Properties of Real Numbers OBJECTIVES What youll learn

Properties of Real Numbers

OBJECTIVES: What you’ll learn • Understand/use Properties & Classifications of Properties of Real Numbers Sounds pretty hard, doesn’t it? It’s not! 2

Commutative Properties • Commutative Property of Addition • Commutative Property of Multiplication • • • Example: • Commutative Property . • The Commutative Property deals with ORDER. It doesn’t matter what order you ADD or MULTIPLY.

Associative Properties • Associative Property of Addition • Associative Property of Multiplication • • • Example: – • Associative Property – • Deals with grouping when you Add or Multiply. • Order does not change.

Distributive Property • Distributive Property – Example: • Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside.

Identity Properties • Identity Property of Addition – le: Examp – Additive Identity Property - A number added by zero is equal to that same number. • Identity Property of Multiplication – ple: Exam – Multiplication Identity Property – A number multiply by 1 equal that same number.

Inverse Properties • Inverse Property of Addition • Inverse Property of Multiplication – For every a, there is an additive inverse –a such that a + (-a) = 0 – For every a ( ), there is a multiplicative inverse such that – Example: 5 + (-5) = 0 Additive Inverse Property- the additive inverse is the opposite of that number which when add it’s result is zero. Example: Multiplication Inverse Property. The multiplication inverse is the reciprocal of that number, which when multiply it’s result is 1.

Properties of Real Numbers Example – Identifying Properties Name the property that each equation illustrates. Explain. 9+7 = 7+9 t+0=t (d+4) + = d + ( 4 * 3) - (q+3) = -q - 3 Commutative Property of Addition, Identity Property of Addition Associative Property of Multiplication Distributive Property,

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

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