2. An Ordering Activity
Microsoft Office
Word 97 - 2003 Document

3. Fraction Equality: if and only if ad = bc.

4. Figure 9.2

5. Figure 9.5

6. 9.1 THE RATIONAL NUMBERS
Definition: The set of rational numbers is the set
Examples of Rational Numbers: , , , 3, .7
Explanation: , ,

7. 9.1 THE RATIONAL NUMBERS
Definition: The set of rational numbers is the set
Examples of Rational Numbers: , , , 3, .7
Explanation: , ,

8. Equality of Rational Numbers: if and only if ad = bc.
To Do: Show that
Solution: (–12)×(–3) = 36 = 9×4

9. Equality of Rational Numbers: if and only if ad = bc.
To Do: Show that
Solution: (–12)×(–3) = 36 = 9×4

10. Equality of Rational Numbers: if and only if ad = bc.
To Do: Show that
Solution: (–12)×(–3) = 36 = 9×4

11. Equality of Rational Numbers: if and only if ad = bc.
To Do: Show that
Solution: (–12)×(–3) = 36 = 9×4

12. Example:
Definition: a / b is in simplest form if a and b have no
common prime factors and b is positive.
Example: The following are not in simplest form:
Why not?

13. Example:
Definition: a / b is in simplest form if a and b have no
common prime factors and b is positive.
Example: The following are not in simplest form:
Why not?

14. Example:
Definition: a / b is in simplest form if a and b have no
common prime factors and b is positive.
Example: The following are not in simplest form:
Why not?

15. Example:
Definition: a / b is in simplest form if a and b have no
common prime factors and b is positive.
Example: The following are not in simplest form:
Why not?

16. Example:
Notice that

17. Example:
Notice that

18. Example:
Notice that

19. To Do: Add
Answer:

20. To Do: Add
Answer:

21. Notice that since .
Also, notice that
.
Therefore, is the additive inverse of .
That is, .
So,

22. Notice that since .
Also, notice that
.
Therefore, is the additive inverse of .
That is, .
So,

23. Notice that since .
Also, notice that
.
Therefore, is the additive inverse of .
That is, .
So,

24. Rational numbers on the number line:

25. Rational numbers on the number line:

26. To Do: Subtract
Solution:

27. To Do: Subtract
Solution:

28. To Do: Subtract
Solution:

29. To Do: Multiply and simplify
Answer:

30. To Do: Multiply and simplify
Answer:

31. To Do: Multiply and simplify
Answer:

34. Why does ?
Well, why does 6 ÷ 2 = 3?
Because 2 × 3 = 6.
Let’s check :
. Yay!
To Do: Divide and simplify
Answer:

35. Why does ?
Well, why does 6 ÷ 2 = 3?
Because 2 × 3 = 6.
Let’s check :
. Yay!
To Do: Divide and simplify
Answer:

36. Why does ?
Well, why does 6 ÷ 2 = 3?
Because 2 × 3 = 6.
Let’s check :
. Yay!
To Do: Divide and simplify
Answer:

37. Why does ?
Well, why does 6 ÷ 2 = 3?
Because 2 × 3 = 6.
Let’s check :
. Yay!
To Do: Divide and simplify
Answer:

38. Why does ?
Well, why does 6 ÷ 2 = 3?
Because 2 × 3 = 6.
Let’s check :
. Yay!
To Do: Divide and simplify
Answer:

39. Why does ?
Well, why does 6 ÷ 2 = 3?
Because 2 × 3 = 6.
Let’s check :
. Yay!
To Do: Divide and simplify
Answer:

40. Why does ?
Well, why does 6 ÷ 2 = 3?
Because 2 × 3 = 6.
Let’s check :
. Yay!
To Do: Divide and simplify
Answer:

41. Example:

42. Example:

44. To Do: Divide
Solution:

45. To Do: Divide
Solution:

46. Error in book:
This should read if and only if a < c and b > 0.

47. Example: Compare and .
Solution: (–4)(7) = -28 and (9)(–3) = -27.
So, (–4)(7) < (9)(–3) ⇒
To Do: Compare and .
Solution: (–10)(8) ??? (9)(–9)
–90 ?? –91
–90 > –91
So,

48. Example: Compare and .
Solution: (–4)(7) = -28 and (9)(–3) = -27.
So, (–4)(7) < (9)(–3) ⇒
To Do: Compare and .
Solution: (–10)(8) ??? (9)(–9)
–90 ?? –91
–90 > –91
So,

49. Example: Compare and .
Solution: (–4)(7) = -28 and (9)(–3) = -27.
So, (–4)(7) < (9)(–3) ⇒
To Do: Compare and .
Solution: (–10)(8) ??? (9)(–9)
–90 ?? –91
–90 > –91
So,

50. Example: Compare and .
Solution: (–4)(7) = -28 and (9)(–3) = -27.
So, (–4)(7) < (9)(–3) ⇒
To Do: Compare and .
Solution: (–10)(8) ??? (9)(–9)
–90 ?? –91
–90 > –91
So,

51. Example: Compare and .
Solution: (–4)(7) = -28 and (9)(–3) = -27.
So, (–4)(7) < (9)(–3) ⇒
To Do: Compare and .
Solution: (–10)(8) ??? (9)(–9)
–90 ?? –91
–90 > –91
So,

52. Assignment
9.1 A: 2-14
(& e-mail me something interesting about yourself plus a picture)