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Properties of Real Numbers

Properties of Real Numbers. The properties of real numbers allow us to manipulate expressions and equations and find the values of a variable. Natural numbers are the counting numbers. Whole numbers are natural numbers and zero.

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Properties of Real Numbers

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  1. Properties of Real Numbers The properties of real numbers allow us to manipulate expressions and equations and find the values of a variable.

  2. Naturalnumbers are the counting numbers. Wholenumbers are natural numbers and zero. Integers are whole numbers and their opposites. Rationalnumbers can be written as a fraction. Irrationalnumbers cannot be written as a fraction. All of these numbers are real numbers. Number Classification

  3. Subsets of the Real Numbers Number Classifications Q - Rational Z - Integers I -Irrational W - Whole N - Natural

  4. -1 real, rational, integer real, rational, integer, whole, natural real, irrational real, rational real, rational, integer, whole real, rational Classify each number 6 0 -2.222

  5. Commutative Property Think… commuting to work. Deals with ORDER. It doesn’t matter what order you ADD or MULTIPLY. a+b = b+a 4 • 6 = 6 • 4 Properties of Real Numbers

  6. Associative Property Think…the people you associate with, your group. Deals with grouping when you Add or Multiply. Order does not change. Properties of Real Numbers

  7. Associative Property Properties of Real Numbers • (a + b) + c = a + ( b + c) • (nm)p = n(mp)

  8. Properties of Real Numbers Additive Identity Property • s + 0 = s Multiplicative Identity Property • 1(b) = b

  9. Properties of Real Numbers Distributive Property • a(b + c) = ab + ac • (r + s)9 = 9r + 9s

  10. 5 = 5 + 0 5(2x + 7) = 10x + 35 8 • 7 = 7 • 8 24(2) = 2(24) (7 + 8) + 2 = 2 + (7 + 8) Additive Identity Distributive Commutative Commutative Commutative Name the Property

  11. 7 + (8 + 2) = (7 + 8) + 2 1 • v + -4 = v + -4 (6 - 3a)b = 6b - 3ab 4(a + b) = 4a + 4b Associative Multiplicative Identity Distributive Distributive Name the Property

  12. Reflexive Property a + b = a + b Properties of Real Numbers The same expression is written on both sides of the equal sign.

  13. Properties of Real Numbers Symmetric Property • If a = b then b = a • If 4 + 5 = 9 then 9 = 4 + 5

  14. Properties of Real Numbers TransitiveProperty • If a = b and b = c then a = c • If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5

  15. Properties of Real Numbers Substitution Property • If a = b, then a can be replaced by b. • a(3 + 2) = a(5)

  16. 5(4 + 6) = 20 + 30 5(4 + 6) = 5(10) 5(4 + 6) = 5(4 + 6) If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6) 5(4 + 6) = 5(6 + 4) If 5(10) = 5(4 + 6) and 5(4 + 6) = 20 + 30 then 5(10) = 20 + 30 Distributive Substitution Reflexive Symmetric Commutative Transitive Name the property

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