Properties of Real Numbers The properties of real

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

Number Classification • • • Natural numbers are the counting numbers. Whole numbers are natural numbers and zero. Integers are whole numbers and their opposites. Rational numbers can be written as a fraction. Irrational numbers cannot be written as a fraction. All of these numbers are real numbers.

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

Classify each number -1 6 real, rational, integer, whole, natural real, irrational real, rational 0 -2. 222 real, rational, integer, whole real, rational

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

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

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

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

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

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

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

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

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

Name the property • • • 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(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