grammar! Some
people think of a negative as
meaning “not”.
So if I say I’m not not going to the
store, doesn’t that mean I AM going
to the store?
(two negatives results in a positive
answer?)
Think about patterns:
4
3
2
1
0
x
x
x
x
x
5
5
5
5
5
=
=
=
=
=
20
15
10
5
0
Both numbers are going down!
What about this pattern?:
4 x -5 = -20
3 x -5 = -15
2 x -5 = -10
1 x -5 = -5
0 x -5 = 0
The left numbers are going down
and the right #s are going up!
But if we continue that pattern:
3 x -5 = -15
2 x -5 = -10
1 x -5 = -5
0 x -5 = 0
-1 x -5 = 5
-2 x -5 = 10
-3 x -5 = 15
-4 x -5 = 20
The left #s are still going down
& the right #s are still going up!
(Neg x neg = positive)
You have learned lots of things
about multiplying and dividing
integers. Review what you think
you know with a partner!