232 CHAPTER 5 Number Theory and the Real Number System In the expression + ⋅ 2 5 4, since multiplication is performed before addition: + ⋅ = + = 2 5 4 2 20 22 ORDER OF OPERATIONS 1. First, perform all operations within parentheses or other grouping symbols. 2. Next, evaluate all exponents. 3. Next, perform all multiplications and divisions going from left to right. 4. Finally, perform all additions and subtractions going from left to right. PROCEDURE Example 11 Using the Order of Operations Evaluate − ⋅ + 100 3 5 8. 2 Solution We will evaluate this expression using the order of operations. − ⋅ + = − ⋅ + = − + = + = 100 3 5 8 100 3 25 8 100 75 8 25 8 33 2 7 Now try Exercise 51 Example 12 Using the Order of Operations Evaluate + ÷ ⋅ − (41 23) 8 (13 15) .2 Solution We begin by evaluating the expressions within the parentheses. ( ) ( ) + ÷ ⋅ − = ÷ ⋅ − = ÷ ⋅ = ⋅ = 41 23 8 13 15 64 8 ( 2) 64 8 4 8 4 32 2 2 7 Now try Exercise 55 Exercises SECTION 5.2 Warm Up Exercises In Exercises 1– 4, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. The set of numbers … {0, 1, 2, 3, 4, } is known as the ________ numbers. Whole 2. The rule for subtraction indicates that to subtract b from a, ________ the additive inverse of b to a. Add 3. a) The product of two numbers with like signs is a(n) ________ number. Positive b) The product of two numbers with unlike signs is a(n) ________ number. Negative 4. a) The quotient of two numbers with unlike signs is a(n) ________ number. Negative b) The quotient of two numbers with like signs is a(n) ________ number. Positive Practice the Skills In Exercises 5–8, write the natural number given its spoken form. 5. Two million, four hundred eighty-nine thousand 2,489,000 6. Eighty-two billion, four million, twenty-two 82,004,000,022 7. Four point zero nine billion 4,090,000,000 8. Eighty-two point four three trillion 82,430,000,000,000 Learning Catalytics Keyword: Angel-SOM-5.3 (See Preface for additional details.) Instructor Resources for Section 5.2 in MyLab Math • Objective-Level Videos 5.2 • Animation: Adding and Subtracting Integers • PowerPoint Lecture Slides 5.2 • MyLab Exercises and Assignments 5.2
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