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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.

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Presentation on theme: "Working with positive and negative numbers is like driving in traffic. You have to watch the traffic signs and follow the."— Presentation transcript:

1 http://www.mathslideshows.com

2 Working with positive and negative numbers is like driving in traffic. You have to watch the traffic signs and follow the driving rules.

3 http://www.mathslideshows.com Positive number – a greater than zero. 0123456

4 http://www.mathslideshows.com Negative number – a less than zero. 0123456-2-3-4-5-6

5 http://www.mathslideshows.com A great way to solve integers problems is to use a number line. 0123456-2-3-4-5-6 Most algebra textbooks use a horizontal number line.

6 http://www.mathslideshows.com You start at the origin or zero. 0123456-2-3-4-5-6 Positive numbers move to the right. Origin (Start) Negative numbers move to the left.

7 http://www.mathslideshows.com 0123456-2-3-4-5-6 -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

8 http://www.mathslideshows.com 0123456-2-3-4-5-6 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.

9 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Elevator Entrance -4 + 2 = -2 -4 +2+2 Positive = Up Negative = Down Using a vertical number line is easier to relate to since most of us have been in an elevator!

10 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance Watch the direction of the elevator when we do integer problems with the SAME SIGN!

11 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 1) +3 + 5 = 8 +3+3 +5+5

12 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 1) +3 + 5 = 8 +1+1 +4+4 2) +1 + 4 = 5

13 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 1) +3 + 5 = 8 -2 -3 2) +1 + 4 = 5 3) -2 + - 3 = -5

14 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 1) +3 + 5 = 8 -3 -4 2) +1 + 4 = 5 3) -2 + - 3 = -5 4) -3 + - 4 = -7

15 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 1) +3 + 5 = 8 2) +1 + 4 = 5 3) -2 + - 3 = -5 4) -3 + - 4 = -7 5) +2+6 = +8 +2+2 +6+6

16 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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 What do you notice about the direction of the integer elevator?

17 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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 A positive plus a positive travels up up. A negative plus a negative travels down down.

18 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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 Both signs are the same so you end up traveling the same direction.

19 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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

20 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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.

21 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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!

22 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance Watch the direction of the elevator when we do integer problems with the DIFFERENT SIGNS!

23 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance -3 +5 1) -3 + 5 = 2

24 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance -5 +1 1) -3 + 5 = 2 2) -5 + 1 = -4

25 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance +2 -4-4 1) -3 + 5 = 2 2) -5 + 1 = -4 3) +2 + - 4 = -2

26 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance +8 -3-3 1) -3 + 5 = 2 2) -5 + 1 = -4 3) +2 + - 4 = -2 4) +8 + -3 = 5

27 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance +4 -4-4 1) -3 + 5 = 2 2) -5 + 1 = -4 3) +2 + - 4 = -2 4) +8 + -3 = 5 5) +4 + - 4 = 0

28 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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?

29 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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.

30 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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!

31 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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

32 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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.

33 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Entrance 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!

34 http://www.mathslideshows.com Write a rule to explain how to combine these types of integers. Different signs Difference of numbers Larger number determines the sign. 5 + -12 = -7 -4 + 9 = 5

35 http://www.mathslideshows.com 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

36 http://www.mathslideshows.com -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 = -9 + -9 = -8 -18 14 -13 7 11

37 http://www.mathslideshows.com 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 = 4 Subtract the numbers - 4 _ _ _ _ _ + + + + + _ _ Answer -4 because you started with more negatives

38 http://www.mathslideshows.com 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 = -9 + 9 = -2 5 – 3 = 2 0 -4 1 3 9 – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

39 http://www.mathslideshows.com Aren’t integers interesting? Take out your Study Guide!

40 http://www.mathslideshows.com 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 = 4 Subtract the numbers -4 #5 _ _ _ _ _ + + + + + _ _ Answer -4 because you started with more negatives

41 http://www.mathslideshows.com 8 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Elevator Entrance -5 + 2 = -3 -5 +2+2 Positive = Up Negative = Down #6

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