303B Section 09.1

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303B Section 09.1

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

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