Real Numbers

1. Chapter 2
Foundations of Algebra

2. Section 2-1
Real Numbers

3. Essential Questions
How do you graph sets of numbers on a number line?
How do you evaluate expressions with absolute value?
Where you’! see these topics:
Weather, sports, population

4. Vocabulary
1. Integers:
2. Opposites:
3. Rational Number:

5. Vocabulary
1. Integers: The set of whole numbers and their opposites
2. Opposites:
3. Rational Number:

6. Vocabulary
1. Integers: The set of whole numbers and their opposites
{..., -2, -1, 0, 1, 2, ...}
2. Opposites:
3. Rational Number:

7. Vocabulary
1. Integers: The set of whole numbers and their opposites
{..., -2, -1, 0, 1, 2, ...}
2. Opposites: Numbers that are the same distance %om 0
but in different directions
3. Rational Number:

8. Vocabulary
1. Integers: The set of whole numbers and their opposites
{..., -2, -1, 0, 1, 2, ...}
2. Opposites: Numbers that are the same distance %om 0
but in different directions
3. Rational Number: Any number that can be written as
a ratio; this includes integers, repeating decimals, and
terminating decimals

9. Vocabulary
4. Irrational Number:
5. Real Number:
6. Coordinate of the Point:

10. Vocabulary
4. Irrational Number: Any number that cannot be
written as a ratio; this includes non-terminating, non-
repeating decimals such as pi and 2
5. Real Number:
6. Coordinate of the Point:

11. Vocabulary
4. Irrational Number: Any number that cannot be
written as a ratio; this includes non-terminating, non-
repeating decimals such as pi and 2
5. Real Number: The set of rational and irrational numbers
6. Coordinate of the Point:

12. Vocabulary
4. Irrational Number: Any number that cannot be
written as a ratio; this includes non-terminating, non-
repeating decimals such as pi and 2
5. Real Number: The set of rational and irrational numbers
6. Coordinate of the Point: The number that corresponds
to a point on a number line

13. Vocabulary
7. Graph of the Number:
8. Variable:
9. Absolute Value:
10. Opposite of the Opposite:

14. Vocabulary
7. Graph of the Number: The point that corresponds to a
number
8. Variable:
9. Absolute Value:
10. Opposite of the Opposite:

15. Vocabulary
7. Graph of the Number: The point that corresponds to a
number
8. Variable: A symbol that is used to hold the place of a
number or algebraic expression; it’s just a place holder
9. Absolute Value:
10. Opposite of the Opposite:

16. Vocabulary
7. Graph of the Number: The point that corresponds to a
number
8. Variable: A symbol that is used to hold the place of a
number or algebraic expression; it’s just a place holder
9. Absolute Value: The distance a number is %om 0
10. Opposite of the Opposite:

17. Vocabulary
7. Graph of the Number: The point that corresponds to a
number
8. Variable: A symbol that is used to hold the place of a
number or algebraic expression; it’s just a place holder
9. Absolute Value: The distance a number is %om 0
10. Opposite of the Opposite: If n is a real number, then
-(-n) = n

18. Example 1
Graph on a number line.
1 5 2 1 
 , , ,− 
2 6 3 6 

19. Example 1
Graph on a number line.
1 5 2 1 
 , , ,− 
2 6 3 6 

20. Example 1
Graph on a number line.
1 5 2 1 
 , , ,− 
2 6 3 6 
1 1 1 1 1 2 5
−
3
−
6
0 6 3 2 3 6
1

21. Example 1
Graph on a number line.
1 5 2 1 
 , , ,− 
2 6 3 6 
1 1 1 1 1 2 5
−
3
−
6
0 6 3 2 3 6
1

22. Example 1
Graph on a number line.
1 5 2 1 
 , , ,− 
2 6 3 6 
1 1 1 1 1 2 5
−
3
−
6
0 6 3 2 3 6
1

23. Example 1
Graph on a number line.
1 5 2 1 
 , , ,− 
2 6 3 6 
1 1 1 1 1 2 5
−
3
−
6
0 6 3 2 3 6
1

24. Example 1
Graph on a number line.
1 5 2 1 
 , , ,− 
2 6 3 6 
1 1 1 1 1 2 5
−
3
−
6
0 6 3 2 3 6
1

25. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6

26. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6

27. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4

28. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4 0

29. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4 0 2

30. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
< <
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4 0 2

31. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
< <
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4 0 2

32. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
< <
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4 0 2
-6

33. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
< <
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4 0 2
-6 -3

34. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
< <
a. -4 ___ 0 ___ 2 b. -1 ___− 3 ___− 6
-4 0 2
-6 -3 -1

35. Example 2
Use a number line to compare numbers. In each part,
replace the “___” with either < or >.
< <
a. -4 ___ 0 ___ 2 > >
b. -1 ___− 3 ___− 6
-4 0 2
-6 -3 -1

36. Example 3
Graph each set of numbers on a number line.
a. The real numbers that are greater than 2 or less than -1.

37. Example 3
Graph each set of numbers on a number line.
a. The real numbers that are greater than 2 or less than -1.

38. Example 3
Graph each set of numbers on a number line.
a. The real numbers that are greater than 2 or less than -1.
-4 -3 -2 -1 0 1 2 3 4

39. Example 3
Graph each set of numbers on a number line.
a. The real numbers that are greater than 2 or less than -1.
-4 -3 -2 -1 0 1 2 3 4

40. Example 3
Graph each set of numbers on a number line.
a. The real numbers that are greater than 2 or less than -1.
-4 -3 -2 -1 0 1 2 3 4

41. Example 3
Graph each set of numbers on a number line.
a. The real numbers that are greater than 2 or less than -1.
-4 -3 -2 -1 0 1 2 3 4

42. Example 3
Graph each set of numbers on a number line.
a. The real numbers that are greater than 2 or less than -1.
-4 -3 -2 -1 0 1 2 3 4

43. Example 3
b. The integers that are greater than -3 and less than or
equal to 2

44. Example 3
b. The integers that are greater than -3 and less than or
equal to 2

45. Example 3
b. The integers that are greater than -3 and less than or
equal to 2
-5 -4 -3 -2 -1 0 1 2 3

46. Example 3
b. The integers that are greater than -3 and less than or
equal to 2
-5 -4 -3 -2 -1 0 1 2 3

47. Example 3
b. The integers that are greater than -3 and less than or
equal to 2
-5 -4 -3 -2 -1 0 1 2 3

48. Example 3
b. The integers that are greater than -3 and less than or
equal to 2
-5 -4 -3 -2 -1 0 1 2 3

49. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4

50. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4
−3 − 4

51. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4
−3 − 4
= −7

52. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4
−3 − 4
= −7 = 7

53. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4
−3 − 4 9− 1−4
= −7 = 7

54. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4
−3 − 4 9− 1−4
= −7 = 7 = 9 − −3

55. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4
−3 − 4 9− 1−4
= −7 = 7 = 9 − −3
=9−3

56. Example 4
Evaluate each expression.
a. m − 4 when m = −3 b. 9- 1 − k when k = 4
−3 − 4 9− 1−4
= −7 = 7 = 9 − −3
=9−3 =6

57. Homework

58. Homework
p. 54 #1-43 odd
Do the one thing you think you cannot do. Fail at it. Try
again. Do better the second time. The only people who
never tumble are those who never mount the high wire.
This is your moment. Own it. - Oprah Win%ey