1. OR a RATIONAL NUMBER is any number that can be written as a fraction.
RATIONAL NUMBERS
NATURAL NUMBERS {1, 2, 3,…}
+ {0}
= WHOLE NUMBERS {0, 1, 2, 3,…}
+ NEG. WHOLE NOS.
= INTEGERS {…-2, -1, 0, 1, 2,…}
+ PURE FRACTIONS
= RATIONAL NUMBERS
A RATIONAL NUMBER is any number that can be written in the form a/b, where a & b are integers and b ≠ 0.
OR a RATIONAL NUMBER is any number that can be written as a fraction.

2. RATIONAL NUMBERS RATIONAL NUMBERS NATURAL NUMBERS {1, 2, 3,…} ZERO {0}
WHOLE NUMBERS
{0, 1, 2,…}
NEGATIVE WHOLE NO.
{…, -2, -1, 0}
INTEGERS
{…, -2, -1. 0, 1, 2,…}
PURE FRACTIONS
RATIONAL NUMBERS

3. RATIONAL NUMBERS NATURAL NUMBERS (or counting numbers)
GRAPHING THE NUMBER SETS ON THE NUMBER LINE 2 4 6 -2 -4 -6
NATURAL NUMBERS
(or counting numbers)

4. RATIONAL NUMBERS WHOLE NUMBERS
GRAPHING THE NUMBER SETS ON THE NUMBER LINE 2 4 6 -2 -4 -6
WHOLE NUMBERS

5. RATIONAL NUMBERS INTEGERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE2 4 6 -2 -4 -6
INTEGERS

6. EXAMPLES OF RATIONAL NUMBERS5
- 7
0.3

7. 0.5 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 2 4 6 -22 4 6 -2 -4 -6
0.5

8. 8/3 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 2 4 6 -22 4 6 -2 -4 -6
8/3

9. –32/5 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 2 4 62 4 6 -2 -4 -6
–32/5

10. RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE 2 4 6 -2 -4 -6
{-3, -2, 0, 5}

11. RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE 2 4 6 -2 -4 -6
{0, 2, 4, 6,…}

12. The absolute value of 3 is written |3|
RATIONAL NUMBERS
The ABSOLUTE VALUE of any number is its distance from zero on the number line.
The absolute value of 3 is written |3|
|3| = 3, because
3 units 2 4 6 -2 -4 -6

13. RATIONAL NUMBERS |-3| = 3, because
The ABSOLUTE VALUE of any number is its distance from zero on the number line.
|-3| = 3, because
3 units 2 4 6 -2 -4 -6

14. RATIONAL NUMBERS
Evaluate: |-2 + 7|
= |5|
= 5
Evaluate: 3 + |-4| + |4| =
= 11
Evaluate: x + |x + 4| + 3, if x = -7
= -7 + |-3| + 3 =
= -1

15. Same Signs: Add their absolute values and use their common sign.
ADDING & SUBTRACTING RATIONAL NUMBERS
ADDING
Same Signs: Add their absolute values and use their common sign.
6 + (+3) = 9
-6 + (-3) = -9
4 + (+8) = 12
-20 + (-45) =
-65

16. ADDING & SUBTRACTING RATIONAL NUMBERS
Different Signs: Subtract their absolute values and use the sign of the larger.
6 + (-3) = 3
-6 + (+3) = -3
3 + (-7) = -4
-20 + (+45) = 25

17. ADDING & SUBTRACTING RATIONAL NUMBERS
The ADDITIVE INVERSE of a number is its opposite.
The additive inverse of 6 is -6
The additive inverse of -3 is 3
The additive inverse of 1/2 is -1/2
The additive inverse of is 6.25

18. ADDING & SUBTRACTING RATIONAL NUMBERS
The ADDITIVE INVERSE of a number is its opposite.
ADDITIVE INVERSE PROPERTY
For every number a, a + (-a) = 0
4 + (-4) =
10 + (-10) =

19. ADDING & SUBTRACTING RATIONAL NUMBERS
To subtract signed numbers, add the opposite.
(A.T.O.) and use the rules of addition.
6 – (+3) =
6 + (-3) = 3
6 – (-3) =
6 + (+3) = 9
-8 – (+2) =
-8 + (-2) =
-10
-30 – (-50) =
-30 + (+50) = 20

20. REVIEW
TRUE OR FALSE
5 is a rational number
YES

21. 0 is the smallest natural number.
REVIEW
TRUE OR FALSE
0 is the smallest natural number.
NO, 1 is the smallest

22. -1 is the largest negative integer.
REVIEW
TRUE OR FALSE
-1 is the largest negative integer.
YES

23. Name a rational number that is not an integer.
REVIEW
TRUE OR FALSE
Name a rational number that is not an integer.
Any pure fraction
½, 0.6, 2.3, etc

24. Name a whole number that is not a natural number.
REVIEW
Name a whole number that is not a natural number.

25. Name a whole number that is not an integer.
REVIEW
Name a whole number that is not an integer.
NOT POSSIBLE

26. ADDING & SUBTRACTING
RATIONAL NUMBERS

27. FLASH CARDS
8 + (+3) 11

28. FLASH CARDS
5 + (-3) 2

29. FLASH CARDS
-7 + (-2) -9

30. FLASH CARDS
-5 + (+2) -3

31. FLASH CARDS
-7 + (+8) 1

32. FLASH CARDS
-3 + (-5) + (+2) -6

33. FLASH CARDS
7 + (-3) + (-6) -2

34. FLASH CARDS
20 + (+30) + (-50)

35. FLASH CARDS
-5 + (-3) + (-2)
-10

36. FLASH CARDS
2 + (-1) + (8) 9

37. FLASH CARDS
7 - (+1)
A.T.O. 6

38. FLASH CARDS
9 - (-1)
A.T.O. 10

39. FLASH CARDS
-20 - (+10)
A.T.O.
-30

40. FLASH CARDS
-5 - (-8)
A.T.O. 3

41. FLASH CARDS
11 - (+8)
A.T.O.?? 3

42. FLASH CARDS
25 - (-10)
A.T.O. 35

43. ABSOLUTE VALUES

44. FLASH CARDS
|-1| 1

45. FLASH CARDS
|777|
777

46. FLASH CARDS
|0|

47. FLASH CARDS
-|5| -5

48. FLASH CARDS
-|-10|
-10

49. FLASH CARDS
|5| + |-2| 7

50. FLASH CARDS
|-2 + (-3)| 5

51. FLASH CARDS
|2| + |-1| + |8| 11

52. FLASH CARDS
|2 - 1| + |-1 + 3| 3

53. FLASH CARDS
|10 - 3| - |-1 - 3| 3

54. FLASH CARDS
3 + 5x
if x = -2 -7

55. FLASH CARDS
|x + 3|
if x = -2 1

56. FLASH CARDS
x + |-x| - |-x+2|
if x = -2 -4