2 Chapter Chapter 2 Integers and Introduction to Variables

Section 2.6 Order of Operations

Simplifying Expressions by Using the Order of Operations. Objective A Simplifying Expressions by Using the Order of Operations.

Chapter 1 / Whole Numbers and Introduction to Algebra Order of Operations Chapter 1 / Whole Numbers and Introduction to Algebra 1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars, starting with the innermost set. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right.

Chapter 1 / Whole Numbers and Introduction to Algebra Helpful Hint Chapter 1 / Whole Numbers and Introduction to Algebra When simplifying expressions with exponents, parentheses make an important difference. (–5)2 and –52 do not mean the same thing. (–5)2 means (–5)(–5) = 25. –52 means the opposite of 5 ∙ 5, or –25. Only with parentheses is the –5 squared.

Example Simplify. Objective A 6

Example Simplify. Add from right to left. Objective A 7

Example Simplify 4(5 – 2) + 42. 4(5 – 2) + 42 = 4(3) + 42 = 4(3) + 16 Simplify inside parentheses. = 4(3) + 16 Write 42 as 16. = 12 + 16 Multiply. Objective D Continued = 28 Add.

Example Simplify. Objective A 9

Example Simplify. Objective A 10

Example Simplify. Objective A 11

Evaluate an Algebraic Expression. Objective B Evaluate an Algebraic Expression.

Example Evaluate 9x2 + 12 for x = –3 Replace x with –3 in 9x2 + 12. = 9 · 9 + 12 = 81 + 12 Objective B = 93

Find the Average of a List of Numbers. Objective C Find the Average of a List of Numbers.

Example The graph shows the monthly normal temperatures for Barrow, Alaska. Use this graph to find the average of the temperatures for the months January through May. Objective A 15

Example (cont) The average of the temperatures is There are 5 months from January through May. Objective A The average of the temperatures is 16