Mrs. Frick

1
Adding Positive and Negative Integers

• Mrs. Frick

2
Math Computation

• Numbers can be added, subtracted, multiplied and
  divided.
• We recently learned that there are negative
  numbers, therefore these numbers can be
  manipulated just like positive numbers.
• There are just a few new tricks youll need to
  learn!

3
So Many Numbers
1,652, 240
4
Addition

• As you saw before, there are very large numbers
  and very small numbers. In the real world you
  will need to know how to compute so you do not
  get taken advantage of.

5
Think About This

• If you are a manager of a company and you order
  500 reams of white paper, but you already order
  500 reams of colored paper (which is more
  expensive) and they did not have it in stock and
  have not given your money back, what do you
  expect your balance or bill to be?

6
Two Scenarios

• You owe Money

• They owe Money

Click on the picture which matches the answer to
the previous question!
7
Youre Right

• They both owe money technically, you owe money
  for the paper but they owe you more for the
  colored paper! They will have to pay you in the
  end.

8
Youre Right

• They owe money because you already paid for the
  colored paper but they owe you more for the
  colored paper! They will have to pay you in the
  end.

9
Try Again

• You already paid more than what your order is
  for, so you dont owe them money!

10
Rules

• There are situations like this where you have to
  think about whether youre adding a larger
  positive number than a negative number or a
  larger negative number than a positive number!

• Just like from before you had a larger positive
  amount than what you owed, so you would get money
  back or be in the positive!

11
More on Rules

• So when adding a larger positive number your
  answer will be positive.
• BUT if you are adding a smaller positive number
  to a negative number then your answer will be
  negative. This would be like you ordering white
  paper and they being out of stock and replacing
  that order with colored paper you would owe
  money or be negative!

12
Different Representations

• Numbers can be added in various ways. They can
  be solved through story problems that involve
  situations in real-life OR they can be number
  sentences which are problems with numbers and
  math computation symbols.

13
Number Sentences

• 15 (-3) 12
• 144 12 12

• 16 (-8) 24
• 3 x 4 12

14
Number Sentences

• Simply, they are numbers and math computation
  symbols arranged together and sometimes
  parentheses.

15
Parentheses Two Notes

• They can separate negative signs from
  computations signs.
• 10 (-4) 6
• 1 (-4) 5
• 2 (-24) -22
• 15 (-6) 21

• They also can indicate multiplication
• (10) (5) 50
• (6) (8) 48
• (12) (6) 72
• (4) (16) 64

16
Solving with Number Sentences

• In this problem, you have positive 4 and negative
  3. If I think about this as money or temperature
  it will make it easier!

• If I have 4 dollars and I owe you 3, I have
  positive 1 left.
• OR
• If it is 4 degrees outside and it drops 3 degrees
  (negative), it would be 1 degrees outside.

17
More Examples

• For the first one the answer is positive one
  because if I owe you a dollar and have two
  dollars I will have 1 dollar left.
• The order does not matter with addition!

• 2 (-1)
• -1 2
• 8 (-5)
• -5 8
• 13 (-4)
• -4 13

3
9
18
Order

• This is a rule that you learned in elementary
  school that when you add two or more numbers, the
  order does not matter this is called the
  commutative property of addition.

19
Now you TRY!!

• 8 (-4)
• Pick One
• -4 12 4 3

20
TRY AGAIN

• 12 IS INCORRECT
• Positive 8 plus positive 4 is positive 12

21
OOPS

• -4 IS INCORRECT
• Negative 8 plus positive 4 is negative 4

22
TRY AGAIN

• 3 IS INCORRECT
• Positive 8 plus negative 5 is positive 3

23
YOURE RIGHT

• SUPER BRAIN!!

24
Now you TRY!!

• 10 -8
• Pick One
• -2 2 1 18

25
OOPS

• 1 IS INCORRECT
• Positive 10 plus negative 9 could be positive 1

26
TRY AGAIN

• -2 IS INCORRECT
• Negative 10 plus positive 8 is -2

27
OOPS

• 18 IS INCORRECT
• Positive 10 plus positive 8 would be positive 18

28
YOURE RIGHT

• SUPER BRAIN!!

29
Now you TRY!!

• 23 (-11)
• Pick One
• 12 34 -17 -12

30
TRY AGAIN

• -17 IS INCORRECT
• Negative 23 plus positive 6 would be negative 17

31
OOPS

• 34 IS INCORRECT
• Positive 23 plus positive 11 would be positive 34

32
TRY AGAIN

• -12 IS INCORRECT
• Negative 23 plus positive 11 would be -23

33
YOURE RIGHT

• SUPER BRAIN!!

34
Now you TRY!!

• -100 210
• Pick One
• -310 90 310 110

35
OOPS

• -310 IS INCORRECT
• Negative 110 plus negative 210 would be negative
  310

36
TRY AGAIN

• 90 IS INCORRECT
• Negative 110 plus positive 200 would be positive
  90

37
OOPS

• 310 IS INCORRECT
• Positive 100 plus positive 210 would be positive
  310

38
YOURE RIGHT

• SUPER BRAIN!!

39
Addition of Larger Negative Numbers

• This relates back to the problem where you
  ordered the white paper first (less expensive)
  and then replaced the order with colored paper
  (more expensive)
• If you have a credit of 50 and then order paper
  that costs 75 dollars. In a number sentence
  this would look like this
• 50 (-75) -25 (I owe 25)

40
Examples

• For the first one the answer is negative one
  because if I owe you two dollars and have one
  dollar you will owe 1 dollar.
• Again, the order does not matter with addition!

• -2 1
• 1 (-2)
• -18 5
• 5 (-18)
• -23 4
• 4 (-23)

41
Order

• This is a rule that you learned in elementary
  school that when you add two or more numbers, the
  order does not matter this is called the
  commutative property of addition.

42
Now you TRY!!

• -4 2
• Pick One
• -6 2 6 -2

43
TRY AGAIN

• -6 is incorrect
• Negative 4 plus negative 2 would be negative 6

44
OOPS!

• 6 is incorrect
• Positive 4 plus positive 2 is positive 6

45
TRY AGAIN

• 2 is incorrect
• Positive 4 plus negative 2 is positive 2

46
YOURE RIGHT

• SUPER BRAIN!!

47
Now you TRY!!

• 16 (-25)
• Pick One
• -41 -9 42 9

48
OOPS

• 9 is incorrect
• Negative 16 plus positive 25 would be positive 9

49
TRY, TRY AGAIN

• -41 is incorrect
• Negative 16 plus negative 25 would be negative 41

50
OOPS

• 42 is incorrect
• Positive 16 plus positive 26 would be positive 42

51
YOURE RIGHT

• SUPER BRAIN!!

52
Now you TRY!!

• -100 22
• Pick One
• -122 -88 122 -22

53
TRY AGAIN

• -122 is incorrect
• Negative 100 plus negative 22 would be negative
  122

54
OOPS

• 122 is incorrect
• Positive 100 plus positive 22 would be positive
  122

55
TRY, TRY AGAIN

• -22 is incorrect
• Negative 100 plus positive 88 would be negative 22

56
YOURE RIGHT

• SUPER BRAIN!!

57
Now you TRY!!

• 13 (-56)
• Pick One
• -69 -23 -43 69

58
OOPS

• -69 is incorrect
• Negative 56 plus negative 13 would be negative 69

59
TRY AGAIN

• -23 is incorrect
• Negative 56 plus positive 33 would be negative 23

60
OOPS

• 69 is incorrect
• Positive 13 plus positive 53 would be positive 69

61
YOURE RIGHT

• SUPER BRAIN!!

62
Another One Bites the Dust

• (-11) (-3) -13
• (-26) (-36) -62
• (-152) (-16) -168
• (-47) (-107) -154
• (-148) (-259) -407

63
Negative Plus Negative

• When you add two negative numbers you will always
  get a negative answer! A trick to finding the
  answer is to add the absolute values of the
  numbers together and put a negative sign in front
  of the sum.

64
Absolute Value

• In order to compare positive and negative
  numbers, you must know what absolute value is.
• The distance any number is from 0 is its absolute
  value.
• Below the arrows are pointing to 100 and 100,
  they both are 100 units from 0 and have an
  absolute value of 100.

-500 -400 -300 -200 -100 0 100
200 300 400 500
65
See What Youve Got

• Click on test your skills link at the end of
  this sentence to go to the practice worksheet to
  test your skills. Do not use a calculator and
  turn it in when youve finished.