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Classifying Numbers

Classifying Numbers. Properties. Number Sets. Natural Numbers : 1, 2, 3, … Whole Numbers : 0, 1, 2, 3, … Integers : …-3, -2, -1, 0, 1, 2, 3, … Rational Numbers : where p and q are integers and q ≠0 Irrational Numbers : non-terminating and non-repeating

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Classifying Numbers

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  1. Classifying Numbers Properties

  2. Number Sets • Natural Numbers: 1, 2, 3, … • Whole Numbers: 0, 1, 2, 3, … • Integers: …-3, -2, -1, 0, 1, 2, 3, … • Rational Numbers: where p and q are integers and q≠0 • Irrational Numbers: non-terminating and non-repeating • Real Numbers: all rational and irrational

  3. These are rational: • 5 • -3.45 • 2.333…

  4. These are irrational • 3.46446444644446…

  5. The number sets do overlap…. Real Numbers Rational Irrational Integer Whole Natural

  6. Classify each number in as many ways as possible. • 0.12122122212222… • 56 • -7

  7. Classify each number in as many ways as possible. • 0 • 23.0 • -2.2

  8. Activity • You are to place the numbers in your bag in the appropriate place on the Venn Diagram.

  9. Properties of Addition & Multiplication:For all real #’s, a, b, c… • Closure: then a+b is a real number ab is a real number • Commutative: a + b = b + a ab = ba • Associative: (a+b)+c = a+(b+c) (ab)c = a(bc) • Identity: a + 0 = 0 + a = a a*1 = 1*a = a • Inverse: a + (-a) = 0

  10. Distributive Property For all real numbers a, b, and c: a(b + c) = ab + ac and (b + c)a = ba + bc)

  11. State a property to justify the following statements… • 6 +(-3) = (-3) + 6 • 2(4 – 5) = (4- 5)2 • 3(4a+5) = 12a + 15 • -5 + (x + 2) = (-5 + x) + 2 • (x+3) + 6 = 6 + (x+ 3) • 4 ( 1) = 4 • -5 + 5 = 0

  12. What type of number do I get when I perform the following operation?

  13. What type of number do I get when I perform the following operation?

  14. What type of number do I get when I perform the following operation?

  15. What type of number do I get when I perform the following operation?

  16. What type of number do I get when I perform the following operation?

  17. What type of number do I get when I perform the following operation?

  18. What type of number do I get when I perform the following operation?

  19. What type of number do I get when I perform the following operation?

  20. What type of number do I get when I perform the following operation?

  21. Homework • Worksheet

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