Objective - To simplify variable expressions involving parenthesis and exponents. Simplify the following.

Evaluate the expression given a = 3.

= Fact: Scientific calculators and computers follow the order of operations. Four function calculators do not. 4 - Function Calculator Scientific Calculator Computer x 2 = * 7 x 2 = = 11

Symbolic Differences in Calculators and Computers Expression Scientific Calculator Computer * / 4 x 2 y

Key Sequences and Computer Input Expression Calculator Key Sequence Computer 3(8 - 2)

Associative - Re-grouping is ok! You can re-group numbers together. Associative Property of Addition (a + b) + c = a + (b + c) (4 + 2) + 9 = 4 + (2 + 9) Associative Property of Multiplication Associative Property

Write an equivalent expression. 2) 3) 4) (6 + 2) + 3 1) (1 + 5) + 9 5) = 1 + (5 + 9) = 6 + (2 + 3)

Addition and multiplication are associative. Give counterexamples to prove that subtraction and division are not associative. Subtraction Counterexample: Therefore, subtraction is not associative. Division Counterexample: Therefore, division is not associative.

Commutative vs. Associative Identify each property shown below. 1) = ) 3) 4) (6 + 2) + 3 = (2 + 6) + 3 Comm. Prop. Of Add. Assoc. Prop. Of Mult. Comm. Prop. Of Mult. Comm. Prop. Of Add.

Commutative vs. Associative CommutativeAssociative (2 + 7) + 8 = (7 + 2) + 8(2 + 7) + 8 = 2 + (7 + 8) Flip-flopRe-group (2 + 7) + 8 = 8 + (2 + 7) Flip-flop ( ) does not imply Associative

Commutative vs. Associative Identify each property shown below. 1) (9 + 3) + 1 = (3 + 9) + 1 2) 3) 4) Comm. Prop. Of Add. Assoc. Prop. Of Mult. Comm. Prop. Of Add. Comm. Prop. Of Mult.

Give the property that justifies each step. StatementReasons 16 + ( )Given 16 + ( ) ( ) + 27 (100) + 27Simplify 127Simplify Comm. Prop. of Add. Assoc. Prop. of Add.

Use the commutative and associative properties to simplify each expression. 1)2) 12 + (29 + 8) 12 + (8 + 29) (12 + 8) + 29 (20)