Order of Operations Chapter 1 Section 1.1

Objective Students will simplify numerical expressions and evaluate algebraic expressions. Students will also simplify expressions with grouping symbols.

Vocabulary Expression Variable Variable expression Numerical expression Substitution Grouping symbols Order of operations

Concept An expression contains numbers, variables, and operations (no equal sign)

Concept A variable is a symbol used to represent one or more numbers. example: a, x, y, n, … , any letter of alphabet

Concept A variable expression is an expression that contains a variable example: 15 X n

Concept Important to Remember: 19 X n can be written as 19n a X b can be written as ab ½ X x can be written as 1/2x

Concept A numerical expression is an expression that names a particular number example: 4.5 X 5

Concept Substitution Principle: An expression may be replaced by another expression that has the same value.

Concept Evaluating the expression = replacing each variable in a variable expression by a given value and simplifying the result

Example Evaluate each expression if a = 5 1. a + 2 7 2. 7a 35

Concept When solving expressions is it important to remember that you must always follow the order of operations Parenthesis Exponents Multiply/Divide Add/Subtract

Example Simplify each expression 1. (42 ÷ 6) + 8 15 2. 54 ÷ (8 – 2) 9

Example Evaluate the expression when x = 12 and y = 9 (5x) – (3 + y) 48

Example Simplify 1. 6(5 – 3) 12 2. 6(5) – 3 27

Concept Some expressions contain grouping symbols other than parenthesis (brackets or fraction bar). Always begin by simplifying the expression in the innermost grouping symbol then work toward the outermost grouping symbol. If the expression contains a fraction bar, simplify top, simplify bottom, simplify top with bottom.

Example Simplify 12 + 4 15 – 7 2 18 – [52 ÷ (7 + 6)] 14

Example Simplify 1. 29 + 15 X 4 89 2. 19 – 7 + 12 X 2 ÷ 8 15

Example Evaluate if x = 3 and y = 8 4x + 5y 3x – y 52

Questions

Assignment Worksheet