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303B Section 09.1

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  • 1. An Ordering Activity Microsoft Office Word 97 - 2003 Document
  • 2. Fraction Equality: if and only if ad = bc.
  • 3. Figure 9.2
  • 4. Figure 9.5
  • 5. 9.1 THE RATIONAL NUMBERS Definition: The set of rational numbers is the set Examples of Rational Numbers: , , , 3, .7 Explanation: , ,
  • 6. 9.1 THE RATIONAL NUMBERS Definition: The set of rational numbers is the set Examples of Rational Numbers: , , , 3, .7 Explanation: , ,
  • 7. Equality of Rational Numbers: if and only if ad = bc. To Do: Show that Solution: (–12)×(–3) = 36 = 9×4
  • 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. 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?
  • 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: Notice that
  • 16. Example: Notice that
  • 17. Example: Notice that
  • 18. To Do: Add Answer:
  • 19. To Do: Add Answer:
  • 20. Notice that since . Also, notice that . Therefore, is the additive inverse of . That is, . So,
  • 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. Rational numbers on the number line:
  • 24. Rational numbers on the number line:
  • 25. To Do: Subtract Solution:
  • 26. To Do: Subtract Solution:
  • 27. To Do: Subtract Solution:
  • 28. To Do: Multiply and simplify Answer:
  • 29. To Do: Multiply and simplify Answer:
  • 30. To Do: Multiply and simplify Answer:
  • 31. Why does ? Well, why does 6 ÷ 2 = 3? Because 2 × 3 = 6. Let’s check : . Yay! To Do: Divide and simplify Answer:
  • 32. Why does ? Well, why does 6 ÷ 2 = 3? Because 2 × 3 = 6. Let’s check : . Yay! To Do: Divide and simplify Answer:
  • 33. Why does ? Well, why does 6 ÷ 2 = 3? Because 2 × 3 = 6. Let’s check : . Yay! To Do: Divide 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. Example:
  • 39. Example:
  • 40. To Do: Divide Solution:
  • 41. To Do: Divide Solution:
  • 42. Error in book: This should read if and only if a < c and b > 0.
  • 43. 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,
  • 44. 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,
  • 45. 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,
  • 46. 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,
  • 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. Assignment 9.1 A: 2-14 (& e-mail me something interesting about yourself plus a picture)

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