Algebra 1 Chapter 1 Section 6

1-6 Properties of Real Numbers The commutative and associate properties of addition and multiplication allow you to rearrange an expression. Commutative Property - You can add or multiply real numbers in any order. a + b = b + aa · b = b · a

Associative Property – When you add or multiply 3 or more numbers, changing the grouping will not change the answer. a + (b + c) = (a + b) + c a · (b · c) = (a · b) · c

Example 1: Identifying Properties Name the property that is illustrated in each equation. A) (4 + x) + y = 4 + (x + y) B) -5 · b = b · (-5) C) 2 + (6 + m) = 2 + (m + 6)

The commutative and associative properties are true for addition and multiplication. They may not be true for other operations. A counterexample is an example that disproves a statement, or shows that it is false. One counterexample is enough to disprove a statement.

Example 2: Finding Counterexamples to Statements about Properties Find a counterexample to disprove the statement “ The Associative Property is true for subtraction.” Find three real numbers, a, b, c, such that a - (b - c) ≠ (a - b) – c. Let’s try some numbers.

The Distributive Property For real numbers a, b, and c, a(b + c) = ab + ac Ex.)3(4 + 8) = 3(4) + 3(8) 3(12) = = 36

Example 3: A) 3(x + 2) B) 6(x - 8) c) x(x + 5)