1. -8 5
INTERESTING INTEGERS! 4 -7 -3

2. Are you ready?? What You Will Learn: Vocabulary related to integers
Rules for adding and subtracting integers
A method for proving that a rule is true
Are you ready??

3. Part I: Introduction to Integers
Vocabulary
positive number
negative number
Horizontal & vertical number lines
Comparing Integers
Ordering Integers
Vocabulary - continued
opposite number
integer
Real World Applications & Examples
temperature
sea level
money

4. Vocabulary:
Positive number – a number greater than (>) zero 1 2 3 4 5 6

5. Hint:
If you don’t see a negative or positive sign in front of a number, the number is positive.
9 is the same as +9

6. Vocabulary:
Negative number – a number less than (<) zero 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

7. Horizontal Integer Number Line ZERO Numbers below or left of 0
are negative
Numbers above or right of 0
are positive
ZERO

8. Integer Number Line Vertical ZERO Numbers above 0 are positive
Numbers below 0
are negative

9. Comparing Integers -4 -2 1 -3 -5
Use the number line to compare the following integers with >, <, or =. -4 -2 1 -3 -5
<
<
>
Hint: On a number line, the number to the left is always less than the number to the right.

10. Comparing Integers -3 -5 -1
Use the number line to compare the following integers with >, <, or =. -3 -5 -1
>
>
>
Hint: On a number line, the number on the top is always greater than the number on the bottom.

11. Ordering Integers -4, 3, 0, and -5 -5, -4, 0, 3
Use the number line to put the following integers in order from least to greatest.
-4, 3, 0, and -5
-5, -4, 0, 3

12. Vocabulary:
Opposite Numbers – numbers that are the same distance from zero in the opposite direction 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

13. What is the opposite of each integer?+1 -1 +7 -7 5 +5 -8 +8

14. 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 integers Vocabulary:
Integers – all the whole numbers and all of their opposites on the number line including zero 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
integers

15. Now, you’re probably saying, “That’s interesting and everything, BUT where are negative numbers in the real world?? ??

16. Negative Numbers Are Used to Measure Temperature

17. Negative Numbers Are Used to Measure Under Sea Level30 20 10
-10
-20
-30
-40
-50

18. Positive and negative numbers are used when keeping track of money.
$$ you earn
- Negative -
$$ you spend

19. Positive Numbers are Used to Show Earnings or Assets
When you get paid (or win the lottery), you add that $$ to your account.

20. Negative Numbers are Used to Show What You Owe or Debt
If your mom loaned you $10 for pizza,
Mom,
I. O. U.
$10
The $10 you owe her is described by the integer -10.

21. Write an integer to describe the real world situation:
Gain 3 pounds:
Withdraw $15:
5 feet below sea level:
Move ahead 4 spaces:
-15 -5
4 or +4

22. End - Part I: Introduction to Integers
Vocabulary
positive number
negative number
Horizontal & vertical number lines
Comparing Integers
Ordering Integers
Vocabulary - continued
opposite number
integer
Real World Applications & Examples
temperature
sea level
money

23. Part II: Adding Integers
Key Concepts
Integer Addition Rules
Using Number Lines

24. ** Key Concepts **
The sum of two positive numbers is always positive  (+) + (+) = (+)
ex = 6
The sum of two negative numbers is always negative  (-) + (-) = (-)
ex = -6

25. AND ** Key Concepts ** (+) + (+) = (+) (-) + (-) = (-)
(+) + (+) = (+) (-) + (-) = (-)
AND
(+) + (-) = sometimes (+)
= sometimes (-)
= sometimes 0

26. Integer Addition Rules
Rule #1 – If the signs are the same, add the numbers and then put the sign of the addends in front of your answer.
a) =
b) = -14

27. Solve the Problems -3 + -5 = -8 4 + 6 = +3 + (+4) = 10 -6 + -7 =
5 + 9 = = -8 10 7
-13 14
-18

28. Integer Addition Rules
Rule #2 – If the signs of the addends are DIFFERENT, start at the location of the first integer on the number line and:
a) move RIGHT to add a positive integer 1 2 3 = -2

29. Adding Integers Using a Number Line * adding a positive integer *
ex. (-6) + 5 = -1
Start here at -6 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +
then count forward or right 5 spaces

30. Solve the Problems
8 + 6 =
(-9) + 5 =
(–11) + 11 =
(–8) + 16 = 14 -4 8

31. Integer Addition Rules
Rule #2 – If the signs of the addends are DIFFERENT, start at the location of the first integer on the number line and:
b) move LEFT to add a negative integer 1 2 3 = 1

32. Adding Integers Using a Number Line * adding a negative integer *
ex (-5) = -2
Start here at +3 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -
Then count back or left 5 spaces

33. Solve the Problems -10 -13 7 2 + (-12) = –8 + (-5) = 14 + (-7) =
15 + (-15) =
-10
-13 7

34. Part III

35. Part III: Subtracting Integers
** Key Concept **
To subtract an integer, add its opposite
ex – 2 = 5 + (-2) = 3
KEEP
CHANGE
CHANGE

36. Integer Subtraction Rule
Subtracting a negative number is the same as adding a positive. Change the signs and add.
ex. -1 – (-2) is the same as
-1 + (+2) and = 1
KEEP
CHANGE
CHANGE

37. More Examples 2 – (-7) is the same as 2 + (+7) and 2 + 7 = 9
KEEP the sign of the 1st integer the same
CHANGE the operation ( + to – or – to +)
CHANGE the sign of the 2nd integer
2 – (-7) is the same as
2 + (+7) and = 9
-3 – 4 is the same as
-3 + (-4) and -3 + (-4) = -7

38. More Examples 12 – (-8) is the same as 12 + (+8) and 12 + 8 = 20
KEEP the sign of the 1st integer the same
CHANGE the operation ( + to – or – to +)
CHANGE the sign of the 2nd integer
More Examples
12 – (-8) is the same as
12 + (+8) and = 20
-3 – (-11) is the same as
-3 + (+11) and = 8

39. Problems to Solve 8 + (+12) and 8 + 12 = 20 22 – (-30) is the same as
KEEP the sign of the 1st integer the same
CHANGE the operation ( + to – or – to +)
CHANGE the sign of the 2nd integer
Problems
to Solve
8 – (-12) is the same as
8 + (+12)
and
= 20
22 – (-30) is the same as
22 + (+30)
and
= 52

40. Problems to Solve -17 + (+3) and -17 + 3 = -14 -8 – 3 is the same as
KEEP the sign of the 1st integer the same
CHANGE the operation ( + to – or – to +)
CHANGE the sign of the 2nd integer
Problems to Solve
-17– (-3) is the same as
-17 + (+3)
and
= -14
-8 – 3 is the same as
-8 + (-3)
and
= -11

41. Part IV

42. How do we know that “Subtracting a negative number is the same as adding a positive” is true?
We can use the same method we use to check our answers when we do regular subtraction.

43. When you subtract a – b it equals c
a – b = c
ex. 5 – 2 = 3
To check if your answer is correct, add b and c
a = b + c
ex. 5 = 2 + 3

44. If a – b = c, and….
2 – (-5) is the same as
2 + (+5), which equals 7,
Then let’s check with the negative numbers to see if it’s true…

45. Here are some examples:
a – b = c a = b + c
9 – 5 = 4 9 = 5 + 4
20 – 3 = =

46. If the method for checking
subtraction works, it should
also work for subtracting
negative numbers.

47. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works!
2 – (-5) = =
It works!
a – b = c a = b + c
-11 – (-3) = =
YES!

48. Aren’t integers
interesting?