1. INTEGERS INTEGERS Describe an integer.
What integer would represent diving 50 meters down?
Order the following from smallest to largest:
-3, √81, 0, -17, 2, 22, -(12)

2. Intro To Integers

3. -$1.24
-3.4 53
+$90
Integers
-21 +4
+ 1/2
-50%

4. Integers
Integers are whole numbers that describe opposite ideas in mathematics.
Integers can either be negative(-), positive(+) or zero.
The integer zero is neutral. It is neither positive nor negative, but is an integer.
Integers can be represented on a number line, which can help us understand the value of the integer.

6. Opposite Integers

7. The “net worth” of opposite integers is zero.

8. Opposite Integers
Opposite integers always have a “net worth” of 0. This is called the ZERO PRINCIPAL.
Opposite integers have the same “absolute value”, meaning the distance from the points on a number line to zero is the same.
This can be referred to as the integers magnitude.

9. Movement on a Number Line Magnitude and Direction
Every integer represents a magnitude and a direction.
The integer +3 describes a movement of 3 units in a positive direction.(right)
The sign (+) tells you the direction.
The number (3) indicates how far to move or the MAGNITUDE( a move- ment of 3 units)
+ 3
Direction
Magnitude

10. Which integer has a higher value?
Comparing Integers
Which integer has a higher value?
-4 or -8

13. Comparing Integers
Use your number line to help you compare each set of number.
(i.e. for the numbers 3 ,and - 2 …. 3 > < 3)
- 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15
e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14

16. (3,5)
(4,-2)
(-1,-3)
(-2,1)

17. Intro To Adding Integers

18. Net Result
Positive 9
(+5) + (+4) = +9 Or
(+4) + (+5) = +9

20. Finding The Sum of Positive Integers
When finding the sum of positive integers you add the magnitudes and keep the positive sign.

21. Net Result
Positive 10
(+3) + (+7) = +10 Or
(+7) + (+3) = +10

22. Finding The Sum of Negative Integers
When finding the sum of negative integers you add the magnitudes and keep the negative sign.

23. Net Result
Negative 10
(-3) + (-7) = -10 Or
(-7) + (-3) = -10

24. Finding The Sum of a Positive and a Negative Integer
When finding the sum of a positive and a negative integer you subtract the magnitudes and keep the sign of the integer with the largest magnitude.

26. Net Result
Positive 2
(+7) + (-5) = +2 Or
(-5) + (+7) = +2

28. Net Result
Zero
(+5) + (-5) = 0 Or
(-5) + (+5) = 0

29. Integer Recap You Have or Positive symbol means You’ve Earned
Negative symbol means
You Owe

30. NUMBER LINE ACTIVITY Get a piece of masking tape & a marker
Stick it on your desk and draw a line through the middle of the tape
Mark 0 on the middle line
Make vertical lines to the right of the 0 for positive numbers (at least 10)
Make vertical lines to the left of the 0 for negative numbers (at least 10)

31. EXAMPLE
(-5) + (+2) = ?
Start at 0 and move 5 (magnitude) to the left (direction)
-5 is where you begin the equation
Move to the right (direction) 2 (magnitude) spots
Where you end up is the answer to the equation!

32. (+3) + (-7)
(-5) + (-2)
(-3) + (-6) + (+4)
(+3) + (-2) + (+2)

33. (+50) + (-100)
(-25) + (+10)

34. Rules For Adding Integers
Positive Integers
To add two positive integers you add the magnitude and keep the positive sign.
Negative Integers
To add two negative integers you add the magnitude and keep the negative sign.
A Negative and a Positive Integer
To add a positive and a negative integer you subtract the magnitudes and keep the sign of the integer with the largest magnitude.

35. Intro To Subtracting Integers

36. (+5) – (+3) = +2
(+5) – (+3) =

37. (-6) – (-2) = -4
(-6) – (-2) =

38. (+3) – (+5) = -2
(+3) – (+5) =

39. (-2) – (-6) = +4
(-2) – (-6) =

40. (+3) – (-2) = +5
(+3) – (-2) =

41. (+1) – (+4) = -3
(+1) – (+4) =

42. (-5) – (+3) = -8
(-5) – (+3) =

43. (-2) – (-5) = +3
(-2) – (-5) =

44. Try These (-8) – (-3) = (+4) – (-5) = (-4) – (-5) = (+1) – (-6) =
(-5) – (+6) =
(-2) – (-3) =
(-20) – (-10) =
(+30) – (-3) =
(-20) – (-30) =

45. Try These (-3) – (-2) = (+6) – (-2) = (-1) – (-4) = (+3) – (-2) =
(-5) – (+2) =
(-2) – (-4) =
(-30) – (-20) =
(+50) – (-10) =
(-20) – (-30) =

46. Try These (-5) + (+2) = (+6) + (-2) = (-2) – (-6) = (+7) + (-2) =
(+8) + (-4) =
(-3) – (+6) =
(+50) – (-10) =
(-20) + (-30) =

47. Try These (-5) + (+2) = -3 (+6) + (-2) = +4 (-2) – (-6) = +4
(+7) + (-2) = +5
(+8) + (-4) = +4
(-3) – (+6) = -9
(+50) – (-10) = +60
(-20) + (-30) = -50

48. Multiplying and Dividing Integers

49. (+2) x (+4) = +8
(+2) x (+4) =
This means you have two sets of four positive tiles or you have earned two groups of four dollars.

50. (+2) x (-4) = -8
(+2) x (-4) =
This means you have two sets of four negative tiles or you have two bills that you owe,each bill is for four dollars.

51. (-2) x (-4) = +8
(-2) x (-4) =
This means you don’t have two sets of four negative tiles or you don’t owe two bills, each bill is for four dollars.

52. (-2) x (+4) = -8
(-2) x (+4) =
This means you don’t have two sets of four positive tiles or you don’t have two groups of four dollars.

53. Try These (+3) x (-2) = (-2) x (-2) = (+5) x (-2) = (-3) x (+2) =

54. Try These (-91) x (-101) = (+152) x (-21) = (-19) x (+203) =

55. Try These (-91) x (-101) = (+152) x (-21) = (-19) x (+203) =

56. Multiplying Integers
FACTOR
PRODUCT + _

57. Dividing Integers
DIVIDEND
DIVISOR
QUOTIENT + _

58. Try These (-1) x (+1) x (-1) = (+1) x (+1) x (-1) =

59. Short Cuts For Multiplying Several Integer Factors
If there is an even number of negative signs, the product is positive
(-1) x (+1) x (-1) = +1
(+1) x (+1) x (-1) = -1
c. (-1) x (-1) x (+1) = +1
d. (-1) x (-1) x (-1) = -1
If there is an odd number of negative signs, the product is negative

60. Short Cuts For Multiplying Several Integer Factors
a. (-1) x (+1) x (-1) x (+1) =
b. (+1) x (+1) x (-1) x(-1) =
c. (-1) x (+1) x (-1) x (-1) x (+1) =
d. (-1) x (-1) x (-1) x (-1) x (+1) x (-1) =
e. (1) x (+1) x (-1) x (-1) x (+1) x (-1) =
(-1) x (-1) x (-1) x (-1) x (-1) x (-1) =
(-2) x (-3) x (-2) x (+1) =
(-1) x (-3) x (-2) x (-2) x (-3) =

61. Try These (-2) x (+2) x (-1)(-3)= (+1) x (+4) x (-5) =

62. (+2) x (+4) = +2
(+2) x (+4) =

63. Positive and Negative Integers
For each of the following numbers, write down an example of where it could be used and what it means in that situation. m
+3050m -$45.83

64. Order of Operations With Integers

65. Order of Operations With Integers
3 x (–7) + 4 x (-5)
15 + (+5)2 x 2
(-18) – 9 x 2

66. Practice for Problem Solving
Fiona spends $5 per week on bus fare. How much does she spend in 2 weeks?
Lucy spends 2 per week on snacks. How much does she spend in 4 weeks?
Anton earns $8 each week for baby- sitting. How much does he earn in 3 weeks?

67. Practice for Problem Solving
Lional pays $3 per day for bus transportation. How much does she pay in a school week?
Jill has $100 in the bank. She owes 3 of her friends $10 dollars each. What is her net worth?