Chapter Sections 1.1 – Study Skills for Success in Mathematics 1.2 – Problem Solving 1.3 – Fractions 1.4 – The Real Number System 1.5 – Inequalities and Absolute Value 1.6 – Addition of Real Numbers 1.7 – Subtraction of Real Numbers 1.8 – Multiplication and Division of Real Numbers 1.9 – Exponents, Parentheses and Order of Operations 1.10 – Properties of the Real Number System

Exponents, Parentheses and Order of Operations

Learn the Meaning of Exponents In the expression 42, the 4 is called the base, and the 2 is called the exponent. exponent 42 base 43 is read “4 to the third power” and means 4·4·4 = 43 3 factors of 4

–x2 vs. (-x)2 An exponent refers only to the number or variable that directly precedes it unless parentheses are used to indicate otherwise. – x2 = -(x)(x) (– x)2 = (–x)(–x) = x2 Example: – 32 = – (3)(3) = – 9 (– 3)2 = (–3)(–3) = 9

Learn the Order of Operations To evaluate mathematical expressions, use the following order: First, evaluate the information within parentheses ( ), brackets  , or braces  .These are grouping symbols, for they group information together. A fraction bar, —, also serves as a grouping symbol. If the expression contains nested grouping symbols (one pair of grouping symbols within another pair), evaluate the information in the innermost grouping symbols first.

Learn the Order of Operations Next, evaluate all exponents. Next, evaluate all the multiplications and divisions in the order in which they occur, working from left to right. Finally, evaluate all additions or subtractions in the order in which they occur, working from left to right.

Order of Operations Evaluate: 6 + 3 • 52 – 4 = Steps Taken Exponent 6 + 3 • 25 – 4 = Multiply 6 + 75 - 4= Add 81 – 4 = 77

Order of Operations Evaluate: -7 + 2 [-6 + (36 / 32 )] = Steps Taken Exponent -7 + 2 [-6 + (36 / 9 )] = Divide -7 + 2 [-6 + 4] = Add -7 + 2 [-2] = Multiply -7 - 4 = -11

Expressions Containing Variables Evaluate: -7x + 9 when x = 3 This means to substitute 3 for x. -7(3) + 9 = -21 + 9 = -12 Evaluate: x2 when x = 3 32 = (3)(3) = 9