Download c) Add Integers With a Number Line

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Working with positive and negative
numbers is like driving in traffic.
You have to watch the traffic signs
and follow the driving rules.
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Positive number – a number
greater than zero.
0 1 2 3 4 5 6
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Negative number – a number
less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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A great way to solve integers
problems is to use a number line.
Most algebra textbooks use a
horizontal number line.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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You start at the origin or zero.
Positive numbers move to the right.
Negative numbers move to the left.
Origin
(Start)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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-4 + 2 = -2
Start at the origin and move to -4
Then move to +2
Where you finish is your answer
Origin
(Start)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-4
+2
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The problem with horizontal number lines
is that they can get confusing when you
are subtracting negatives.
I prefer a VERTICAL NUMBER LINE because
it is similar to an elevator.
Origin
(Start)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-4
+2
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-4 + 2 = -2
Negative = Down
Positive = Up
-4
+2
Using a vertical number
line is easier to relate to
since most of us have
been in an elevator!
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
Watch the direction of
the elevator when we do
integer problems with
the SAME SIGN!
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
+5
1) +3 + 5 = 8
+3
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) +3 + 5 = 8
+4
2) +1 + 4 = 5
+1
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) +3 + 5 = 8
2) +1 + 4 = 5
3) -2 + - 3 = -5
-2
-3
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) +3 + 5 = 8
2) +1 + 4 = 5
3) -2 + - 3 = -5
-3
4) -3 + - 4 = -7
-4
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
+6
+2
1) +3 + 5 = 8
2) +1 + 4 = 5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
5) +2+6 = +8
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) +3 + 5 = 8
-5
-1
What do you
2) +1 + 4 = 5 notice about
the direction
3) -2 + - 3 = -5
of the integer
4) -3 + - 4 = -7 elevator?
5) +2+6 = +8
6) -5 + -1 = -6
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) +3 + 5 = 8
2) +1 + 4 = 5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
-5
5) +2+6 = +8
-1
6) -5 + -1 = -6
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A positive plus
a positive
travels up up.
A negative
plus a
negative
travels
down down.
Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) +3 + 5 = 8
-5
-1
Both signs are
2) +1 + 4 = 5 the same so
3) -2 + - 3 = -5 you end up
traveling the
4) -3 + - 4 = -7
same
5) +2+6 = +8 direction.
6) -5 + -1 = -6
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) +3 + 5 = 8
7) +3 + 10 = 13
2) +1 + 4 = 5
8) -8 + -2 = -10
3) -2 + - 3 = -5 9) -6 + - 8 = -14
4) -3 + - 4 = -7 10) +11 + 4 = 15
5) +2+6 = +8 11) -4 + - 4 = -8
6) -5 + -1 = -6 12) -3 + -9 =-12
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
Describe an easy way to add
these integers?
When the signs are the same
and you are adding,
just add the numbers and the
sign stays the same.
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
SIGNS ARE THE SAME =
TAKE THE SUM!
When the signs are the same
and you are adding,
just add the numbers and the
sign stays the same.
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
Watch the direction of
the elevator when we do
integer problems with
the DIFFERENT SIGNS!
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
-3
+5
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
2) -5 + 1 = -4
-5
+1
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
2) -5 + 1 = -4
3) +2 + - 4 = -2
+2
-4
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-3
+8
1) -3 + 5 = 2
2) -5 + 1 = -4
3) +2 + - 4 = -2
4) +8 + -3 = 5
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
2) -5 + 1 = -4
+4 -4
3) +2 + - 4 = -2
4) +8 + -3 = 5
5) +4 + - 4 = 0
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
-6
What do you
2) -5 + 1 = -4 notice about
3) +2 + - 4 =-2 the direction
of
the
integer
4) +8 + -3 = 5
elevator?
5) +4 + - 4 = 0
+3 6) -6 + 3 = -3
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A positive plus
a
negative
2) -5 + 1 = -4
travels
3) +2 + - 4 = -2 up then down .
4) +8 + -3 = 5 A negative plus
Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
-6
5) +4 + - 4 = 0 a positive
travels
6)
-6
+
3
=
-3
+3
down then up.
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
NOTICE: The
2) -5 + 1 = -4 integer elevator
is moving in
3) +2 + - 4 = -2
different
4) +8 + -3 = 5 directions
5) +4 + - 4 = 0 because both
-6
numbers
are
+3 6) -6 + 3 = -3
different!
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
1) -3 + 5 = 2
7) +10 + -2 = 8
2) -5 + 1 = -4 8) -8 + 5 = -3
3) +2 + - 4 = -2 9) -13 + 5= -8
4) +8 + -3 = 5 10)+11 + -5 = 6
-6
5) +4 + - 4 = 0 11) -12 +5 = -7
+3 6) -6 + 3 = -3 12) -9 +6 = -3
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
Describe an easy way to add
these integers?
When the signs are the different
and you are adding,
just subtract the numbers and
the larger number determines
the sign.
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Integer 8
Elevator 76
Elevator
Entrance
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
SIGNS ARE THE DIFFERENT =
TAKE THE DIFFERENCE!
When the signs are the different
and you are adding,
just subtract the numbers and
the larger number determines
the sign.
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-4 + 9 = 5
5 + -12 = -7
Write a rule to explain how to combine these
types of integers.
Different signs
Difference
of numbers
Larger number determines the sign.
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Rule #1: If the signs are the
same, pretend the signs aren’t
there. Add the numbers. The
sign stays the same.
+ + + +
+ + +
4+3=7
-4 + -3 = -7
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____
__ _
-3 + -5 =
-8
11
4+7=
(+3) + (+4) = 7
-13
-6 + -7 =
14
5+9=
-18
-9 + -9 =
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Rule #2 – If the signs are different
pretend the signs aren’t there. Subtract
the smaller number from the larger one.
The larger number determines the sign.
-9 + 5 = - 4
_ _ _ _ _ _ _ _ _
Subtract the numbers
9 - 5 = 4 Answer -4
+ + + + +
because you started with more negatives
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3 + -5 =
-4 + 7 =
(+3) + (-4) =
-6 + 7 =
5 + -9 =
-9 + 9 =
5–3=2
7–4=3
4–3=1
7–6=1
9–5=4
9–9=0
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-2
3
-1
1
-4
0
Aren’t integers
interesting?
Take out your
Study Guide!
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#5
Integer Addition Rules
If the signs are the SAME
Add the numbers. The sign stays the same.
4+3= 7
++++ +++
-7
-4
+
-3
=
_______
If the signs are DIFFERENT
Subtract the numbers. The “larger number”
determines the sign of the answer.
-9 + 5 = -4
_ _ _ _ _ _ _ _ _
Subtract the numbers
9 - 5 = 4 Answer -4
+ + + + +
because you started with more negatives
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#6
Integer 8
Elevator 7
Elevator
Entrance
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-5 + 2 = -3
Negative = Down
Positive = Up
-5
+2
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