Beginning and Intermediate Algebra
5th Edition
ISBN: 9781259616754
Author: Julie Miller, Molly O'Neill, Nancy Hyde
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 1.3, Problem 61PE
Concept 3: Order of Operations
For Exercises 43-74, use the order of operations to simplify each expression.(See Example 3-5.)
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Describe the order of operations and explain how it is used to simplify expressions. Explain specifically the order in which mathematical operations must be performed to correctly simplify an expression.
Provide an example of a real-life situation in your current or future profession where a specific order of steps is necessary for a proper end result. What will happen if the proper order is not followed? (Humor and creativity are encouraged, if used appropriately.)
Develop an original mathematical expression which must be simplified using order of operations. Include addition, subtraction, multiplication, division, exponents, and at least one set of parentheses. Simplify the expression INCORRECTLY, showing each step as you simplify. DO NOT include the reasons for each step. Do not include variables (letters) in your expression.
simplify1/4 b - 1/3 + 5/6 b- 1/5(Use integers or fraction for any numbers in the expression.)
ALGEBRAI PRACTICE/ SECTION 1 / 90F 9
Let r, s, and w represent three distinct numbers.
• r is a nonzero rational number.
s is a nonzero rational number.
w is an irrational number.
For each expression in the following table, indicate whether the value of the expression must be rational or
irrational.
Select one box per row.
Must Be Rational
Must Be Irrational
r+ s
TS
Chapter 1 Solutions
Beginning and Intermediate Algebra
Ch. 1.1 - Write the number as a product of prime factors.Ch. 1.1 - Write the number as a product of prime factors.Ch. 1.1 - Simplify to lowest terms 20 50Ch. 1.1 - Simplify to lowest terms 32 12Ch. 1.1 - Multiply.
5.
Ch. 1.1 - Multiply. 8 9 × 3 4Ch. 1.1 - Multiply. 4 5 × 5 4Ch. 1.1 - Multiply. 10 × 1 10Ch. 1.1 - Divide. 12 25 ÷ 8 15Ch. 1.1 - Divide. 12 25 ÷ 8 15
Ch. 1.1 - Add or subtract as indicated.
11.
Ch. 1.1 - Add or subtract as indicated. 5 8 − 1 8Ch. 1.1 - Find the LCM. 10 and 25.Ch. 1.1 - Write each of the fractions 5 8 and 5 12 as an...Ch. 1.1 - Subtract. 5 8 − 5 12Ch. 1.1 - Add. 2 3 + 1 2 + 5 6Ch. 1.1 - Subtract. 2 3 4 − 1 1 3Ch. 1.1 - Divide. 5 5 6 ÷ 3 2 3Ch. 1.1 - Vocabulary and Key Concepts a. A______ is the...Ch. 1.1 - Concept 1: Basic Definitions For Exercises 2-10,...Ch. 1.1 - Concept 1: Basic Definitions
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For Exercises 2-10,...Ch. 1.1 - Concept 1: Basic Definitions
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For Exercises 11-18,...Ch. 1.1 - Concept 1: Basic Definitions For Exercises 11-18,...Ch. 1.1 - Concept 1: Basic Definitions For Exercises 11-18,...Ch. 1.1 - Concept 1: Basic Definitions
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105. For what numbers, , is ...Ch. 1.2 - Expanding Your Skills For what number, a , is | a...Ch. 1.3 - Evaluate. 4 3Ch. 1.3 - Evaluate. 2 4Ch. 1.3 - Evaluate.
3.
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Ch. 1.3 - Simplify the expression. 60 − 3 2 ⋅ 2 3 + 8 ÷ 2Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Translate each English phrase to an algebraic...Ch. 1.3 - Vocabulary and Key Concepts a. Fill in the blanks...Ch. 1.3 - Review Exercises Which of the following are...Ch. 1.3 - Review Exercises
3. Evaluate.
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6. Find the opposite of –34.2
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2.
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3.
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8. Evaluate the expressions.
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For Exercises 81-90, write...Ch. 1.4 - Concept 3: Translations
For Exercises 81-90, write...Ch. 1.4 - Prob. 88PECh. 1.4 - Prob. 89PECh. 1.4 - Prob. 90PECh. 1.4 - Prob. 91PECh. 1.4 - Prob. 92PECh. 1.4 - Prob. 93PECh. 1.4 - Concept 4: Applications Involving Addition of Real...Ch. 1.4 - Prob. 95PECh. 1.4 - Prob. 96PECh. 1.4 - Prob. 97PECh. 1.4 - Concept 4: Applications Involving Addition of Real...Ch. 1.5 - Subtract. 1 − ( − 3 )Ch. 1.5 - Subtract.
2.
Ch. 1.5 - Prob. 3SPCh. 1.5 - Prob. 4SPCh. 1.5 - Prob. 5SPCh. 1.5 - Prob. 6SPCh. 1.5 - Prob. 7SPCh. 1.5 - Prob. 8SPCh. 1.5 - Prob. 9SPCh. 1.5 - Prob. 10SPCh. 1.5 - 11. During Harold’s first round on Jeopardy, he...Ch. 1.5 - Prob. 12SPCh. 1.5 - Prob. 13SPCh. 1.5 - Simplify the expressions. ( 12 − 5 ) 2 + 4 − ( −...Ch. 1.5 - Prob. 15SPCh. 1.5 - Prob. 16SPCh. 1.5 - Vocabulary and Key Concepts a. The expression a −...Ch. 1.5 - Review Exercise For Exercises 2-5, write each...Ch. 1.5 - Prob. 3PECh. 1.5 - Prob. 4PECh. 1.5 - Prob. 5PECh. 1.5 - Prob. 6PECh. 1.5 - Prob. 7PECh. 1.5 - Review Exercise For Exercises 6-8, simplify the...Ch. 1.5 - Prob. 9PECh. 1.5 - Prob. 10PECh. 1.5 - Prob. 11PECh. 1.5 - Prob. 12PECh. 1.5 - Prob. 13PECh. 1.5 - Prob. 14PECh. 1.5 - Prob. 15PECh. 1.5 - Prob. 16PECh. 1.5 - Concept 1: Subtraction of Real Numbers
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For...Ch. 1.5 - Prob. 26PECh. 1.5 - Prob. 27PECh. 1.5 - Prob. 28PECh. 1.5 - Prob. 29PECh. 1.5 - Prob. 30PECh. 1.5 - Prob. 31PECh. 1.5 - Concept 1: Subtraction of Real Numbers For...Ch. 1.5 - Prob. 33PECh. 1.5 - Prob. 34PECh. 1.5 - Prob. 35PECh. 1.5 - Prob. 36PECh. 1.5 - Prob. 37PECh. 1.5 - Prob. 38PECh. 1.5 - Prob. 39PECh. 1.5 - Prob. 40PECh. 1.5 - Prob. 41PECh. 1.5 - Prob. 42PECh. 1.5 - Prob. 43PECh. 1.5 - Prob. 44PECh. 1.5 - Prob. 45PECh. 1.5 - Prob. 46PECh. 1.5 - Prob. 47PECh. 1.5 - Prob. 48PECh. 1.5 - Prob. 49PECh. 1.5 - Prob. 50PECh. 1.5 - Prob. 51PECh. 1.5 - Prob. 52PECh. 1.5 - Prob. 53PECh. 1.5 - Prob. 54PECh. 1.5 - Prob. 55PECh. 1.5 - Prob. 56PECh. 1.5 - Prob. 57PECh. 1.5 - Prob. 58PECh. 1.5 - Prob. 59PECh. 1.5 - Prob. 60PECh. 1.5 - Prob. 61PECh. 1.5 - Prob. 62PECh. 1.5 - Prob. 63PECh. 1.5 - Prob. 64PECh. 1.5 - Prob. 65PECh. 1.5 - Prob. 66PECh. 1.5 - Concept 2: Translations
For Exercises 61-70, write...Ch. 1.5 - Concept 2: Translations For Exercises 61-70, write...Ch. 1.5 - Concept 2: Translations For Exercises 61-70, write...Ch. 1.5 - Prob. 70PECh. 1.5 - Prob. 71PECh. 1.5 - Concept 3: Applications involving Subtraction On...Ch. 1.5 - Prob. 73PECh. 1.5 - Prob. 74PECh. 1.5 - Prob. 75PECh. 1.5 - Prob. 76PECh. 1.5 - Prob. 77PECh. 1.5 - Prob. 78PECh. 1.5 - Prob. 79PECh. 1.5 - Prob. 80PECh. 1.5 - Prob. 81PECh. 1.5 - Prob. 82PECh. 1.5 - Prob. 83PECh. 1.5 - Prob. 84PECh. 1.5 - Prob. 85PECh. 1.5 - Prob. 86PECh. 1.5 - Prob. 87PECh. 1.5 - Prob. 88PECh. 1.5 - Prob. 89PECh. 1.5 - Concept 4: Applying the Order of Operations For...Ch. 1.5 - Prob. 91PECh. 1.5 - Prob. 92PECh. 1.5 - Prob. 93PECh. 1.5 - Prob. 94PECh. 1.5 - Prob. 95PECh. 1.5 - Prob. 96PECh. 1.5 - Prob. 97PECh. 1.5 - Prob. 98PECh. 1.5 - Prob. 99PECh. 1.5 - Prob. 100PECh. 1.5 - Prob. 101PECh. 1.5 - Concept 4: Applying the Order of Operations For...Ch. 1.5 - Prob. 103PECh. 1.5 - Prob. 104PECh. 1.5 - Addition and Subtraction of Real Numbers
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1.
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For Exercise...Ch. 1.7 - Expanding Your Skills For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills
For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills
For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills For Exercises 127-134,...Ch. 1.7 - Expanding Your Skills As a small child in school,...Ch. 1 - For Exercises 1-4, identify as a proper or...Ch. 1 - For Exercises 1-4, identify as a proper or...Ch. 1 - For Exercises 1-4, identify as a proper or...Ch. 1 - For Exercises 1-4, identify as a proper or...Ch. 1 - Write 112 as a product of primes.Ch. 1 - Prob. 6RECh. 1 - For Exercises 7-12, perform the indicated...Ch. 1 - For Exercises 7-12, perform the indicated...Ch. 1 - For Exercises 7-12, perform the indicated...Ch. 1 - For Exercises 7-12, perform the indicated...Ch. 1 - For Exercises 7-12, perform the indicated...Ch. 1 - For Exercises 7-12, perform the indicated...Ch. 1 - The surface area of the Earth is approximately 510...Ch. 1 - 14. Given the set,
a. List the natural...Ch. 1 - For Exercises 15-18, determine the absolute...Ch. 1 - For Exercises 15-18, determine the absolute value....Ch. 1 - For Exercises 15-18, determine the absolute value....Ch. 1 - For Exercises 15-18, determine the absolute value....Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 19-27, identify whether the...Ch. 1 - For Exercises 28-31, evaluate each expression for...Ch. 1 - For Exercises 28-31, evaluate each expression for...Ch. 1 - For Exercises 28-31, evaluate each expression for...Ch. 1 - For Exercises 28-31, evaluate each expression for,...Ch. 1 - For Exercises 32-37, write each English phrase as...Ch. 1 - For Exercises 32-37, write each English phrase as...Ch. 1 - For Exercises 32-37, write each English phrase as...Ch. 1 - For Exercises 32-37, write each English phrase as...Ch. 1 - For Exercises 32-37, write each English phrase as...Ch. 1 - For Exercises 32-37, write each English phrase as...Ch. 1 - For Exercises 38-43, simplify the expressions. 6 3Ch. 1 - For Exercises 38-43, simplify the expressions.
39....Ch. 1 - For Exercises 38-43, simplify the expressions. 36Ch. 1 - For Exercises 38-43, simplify the expressions.
41....Ch. 1 - For Exercises 38-43, simplify the expressions. ( 1...Ch. 1 - For Exercises 38-43, simplify the expressions. ( 3...Ch. 1 - For Exercises 44-47, perform the indicated...Ch. 1 - For Exercises 44-47, perform the indicated...Ch. 1 - For Exercises 44-47, perform the indicated...Ch. 1 - For Exercises 44-47, perform the indicated...Ch. 1 - For Exercises 48-60, add. − 6 + 8Ch. 1 - For Exercises 48-60, add. 14 + ( − 10 )Ch. 1 - For Exercises 48-60, add. 21 + ( − 6 )Ch. 1 - For Exercises 48-60, add. − 12 + ( − 5 )Ch. 1 - For Exercises 48-60, add. 2 7 + ( − 1 9 )Ch. 1 - For Exercises 48-60, add. ( − 8 11 ) + ( 1 2 )Ch. 1 - For Exercises 48-60, add. ( − 1 10 ) + ( − 5 6 )Ch. 1 - For Exercises 48-60, add. ( − 5 2 ) + ( − 1 5 )Ch. 1 - For Exercises 48-60, add. − 8.17 + 6.02Ch. 1 - For Exercises 48-60, add. 2.9 + ( − 7.18 )Ch. 1 - For Exercises 48-60, add. 13 + ( − 2 ) + ( − 8 )Ch. 1 - For Exercises 48-60, add.
59.
Ch. 1 - For Exercises 48-60, add.
60.
Ch. 1 - Under what conditions will the expression a + b be...Ch. 1 - 62. Richard’s checkbook was overdrawn by $45 (that...Ch. 1 - For Exercises 63-75, subtract. 13 − 25Ch. 1 - For Exercises 63-75, subtract. 31 − ( − 2 )Ch. 1 - For Exercises 63-75, subtract. − 8 − ( − 7 )Ch. 1 - For Exercises 63-75, subtract. − 2 − 15Ch. 1 - For Exercises 63-75, subtract. ( − 7 9 ) − 5 6Ch. 1 - For Exercises 63-75, subtract. 1 3 − 9 8Ch. 1 - For Exercises 63-75, subtract. 7 − 8.2Ch. 1 - For Exercises 63-75, subtract. − 1.05 − 3.2Ch. 1 - Prob. 71RECh. 1 - Prob. 72RECh. 1 - Prob. 73RECh. 1 - Prob. 74RECh. 1 - Prob. 75RECh. 1 - Prob. 76RECh. 1 - For Exercises 77-81, write an algebraic expression...Ch. 1 - Prob. 78RECh. 1 - Prob. 79RECh. 1 - Prob. 80RECh. 1 - Prob. 81RECh. 1 - Prob. 82RECh. 1 - Prob. 83RECh. 1 - Prob. 84RECh. 1 - Prob. 85RECh. 1 - Prob. 86RECh. 1 - Prob. 87RECh. 1 - Prob. 88RECh. 1 - Prob. 89RECh. 1 - For Exercises 83-100, multiply or divide as...Ch. 1 - Prob. 91RECh. 1 - Prob. 92RECh. 1 - Prob. 93RECh. 1 - Prob. 94RECh. 1 - Prob. 95RECh. 1 - Prob. 96RECh. 1 - Prob. 97RECh. 1 - Prob. 98RECh. 1 - Prob. 99RECh. 1 - For Exercises 83-100, multiply or divide as...Ch. 1 - For Exercises 101-106, perform the indicated...Ch. 1 - Prob. 102RECh. 1 - Prob. 103RECh. 1 - Prob. 104RECh. 1 - Prob. 105RECh. 1 - Prob. 106RECh. 1 - Prob. 107RECh. 1 - Prob. 108RECh. 1 - For Exercises 107-110, evaluate each expression...Ch. 1 - Prob. 110RECh. 1 - Prob. 111RECh. 1 - Prob. 112RECh. 1 - Prob. 113RECh. 1 - Prob. 114RECh. 1 - Prob. 115RECh. 1 - Prob. 116RECh. 1 - Prob. 117RECh. 1 - Prob. 118RECh. 1 - Prob. 119RECh. 1 - Prob. 120RECh. 1 - Prob. 121RECh. 1 - Prob. 122RECh. 1 - Prob. 123RECh. 1 - Prob. 124RECh. 1 - Prob. 125RECh. 1 - Prob. 126RECh. 1 - Prob. 127RECh. 1 - Prob. 128RECh. 1 - Prob. 129RECh. 1 - Identify the coefficients for the terms listed in...Ch. 1 - Prob. 131RECh. 1 - Prob. 132RECh. 1 - Prob. 133RECh. 1 - Prob. 134RECh. 1 - Prob. 135RECh. 1 - Prob. 136RECh. 1 - Prob. 137RECh. 1 - Prob. 138RECh. 1 - Prob. 139RECh. 1 - Prob. 140RECh. 1 - 1. Simplify.
Ch. 1 - Add and subtract. 5 4 − 5 12 + 2 3Ch. 1 - 3. Divide.
Ch. 1 - Subtract. 4 1 4 − 1 7 8Ch. 1 - Is 0. 315 ¯ a rational number or an irrational...Ch. 1 - Use the definition of exponents to expand the...Ch. 1 - Plot the points on a number line: | 3 | , 0 , − 2...Ch. 1 - 8. Use the number line in Exercise 7 to identify...Ch. 1 - Identify the property that justifies each...Ch. 1 - 10. Write each expression as an English...Ch. 1 - Write the phrase as an algebraic expression: “The...Ch. 1 - For Exercises 12-14, write each English statement...Ch. 1 - For Exercises 12-14, write each English statement...Ch. 1 - For Exercises 12-14, write each English statement...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - For Exercises 15-29, perform the indicated...Ch. 1 - The average high temperature in January for Nova...Ch. 1 - 31. In the third quarter of a football game, a...Ch. 1 - For Exercises 32-36, simplify each expression. 3 k...Ch. 1 - For Exercises 32-36, simplify each expression. − 5...Ch. 1 - For Exercises 32-36, simplify each expression. 4 (...Ch. 1 - For Exercises 32-36, simplify each expression. − 3...Ch. 1 - For Exercises 32-36, simplify each expression. 1 2...Ch. 1 - For Exercises 37-40, evaluate each expression...Ch. 1 - For Exercises 37-40, evaluate each expression...Ch. 1 - For Exercises 37-40, evaluate each expression...Ch. 1 - For Exercises 37-40, evaluate each expression...
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