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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.
0 1 2 3 4 5 6-1-2-3-4-5-6
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A great way to solve integers problems is to use a number line.
0 1 2 3 4 5 6-1-2-3-4-5-6
Most algebra textbooks use a horizontal number line.
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You start at the origin or zero.
0 1 2 3 4 5 6-1-2-3-4-5-6
Positive numbers move to the right.
Origin(Start)
Negative numbers move to the left.
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0 1 2 3 4 5 6-1-2-3-4-5-6
-4 + 2
Origin(Start)
Start at the origin and move to -4
-4
Then move to +2
+2
Where you finish is your answer
= -2
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0 1 2 3 4 5 6-1-2-3-4-5-6
Origin(Start)
The problem with horizontal number lines is that they can get confusing when you are subtracting negatives.
-4
+2
I prefer a VERTICAL NUMBER LINE because it is similar to an elevator.
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
-4 + 2 =-2
-4+2
Positive = UpNegative = Down
Using a vertical number line is easier to relate to since most of us have been in an elevator!
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
Watch the direction of the elevator when we do integer problems with the SAME SIGN!
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
+3
+5
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
+1
+42) +1 + 4 =5
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
-2
-3
2) +1 + 4 =5
3) -2 + - 3 = -5
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
-3
-4
2) +1 + 4 =5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
2) +1 + 4 =5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
5) +2+6 =+8
+2
+6
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
2) +1 + 4 =5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
5) +2+6 =+8
6) -5 + -1 = -6
-5
-1
What do you notice about the direction of the integer elevator?
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
2) +1 + 4 =5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
5) +2+6 =+8
6) -5 + -1 = -6
-5
-1
A positive plus a positive travels up up.A negative plus a negative travels down down.
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
2) +1 + 4 =5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
5) +2+6 =+8
6) -5 + -1 = -6
-5
-1
Both signs are the same so you end up traveling the same direction.
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) +3 + 5 =8
2) +1 + 4 =5
3) -2 + - 3 = -5
4) -3 + - 4 = -7
5) +2+6 =+8
6) -5 + -1 = -6
7) +3 + 10 =13
8) -8 + -2 = -10
9) -6 + - 8 = -14
10) +11 + 4 =15
11) -4 + - 4 = -8
12) -3 + -9 = -12
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
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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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
When the signs are the same and you are adding, just add the numbers and the sign stays the same.
SIGNS ARE THE SAME = TAKE THE SUM!
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
Watch the direction of the elevator when we do integer problems with the DIFFERENT SIGNS!
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
-3+5
1) -3 + 5 =2
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
-5+1
1) -3 + 5 =2
2) -5 + 1 =-4
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
+2-4
1) -3 + 5 =2
2) -5 + 1 =-4
3) +2 + - 4 = -2
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
+8
-31) -3 + 5 =2
2) -5 + 1 =-4
3) +2 + - 4 = -2
4) +8 + -3 = 5
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
+4
-4
1) -3 + 5 =2
2) -5 + 1 =-4
3) +2 + - 4 = -2
4) +8 + -3 = 5
5) +4 + - 4 = 0
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) -3 + 5 =2
2) -5 + 1 =-4
3) +2 + - 4 = -2
4) +8 + -3 = 5
5) +4 + - 4 = 0
6) -6 + 3 =-3 -6
+3
What do you notice about the direction of the integer elevator?
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) -3 + 5 =2
2) -5 + 1 =-4
3) +2 + - 4 = -2
4) +8 + -3 = 5
5) +4 + - 4 = 0
6) -6 + 3 =-3 -6
+3
A positive plus a negative travels up then down .A negative plus a positive travels down then up.
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) -3 + 5 =2
2) -5 + 1 =-4
3) +2 + - 4 = -2
4) +8 + -3 = 5
5) +4 + - 4 = 0
6) -6 + 3 =-3 -6
+3
NOTICE: The integer
elevator is moving in different
directions because
both numbers are
different!
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
1) -3 + 5 =2
2) -5 + 1 =-4
3) +2 + - 4 = -2
4) +8 + -3 = 5
5) +4 + - 4 = 0
6) -6 + 3 =-3 -6
+3
7) +10 + -2 = 8
8) -8 + 5 =-3
9) -13 + 5=-8
10)+11 + -5 = 6
11) -12 +5 = -7
12) -9 +6 =-3
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
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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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
ElevatorEntrance
When the signs are the different and you are adding, just subtract the numbers and the larger number determines the sign.
SIGNS ARE THE DIFFERENT = TAKE THE DIFFERENCE!
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Write a rule to explain how to combine thesetypes of integers.
Different signs Differenceof numbers
Larger number determines the sign.
5 + -12 =-7-4 + 9 = 5
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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 =-4 + -3 =
+ + + + + + + 7
_ _ _ __ _ _-7
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-3 + -5 =
4 + 7 =
(+3) + (+4) =
-6 + -7 =
5 + 9 =
-9 + -9 =
-8
-18 14
-137
11
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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 =
9 - 5 = 4Subtract the numbers
- 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 =
-25 – 3 = 2
0 -41-13
9 – 9 = 0 9 – 5 = 47 – 6 = 1
4 – 3 = 17 – 4 = 3
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Aren’t integersinteresting?
Take out yourStudy Guide!
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Integer Addition Rules If the signs are the SAME Add the numbers. The sign stays the
same.4 + 3 = -4 + -3 =+ + + + + + +
7 _ _ _ _ _ _ _-7
If the signs are DIFFERENT Subtract the numbers. The “larger number” determines the sign of the answer.
-9 + 5 =
9 - 5 = 4Subtract the numbers
-4
#5
_ _ _ _ _ + + + + +
_ _ _ _
Answer -4 because you started with more negatives
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8 7 6 5 4 3 2 1 0-1-2-3-4-5-6-7-8
IntegerElevator
Elevator Entrance
-5 + 2 =-3
-5+2Positive = UpNegative = Down
#6
