Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ Study Set 1.1 CHAPTER CONCEPTS STUDY SET Section 1.1 Classify as expression or equation: 18 + m = 23 is an equation VOCABULARY Complete the statement: The answer to an addition problem is called a sum The answer to a subtraction problem is called a difference Complete the statement: The answer to a multiplication problem is called a product The answer to a division problem is called a quotient Complete the statement: Variables are letters that stand for numbers 10 Classify as expression or equation: 18 + m is an algebraic expression 11 Classify as expression or equation: y – is an algebraic expression 12 Classify as expression or equation: y – = is an equation 13 Classify as expression or equation: 30x is an algebraic expression 14 Classify as expression or equation: t = 16b is an equation Complete the statement: Variables and numbers can be combined with the operations of addition, subtraction, multiplication, and division to create algebraic expressions Complete the statement: An equation is a mathematical sentence that contains an = symbol Complete the statement: An equation such as t = 2b, which expresses a known relationship between two or more variables, is called a formula Complete the statement: The illustration in Exercise shows a line graph shown Complete the statement: In the illustration below, the horizontal axis of the graph has been scaled in units of second The vertical axis of the graph has been scaled in units of 50 feet 15 Classify as expression or equation: r = is an equation 16 Classify as expression or equation: c−7 is an algebraic expression 17 Complete the statement: a The expression 5x – 16 contains the operations of multiplication and subtraction b The variable in the expression is x 18 Complete the statement: 12 + t a The expression contains the 25 operations of addition and division b The variable is t 19 Complete the statement: a The equation m + = 20 – m contains the operations of addition and subtraction b The variable is m INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 20 Complete the statement: a The equation y + 14 = 5(6) contains the operations of addition and multiplication b The variable is y 31 Basic Operations: l ∙ w = lw 21 Interpret the graph: a The dashed lines help us determine that 15–year–old machinery is worth $35,000 b As the machinery ages, its value decreases 33 Basic Operations: P ∙ r ∙ t = Prt 22 Interpret the graph: a The income received from 30 customers is $250 The income received from 50 customers is $350 The income received from 70 customers is $450 b As the number of customers increases, the income increases 32 Basic Operations: b ∙ h = bh 34 Basic Operations: l ∙ w ∙ h = lwh 35 Basic Operations: 2(w) = 2w 36 Basic Operations: 2(l) = 2l 37 Basic Operations: (x)(y) = xy 38 Basic Operations: (r)(t) = rt NOTATION 39 Basic Operations: 32 32 ÷ x = x 23 Basic Operations: × = ∙ = 5(6) 24 Basic Operations: × = ∙ = 4(7) 40 Basic Operations: y y ÷ 15 = 15 25 Basic Operations: 34 × 75 = 34 ∙ 75 = 34(75) 41 Basic Operations: 90 30 90 = 30 26 Basic Operations: 90 × 12 = 90 ∙ 12 = 90(12) 27 Basic Operations: ∙ x = 4x 42 Basic Operations: 80 20 80 = 20 28 Basic Operations: ∙ y = 5y GUIDED PRACTICE 29 Basic Operations: ∙ r ∙ t = 3rt 43 Interpret the graph: 250 tires are needed to make 125 bicycles 30 Basic Operations: 22 ∙ q ∙ s = 22qs 44 Interpret the graph: 800 tires are needed to make 400 bicycles INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ 45 Interpret the graph: 200 tires are needed to make 100 bicycles 46 Interpret the graph: 400 tires are needed to make 200 bicycles Study Set 1.1 58 Translate verbal model into equation: y c= 100 59 Complete the table: 47 Vocabulary: 18(24) = 432 means the product of 18 and 24 is equal to 432 48 Vocabulary: 45 ∙ 12 = 540 means the product of 45 and 12 is equal to 540 60 Complete the table: 49 Vocabulary: 11 – = means the difference of 11 and is equal to 50 Vocabulary: 65 + 89 = 154 means the sum of 65 and 89 is equal to 154 61 Complete the table: 51 Vocabulary: 2x = means the product of and x is equal to 52 Vocabulary: 16t = means the product of 16 and t is equal to 62 Complete the table: 53 Vocabulary: 66 = means the quotient of 66 and 11 is 11 equal to 54 Vocabulary: 12 ÷ = means the quotient of 12 and is equal to 55 Translate verbal model into equation: p = 100 – d TRY IT YOURSELF 63 Translate verbal model into equation: s = 3c 64 Translate verbal model into equation: c w= 10 56 Translate verbal model into equation: c=m+7 65 Translate verbal model into equation: w = e + 1,200 57 Translate verbal model into equation: 7d = h INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 66 Translate verbal model into equation: n = 150 – c 78 Construct a line graph: 67 Translate verbal model into equation: p = r – 600 68 Translate verbal model into equation: d = 3r 69 Translate verbal model into equation: n =m 70 Translate verbal model into equation: t + 35 = c 79 a Complete the table: 71 Complete the formula: e d= 12 72 Complete the formula: p = 2c b Construct a line graph: 73 Complete the formula: I = 2c 74 Complete the formula: p t= 75 Complete the formula: l = 4c, a = 2c, S = c, b = c, p = 2c, s = 20c 80 a Complete the table: 76 Complete the formula: b = 16h, p = 3h, r = 2h, t = 8h 77 Construct a bar graph: INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ b Construct a line graph: Study Set 1.2 Complete the statement: is the reciprocal of , because their product is Complete the statement: The least or lowest common denominator for a set of fractions is the smallest number each denominator will divide exactly Complete the statement: The mixed number represents the sum of a whole number and a fraction: + WRITING 81–84 Answers may vary STUDY SET Section 1.2 CONCEPTS VOCABULARY Complete the statement: A factor is a number being multiplied Complete the statement: Numbers that have only and themselves as factors, such as 23, 37, and 41, are called prime numbers Complete the statement: When we write 60 as ⋅ ⋅ ⋅ , we say that we have written 60 in prime–factored form Complete the statement: The numerator and the of the fraction denominator is 3, is Complete the statement: Two fractions that represent the same number, such as and , are called equivalent fractions Complete the statement: a a =1 a a c a⋅c c ⋅ = b d b⋅d a b a+b e + = d d d a =a a c d ÷ = b d a b f − = d d b a⋅d b⋅c a−b d 10 Equivalent fractions: = 12 11 Complete the statement: a To simplify a fraction, we remove factors equal to in the form of , , , and so on b To build a fraction, we multiply it by in the form of , , , and so on 12 Find the LCD: 24 = ∙ ∙ ∙ 36 = ∙ ∙ ∙ LCD = ⋅ ⋅ ⋅ ⋅ = 72 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 25 Prime factorization: 1254 = ⋅ ⋅ 11 ⋅ 19 NOTATION 13 Equivalent fractions: 5 25 a ⋅ = 30 26 Prime factorization: 1122 = ⋅ ⋅11 ⋅17 12 ⋅ ⋅ b = = 42 ⋅ ⋅ 7 27 Perform the operation: 5 ⋅1 ⋅ = = ⋅ 48 14 Convert the fraction: 15 ⋅ 16 + 15 47 a = = 16 16 16 b 49 ÷ 12 = with a remainder of 1, so 49 =4 12 12 28 Perform the operation: 2 ⋅1 ⋅ = = ⋅ 15 29 Perform the operation: 7 ⋅ 21 ⋅ = = 11 11 ⋅ 55 GUIDED PRACTICE 30 Perform the operation: 8 ⋅ 24 ⋅= = 19 19 ⋅ 95 15 Prime factorization: 75 = ∙ ∙ 16 Prime factorization: 20 = ∙ ∙ 31 Perform the operation: 3 ⋅ 15 ÷ = = 4⋅2 17 Prime factorization: 28 = ∙ ∙ 32 Perform the operation: 7 ⋅ 13 91 ÷ = = 13 ⋅ 48 18 Prime factorization: 54 = ∙ ∙ ∙ 19 Prime factorization: 81 = ⋅ ⋅ ⋅ 33 Perform the operation: 6 ⋅ 42 ÷ = = ⋅ 25 20 Prime factorization: 125 = ⋅ ⋅ 34 Perform the operation: 4⋅2 ÷ = = 3⋅3 21 Prime factorization: 117 = ∙ ∙ 13 22 Prime factorization: 147 = ∙ ∙ 35 Equivalent fractions: 1⋅ 3 = = 3⋅3 23 Prime factorization: 220 = ∙ ∙ ∙ 11 36 Equivalent fractions: 3⋅3 = = 8 ⋅ 24 24 Prime factorization: 270 = ∙ ∙ ∙ ∙ INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ Study Set 1.2 37 Equivalent fractions: 4 ⋅ 24 = = 9 ⋅ 54 48 Simplify the fraction: 15 15 ÷ = = 21 21 ÷ 38 Equivalent fractions: 9 ⋅ 36 = = 16 16 ⋅ 64 49 Simplify the fraction: 33 is in lowest terms because 33 and 56 56 have no common factors 39 Equivalent fractions: 7 ⋅ 35 = = 1⋅ 5 50 Simplify the fraction: 26 is in lowest terms because 26 and 21 21 have no common factors 40 Equivalent fractions: 15 15 ⋅ 45 = = 1⋅ 3 51 Simplify the fraction: 26 26 ÷ 13 = = 39 39 ÷ 13 41 Equivalent fractions: 5 ⋅ 35 = = 1⋅ 7 52 Simplify the fraction: 72 72 ÷ = = 64 64 ÷ 8 42 Equivalent fractions: 6 ⋅ 48 = = 1⋅ 8 53 Simplify the fraction: 36 36 ÷ = = 225 225 ÷ 25 43 Simplify the fraction: 6÷6 = = 18 18 ÷ 54 Simplify the fraction: 175 175 ÷ 35 = = 490 490 ÷ 35 14 44 Simplify the fraction: 6÷3 = = 9÷3 55 Perform the operation: 3 3+3 + = = 5 5 45 Simplify the fraction: 24 24 ÷ = = 28 28 ÷ 56 Perform the operation: 4 −1 − = = = 9 9 46 Simplify the fraction: 35 35 ÷ = = 14 14 ÷ 57 Perform the operation: 6−2 − = = 7 7 47 Simplify the fraction: 15 15 ÷ = = 40 40 ÷ 58 Perform the operation: + 11 + = = 13 13 13 13 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 59 Perform the operation: 1 4 +1 + = + = = 24 24 24 24 24 70 Perform the operation: 14 42 14( ) = ⋅ = =6 7 60 Perform the operation: 17 17 10 17 − 10 − = − = = 25 25 25 25 25 71 Perform the operation: 12 14 − + = − + = = 18 18 18 18 18 61 Perform the operation: 49 49 − 44 22 − = − = = = 10 14 70 70 70 70 35 72 Perform the operation: 7 12 14 − + = − + = = 10 20 20 20 20 20 62 Perform the operation: 27 20 27 − 20 − = − = = 24 24 24 24 73 Perform the operation: 25 20 24 21 + − = + − = = 12 60 60 60 60 20 63 Perform the operation: 35 + 35 41 + = + = = 15 45 45 45 45 74 Perform the operation: 21 20 10 + − = + − = = 15 45 45 45 45 64 Perform the operation: 14 15 29 + = + = 25 10 50 50 50 75 Perform the operation: 14 98 ⋅7 = ⋅ = = 32 3 3 65 Perform the operation: 21 105 63 42 − = − = = 56 40 280 280 280 20 76 Perform the operation: 31 217 31 ⋅1 = ⋅ = = =7 28 28 28 4 66 Perform the operation: 13 65 56 − = − = = 24 40 120 120 120 15 77 Perform the operation: 16 40 8÷3 = ÷ = ⋅ = = =2 5 16 16 2 67 Perform the operation: 16 48 16 = ⋅ = = 24 2 2 78 Perform the operation: 15 10 15 45 15 ÷ = ÷ = ⋅ = = =4 3 10 10 2 68 Perform the operation: 30 30 ⋅ 150 30 = ⋅ = = = 25 1⋅ 79 Perform the operation: 2 74 23 74 69 −7 = − = − = 9 9 80 Perform the operation: 19 31 38 31 −3 = − = − = 10 10 10 10 10 69 Perform the operation: 18 36 18 = ⋅ = = 9 9 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ 81 Perform the operation: 51 53 153 106 +2 = + = + 16 24 16 24 48 48 259 19 = = 48 48 Study Set 1.2 90 Perform the operation: 2 15 14 − + = − + = 35 35 35 35 35 91 Perform the operation: 21 21 ⋅ 14 14 ÷ = = 35 14 35 ⋅ 82 Perform the operation: 5 95 93 380 279 15 + 11 = + = + 8 24 24 659 11 = = 27 24 24 92 Perform the operation: 23 46 23 ⋅ ÷ = = 25 25 ⋅ 46 10 93 Perform the operation: 4⋅6 = = 3⋅5 TRY IT YOURSELF 83 Perform the operation: 10 + 10 19 + = + = = 15 15 15 15 94 Perform the operation: 21 21 ⋅ = = 15 ⋅15 20 84 Perform the operation: 21 + 21 29 + = + = = 6 6 95 Perform the operation: 20 27 + = + = = 63 45 315 315 315 35 85 Perform the operation: 10 21 10 210 21 = ⋅ = = 70 3 96 Perform the operation: 55 57 19 + = + = = 18 99 198 198 198 66 86 Perform the operation: 27 216 27 = ⋅ = = 24 9 97 Perform the operation: 3 12 3− = − = − = 4 4 87 Perform the operation: 55 55 6⋅2 = ⋅ = = 13 24 24 4 98 Perform the operation: 12 4− = − = 3 3 88 Perform the operation: 1 7 ⋅ = ⋅ = 5 10 99 Perform the operation: 1⋅ 3 ⋅ = = ⋅ 10 89 Perform the operation: 1 − + = − + = = 12 12 12 12 12 100 Perform the operation: ⋅ 15 ⋅ = = ⋅ 28 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 101 Perform the operation: 10 11 10 ⋅ 20 ÷1 = ÷ = = =1 6 ⋅11 11 11 110 Solve the problem: Lace trim 135 135 10 135 ÷ = ÷ = ⋅ 10 10 pillows = 150 Corduroy fabric 154 154 154 ÷ = ÷ = ⋅ 8 pillows = 176 Cotton filling 98 98 98 ÷ = ÷ = ⋅ 3 pillows = 147 All pillows require lace trim, corduroy fabric and cotton filling 147 pillows can be manufactured with the material in stock 102 Perform the operation: 5 13 ⋅ 20 ÷1 = ÷ = = =1 8 ⋅ 13 13 13 103 Perform the operation: 11 11 − − = = = 21 21 21 21 104 Perform the operation: 19 12 19 − 12 − = = = 35 35 35 35 APPLICATIONS WRITING 105 Solve the problem: 21 21 10 31 in a + = + = 32 16 32 32 32 21 21 10 11 in b − = − = 32 16 32 32 32 111–114 Answers may vary REVIEW 115 Complete the table: 106 Solve the problem: 10 12 14 + +1 + = + +1 + 8 16 16 16 16 16 41 in =5 =7 16 16 116 Complete the table: 107 Solve the problem: 21 19 42 19 10 − = − = − 4 4 23 = = lb 4 STUDY SET Section 1.3 108 Solve the problem: 20 140 ⋅ 20 = ⋅ = =70 calories 2 VOCABULARY Complete the statement: The set of natural numbers is {1, 2, 3, 4, 5, } 109 Solve the problem: 81 81 ⋅ 10 = ⋅ = = 40 inches 8 2 INSTRUCTOR USE ONLY 10 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ Complete the statement: The set of whole numbers is {0, 1, 2, 3, 4, 5, } Study Set 1.3 12 Complete the statement: The absolute value of a number is the distance on the number line between the number and Complete the statement: The set of integers is { , –2, –1, 0, 1, 2, } CONCEPTS Complete the statement: Numbers less than zero are negative , and numbers greater than zero are positive 13 Express in fraction form: −9 −7 = ; −9 = ; ;3 = ; 1 2 283 −3 − 0.3 = ; 2.83 = 10 100 Complete the statement: The symbols < and > are symbols inequality Complete the statement: A rational number can be written as a quotient (ratio) of two integers Complete the statement: In set–builder notation, the set of rational numbers is written as Complete the statement: An irrational number is a nonterminating, nonrepeating decimal 14 Represent as signed number: a A loss of $15 million –$15 million b A rainfall total 0.75 inch below average –0.75 in c A score 12½ points under the standard –12½ pts d A building foundation inch above 16 grade + in 16 15 Complete the statement: Numbers that are a distance of from on the number line are 13 and − 16 Express as inequality: m a c b > and a < 10 Complete the statement: All numbers that can be represented by points on the number line are called real numbers 18 Express as inequality: a Write the statement –6 < –5 using an inequality symbol that points in the other direction –5 > –6 b Write the statement 16 > –25 using an inequality symbol that points in the other direction –25 , ≤ , and ≥ are called inequalities Study Set 1.3 52 Graph the integers: 53 Graph the integers: 40 Interpret the symbol: The symbol is called an ellipsis and it indicates that a set follows an established pattern that continues forever 41 Name the opposite: The opposite of = −5 –2 –1 55 Compare the numbers: > −4 42 Name the opposite: The opposite of − = 56 Compare the numbers: − 11 < −9 43 Name the opposite: The opposite of − 54 Graph the integers: 7 = 8 57 Compare the numbers: − > −4 44 Name the opposite: The opposite of 6.56 = −6.56 58 Compare the numbers: < 32 45 Simplify the expression: – (− 10 ) = 10 59 Compare the numbers: 3.4 > 10 46 Simplify the expression: – (− 1) = 60 Compare the numbers: 0.08 > 0.079 47 Simplify the expression: – (− 2.3) = 2.3 61 Compare the numbers: − − 1.1 < −1 48 Simplify the expression: 3 –− = 4 62 Compare the numbers: 1 − (− 5.5) = − − 2 49 Name the opposite: The opposite of the absolute value of = −3 63 Classify the numbers: 17 − , 35.99, 0, , , − 50, natural: 5 none; whole: 0; integers: 0, –50; rational: 17 ; irrational: − , 35.99, 0, , –50, ; real: all 50 Simplify the expression: − − = −5 GUIDED PRACTICE 51 Graph the integers: INSTRUCTOR USE ONLY 13 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 64 Classify the numbers: − 0.001, 10 , 6, π , , − 23, − 5.6 natural: 6; whole: 6; integers: 6, –23; rational: –0.001, 10½, 6, –23, –5.6; irrational: π, ; real: all 72 Evaluate the expression: 3 − = 5 65 Classify the numbers: −π , 0,1 ,8, π , 11, −3, 2.6, natural: 2,8; whole: 0,2,8; integers: 0,8, –3,2; rational: 0, ,8,–3,2.6,2; irrational: − π , π , 11 ; real: all 74 Evaluate the expression: − π = −π 73 Evaluate the expression: − − 2.5 = −2.5 66 Classify the numbers: 3 ,9, ,0.00023,−2.7,0,−3 natural: 9; whole: 0,9; integers: 9,0,–3; rational: ,9,0.00023,–2.7,0,–3; irrational: ; real: all 75 Compare the numbers: − − = −2 76 Compare the numbers: −− < 77 Compare the numbers: − > −2 78 Compare the numbers: 3 −− < 4 67 Graph the numbers: 68 Graph the numbers: 79 Compare the numbers: 5 3 − − > − − 8 8 69 Graph the numbers: 80 Compare the numbers: − 19 < −19 3 70 Graph the numbers: 81 Compare the numbers: 15 − = 7.5 71 Evaluate the expression: − 17 = 17 82 Compare the numbers: −−2 Study Set 1.3 95 Write the lengths in order from least to greatest: in., in., in 85 Compare the numbers: 0.333 > 0.3 96 Set the cursor on −1 86 Compare the numbers: 3 > − − 2 97 Perform the operation: C = 26π ≈ 81.7 in 87 Compare the numbers: 98 Perform the operation: C = 34π ≈ 106.8 in −2 – (− 1) > − 15 16 99 Compare the numbers: Arrow 1, − > 88 Compare the numbers: − 0.666 < 89 Compare the numbers: 19 − (−1) < − 13 100 Interpret the graph: a 500 years b B.C./A.D c pos: A.D.; neg: B.C d –500 to 1697 90 Compare the numbers: − 0.666 > −1.34 WRITING 101–104 Answers may vary APPLICATIONS REVIEW 91 Classify the numbers: natural, whole, integers: 750, 5,000; rational: all; irrational: none; real: all 92 Classify the numbers: a natural, whole, integers: 9; rational: 9, 15 , , 1.765; irrational: 2π, 3π, 89 ; 16 real: all b 3π ≈ 9.425, 2π ≈ 6.283, 89 ≈ 9.434 93 Interpret the graph: a 2006, –$90 billion b 2009, –$43 billion 94 Interpret the graph: a years had a surplus b 21 years had a deficit less than $300 billion 105 Simplify the expression: 24 = 54 106 Prime factorization: 60 = ∙ ∙ ∙ 107 Perform the operation: 24 ⋅ = = 20 108 Perform the operation: 17 23 17 51 5 ÷2 = ÷ = ⋅ = =2 9 23 23 23 109 Perform the operation: 13 + = + = 10 15 30 30 30 INSTRUCTOR USE ONLY 15 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 110 Write in decimal form: 0.16 Perform the operation: − + (− ) = −5 111 Write in decimal form: 0.375 Perform the operation: + (− 3) = 112 Perform the operation: + = 7 10 Perform the operation: − + = −2 11 Complete the statement: To add two real numbers, with the same sign, add their absolute values and attach their common sign to the sum STUDY SET Section 1.4 VOCABULARY Complete the statement: Real numbers that are greater than zero are called positive real numbers Real numbers that are less than zero are called negative real numbers Complete the statement: The only real number that is neither positive nor negative is zero Complete the statement: The commutative property of addition states that two numbers can be added in either order to get the same result Complete the statement: The grouping symbols ( parentheses 12 Complete the statement: To add two real numbers with different signs, subtract their absolute values, the smaller from the larger , and attach the sign of the number with the larger absolute value 13 Complete the statement: − + = + (− 5) 14 Complete the statement: 15 + (− 80.5) = − 80.5 + 15 15 Complete the statement: − 20 + (4 + 20) = −20 + (20 + ) ) are called Complete the statement: The property that allows us to group numbers in addition in any way we want is called the associative property of addition Complete the statement: Whenever we add opposites , or additive inverses , the result is 16 Complete the statement: (5 + 7) + = (7 + 5) + 17 Complete the statement: (− + 2) + = − + (2 + 8) 18 Complete the statement: − + (7 + 3) = (− + ) + 19 Complete the statement: − 96 + (4 + 200) = (− 96 + ) + 200 CONCEPTS 20 Complete the statement: (−9 + 4) + 15 = −9 + (4 + 15) Perform the operation: 2+3 = INSTRUCTOR USE ONLY 16 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ 21 Name the opposite: The opposite of is –7 33 Perform the operation: 15 + (–11) = 22 Name the opposite: The opposite of –15 is 15 34 Perform the operation: 27 + (–30) = –3 23 Name the opposite: 1 The opposite of − is 2 35 Perform the operation: + (–5) + 13 = 16 Study Set 1.4 36 Perform the operation: 17 + (–12) + (–23) = –18 24 Name the opposite: 2 The opposite of is − 3 37 Perform the operation: 21 + (–27) + (–9) = –15 NOTATION 38 Perform the operation: –32 + 12 + 17 = –3 25 Complete the statement: (–13 + 6) + = –13 + (6 + 4) = –13 + 10 = –3 39 Perform the operation: –27 + (–3) + (–13) + 22 = –21 40 Perform the operation: 53 + (–27) + (–32) + (–7) = –13 26 Complete the statement: –9 + (9 + 43) = (–9 + 9) + 43 = + 43 = 43 41 Perform the operation: 57 + (−47) + (−64) + 113 = 59 GUIDED PRACTICE 42 Perform the operation: 32 + (−44) + (−37) + (−52) = −101 27 Perform the operation: − 65 + (−12) = −77 43 Perform the operation: –99 + (99 + 215) = (–99 + 99) + 215 = + 215 = 215 28 Perform the operation: − 21 + (−12) = −33 44 Perform the operation: 67 + (–67 + 127) = (67 + –67) + 127 = + 127 = 127 29 Perform the operation: − 4.1 + (−5.7) = −9.8 30 Perform the operation: −2.5 + (−1.7) =−4.2 45 Perform the operation: (−4 + 15) + (−15) =−4 + 15 + ( −15 ) =−4 + =−4 31 Perform the operation: + (–8) = –2 46 Perform the operation: (−18 + 37) + (−37) = −18 + 37 + ( −37 ) 32 Perform the operation: + (–3) = =−18 + =−18 INSTRUCTOR USE ONLY 17 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 61 Perform the operation: − + =− =− 16 16 16 TRY IT YOURSELF 47 Perform the operation: + (−5) = 48 Perform the operation: − 2.2 + 2.2 = 62 Perform the operation: − + =− =− 4 49 Perform the operation: + (−6) = −6 63 Perform the operation: − 20 + (−16 + 10) = −26 50 Perform the operation: 15 15 − +0= − 16 16 64 Perform the operation: − 13 + (−16 + 4) = −25 65 Perform the operation: − + =− + = 12 12 12 51 Perform the operation: 3 − + =0 4 52 Perform the operation: 19 + (−19) = 66 Perform the operation: 3 + (− ) = + (− ) = − 16 16 16 16 53 Perform the operation: −6+8 = 67 Perform the operation: 4.125 + (−7.341) = −3.216 54 Perform the operation: 75 + (−13) = 62 68 Perform the operation: 3, 718 + (−5, 237) =−1,519 55 Perform the operation: 300 + (−335) = −35 69 Perform the operation: 735 + (−462) = 273 56 Perform the operation: 240 + (−340) = −100 70 Perform the operation: 837 + (−429) = 408 57 Perform the operation: − 10.5 + 2.3 = −8.2 71 Perform the operation: − 5,235 + (−17,235) = −22,470 58 Perform the operation: − 2.1 + 0.4 = −1.7 72 Perform the operation: 32.137 + (−34.36) + (−32.137) = −34.36 59 Perform the operation: − 9.1 + (−11) = −20.1 73 Perform the operation: 736 + (67) + (−736) = 67 60 Perform the operation: − 6.7 + (−7.1) = −13.8 74 Perform the operation: − 237.37 + (−315.07) + (−27.4) = −579.84 INSTRUCTOR USE ONLY 18 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ 86 Perform the operation: –240 + 110 + 30 – 55 + 100 – 77 = –132 km The net movement is 132 km southward 75 Perform the operation: −587.77 + (−1,732.13) + 687.39 = −1,632.51 76 Perform the operation: − 37.57 + 85.02 + (−77.1) = −29.65 87 Perform the operation: 1,704.29 + 713.87 + 1,245.57 – 813.45 – 937.49 – 1,532.79 – 500 = –120 (Overdrawn $120) APPLICATIONS 77 Perform the operation: –1,500 + 2,400 + 1,250 = 2,150 m 78 Perform the operation: –4 + + (–3) + + + = Risk 4% 79 Perform the operation: a Tiger Woods –2 + (–6) + (–7) + (–3) = –18 Tom Kite +5 + (–3) + (–6) + (–2) = –6 Tommy Tolles + + + (–5) = –5 Tom Watson +3 + (–4) + (–3) + = –4 b –18 – (–6) = –12 Study Set 1.4 12 Strokes 88 Perform the operation: Matt 50 – (2 + 10 + + 1) = 29 Gonzalo –15 + 50 = 35 Hydecki –2 – (10 + + 6) = –23 89 Perform the operation: –161 + (–28) + (–39) + 61 = –$167 million A net loss of $167 million 90 Perform the operation: 10 + + + = 16 no WRITING 80 Perform the operation: 3,826.58 – (3,660.66 + 1,408.78) = 3,826.58 – 5,069.44 = –1,242.86 New Balance: $1,242.86 91–92 Answers may vary REVIEW 93 True or false: Every real number can be expressed as a decimal true 81 Perform the operation: 1,996 + 776 = 2,772 82 Perform the operation: –1,250 + 550 = –700 ft 83 Perform the operation: –0.81 –0.56 + 0.81 + 0.81 – 0.63 = –0.38 The stock fell $0.38 84 Perform the operation: 6.7 – 4.5 = $2.2 million A gain of $2.2 million 94 True or false: Irrational numbers are nonterminating, nonrepeating decimals true 95 Absolute value: What two numbers are a distance of away from –3 on the number line? –9 and 96 Graph the numbers: 85 Perform the operation: –$120,000,000 + $93,394,462 = –$26,605,538 A loss of $26,605,538 INSTRUCTOR USE ONLY 19 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 10 Simplify the expression: − (− p) = p STUDY SET Section 1.5 VOCABULARY 11 Simplify the expression: − = −7 Complete the statement: Subtraction finds the difference between two numbers 12 Simplify the expression: − − 25 = −25 Complete the statement: In a subtraction, the result is called the difference 13 Perform the operation: − (−3) = + = 11 Complete the statement: To subtract b from a, add the opposite of b to a 14 Perform the operation: 17 − (−21) = 17 + 21 = 38 Complete the statement: The difference between the maximum and the minimum values of a collection of measurements is called the range of the values 15 Perform the operation: − 12 − = −21 CONCEPTS 17 Perform the operation: − 19 − (−17) = −19 + 17 = −2 Complete the statement: –(–a) = a Complete the statement: To subtract two real numbers, change the subtraction to addition and take the opposite of the second number: a − b = a + (−b) NOTATION 16 Perform the operation: − 25 − 17 = −42 18 Perform the operation: − 30 − (−11) = −30 + 11 = −19 19 Perform the operation: − 1.5 − 0.8 = −2.3 20 Perform the operation: − 1.5 − (−0.8) = −1.5 + 0.8 = −0.7 21 Perform the operation: − − =− =− 8 Complete the statement: The expression –7 is read as negative Complete the statement: The expression –(–5) is read as the opposite of –5 22 Perform the operation: − − = − = −1 4 GUIDED PRACTICE 23 Perform the operation: 9 − − (− ) = − + =− 16 16 16 16 Simplify the expression: − (−15) = 15 INSTRUCTOR USE ONLY 20 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ 24 Perform the operation: 1 1 − − (− ) = − + = − 4 4 Study Set 1.5 38 Perform the operation: 4.7 − (−1.9) = 4.7 + 1.9 = 6.6 39 Perform the operation: − 44 − 44 = −88 25 Perform the operation: 17 − (−5) = 17 + = 22 40 Perform the operation: − 33 − 33 = −66 26 Perform the operation: − 50 − 45 = −95 41 Perform the operation: − (−12) = + 12 = 12 27 Perform the operation: − 1.3 − 1.2 = −2.5 42 Perform the operation: − 12 = −12 28 Perform the operation: − − (−1.1) = −2 + 1.1 = −0.9 43 Perform the operation: − 25 − (−25) = −25 + 25 = 29 Perform the operation: − − 10 = −11 44 Perform the operation: 13 − (−13) = 13 + 13 = 26 30 Perform the operation: − − = −4 45 Perform the operation: − = −4 31 Perform the operation: − 25 − (−50) − 75 = −25 + 50 − 75 = −50 46 Perform the operation: − (−3) = + = 32 Perform the operation: − 33 − (−22) − 44 = −33 + 22 − 44 = −55 47 Perform the operation: 8,713 − (−3,753) = 8,713 + 3,753 = 12,466 33 Perform the operation: − + − (−1) − 10 = −6 + + − 10 = −7 48 Perform the operation: − 2,727 − 1,208 = −3,935 34 Perform the operation: − + − (−3) − 13 = −4 + + − 13 = −9 35 Perform the operation: 61 − (−62) + (−64) − 60 = 61 + 62 − 64 − 60 = −1 36 Perform the operation: 93 − (−92) + (−94) − 95 = 93 + 92 − 94 − 95 = −4 49 Perform the operation: − 27,357.875 − 17,213.376 = −44,571.251 50 Perform the operation: − 45,307.039 − (−27,592.47) = −17,714.569 TRY IT YOURSELF 51 Perform the operation: − 62 − 71 − (−37) + 99 = −62 − 71 + 37 + 99 = 37 Perform the operation: 2.8 − (−1.8) = 2.8 + 1.8 = 4.6 52 Perform the operation: − 17 − 32 − (−85) − 51 = −17 − 32 + 85 − 51 = −15 INSTRUCTOR USE ONLY 21 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 53 Perform the operation: − 47.5 = −47.5 66 Perform the operation: − (−18) = + 18 = 21 54 Perform the operation: − 30.3 = −30.3 67 Perform the operation: 1,312 − 282 = 1,030 ft 55 Perform the operation: − − = −12 68 Perform the operation: 109 − (−2)= 109 + = 111 ° F 56 Perform the operation: − (−7) = + = 12 69 Perform the operation: 4.35 − (−2.5) = 4.35 + 2.5 = 6.85 57 Perform the operation: 12 − (−137) = 12 + 137 = 149 70 Perform the operation: −40 − ( −355 ) = −40 + 355 = 315° F 58 Perform the operation: − 47 − 512 = −559 71 Perform the operation: − 2.25 − 3.5 = −5.75 ° 59 Perform the operation: 1 −− = + = = 3 3 72 Perform the operation: Farmers/ranchers: 1,106, 400 − 1, 202,500 = −96,100 Stock clerks: 73,000 − 142,000 = −69,000 Sewing machine operators: 121,100 − 163, 200 = −42,100 60 Perform the operation: 2 − = 5 61 Perform the operation: 10 19 − − =− − =− 12 12 12 73 Perform the operation: 5183 − ( −= ) 5183 += 5189 ft 74 Perform the operation: 0.6 − ( −0.6 )= 0.6 + 0.6= 1.2 m 62 Perform the operation: 15 14 29 − − =− − =− 35 35 35 75 Perform the operation: a iii b –$116.1 billion − 120.2 − (−4.1) = −120.2 + 4.1 = −116.1 63 Perform the operation: 11 − − =− − =− 15 15 15 15 76 Perform the operation: 347 + 81 = 428 B.C 64 Perform the operation: 11 19 − − =− − =− 11 22 22 22 77 Perform the operation: Bower: 2361 − 2400 = −39 Johnson: 2360 − 2400 = −40 Kahne: 2345 − 2400 = −55 Biffle: 2332 − 2400 = −68 APPLICATIONS 65 Perform the operation: 108 − (−52) = 108 + 52 = 160 ° F INSTRUCTOR USE ONLY 22 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ Study Set 1.6 Complete the statement: Division of a nonzero number by zero is undefined 78 Perform the operation: − − = −13 WRITING Complete the statement: If the product of two numbers is 1, the numbers are called reciprocals or multiplicative inverses 79–82 Answers may vary REVIEW CONCEPTS 83 Prime factorization: 30 = ⋅ ⋅ Complete the statement: The expression –5 + (–5) + (–5) + (–5) can be represented by the multiplication statement 4(–5) 84 True or false: true 85 Perform the operation: − 18 + (18 + 89) = 89 Complete the statement: The quotient of two numbers with signs is negative 86 Perform the operation: (−4.5)(−2.3) = 10.35 unlike Complete the statement: The product of two negative numbers is positive STUDY SET Section 1.6 VOCABULARY 10 Complete the statement: The product of zero and any number is Complete the statement: The answer to multiplication is called a product The answer to division is called a quotient Complete the statement: The numbers –4 and –6 are said to have like signs The numbers –10 and 12 are said to have unlike signs Complete the statement: The commutative property of multiplication states that two numbers can be multiplied in either order to get the same result Complete the statement: The statement (ab)c = a(bc) expresses the associative property of multiplication 11 Complete the statement: The product of and any number is that number 12 Complete the statement: 25 The division fact = −5 is related to the −5 multiplication fact –5(–5) = 25 13 Complete the statement: a If we multiply two different numbers and the answer is 0, one of the numbers must be b If we multiply two different numbers and the answer is 1, the numbers must be reciprocals (multiplicative inverses) INSTRUCTOR USE ONLY 23 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 14 Complete the statement: a If we divide two numbers and the answer is 1, the numbers must be the same b If we divide two numbers and the answer is 0, the number being divided (the dividend) must be 0, the number we are dividing by (the divisor) must not be 15 Identify the property: a –5(2 ∙ 17) = (–5 ∙ 2)17 associative property of multiplication 1 b = multiplicative inverse 5 c –5 ∙ = 2(–5) commutative property of multiplication d –5(1) = –5 multiplication property of 16 Complete the statement: a –1(8) = –8 When a number is multiplied by –1, the result is generally the opposite of that number b = −8 In general, when a number is −1 divided by –1, the result is the opposite of that number 17 Determine the sign of the result: a POS ∙ NEG = NEG b POS + NEG = Not possible to tell c POS – NEG = POS d POS = NEG NEG 19 Identify the error: A negative and a positive is a negative If we are multiplying or dividing, this is true If we are adding, the sum of a negative number and a positive number could be positive: For example, –6 + = 20 Apply the inverse property: a The additive inverse of is –2 The multiplicative inverse of is −4 is 5 −4 The multiplicative inverse of is −5 c The additive inverse of 1.75 is –1.75 1.75 = = The multiplicative 4 inverse of 1.75 is d The additive inverse of –5 is b The additive inverse of The multiplicative inverse of –5 is − 21 Interpret the calculator display: Since division by is undefined, the calculator was unable to the division 22 Compare the operation: a Is 80 divided by –5 the same as –5 divided by 80? no b Is 80 times –5 the same as –5 times 80? yes 18 Determine the sign of the result: a NEG ∙ NEG = POS b NEG + NEG = NEG c NEG – NEG = Not possible to tell d NEG = POS NEG NOTATION 23 Complete the statement: (–37 ∙ 5)2 = –37(5 ∙ 2) = –37(10) = –370 INSTRUCTOR USE ONLY 24 © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/ ... https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 110 Write in decimal form: 0.16 Perform the operation:... Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file Chapter at https://TestbankDirect.eu/ 61 Perform the operation: − + =− =− 16 16 16 TRY IT YOURSELF 47 Perform... https://TestbankDirect.eu/ Solution Manual for Introductory Algebra 5th Edition by Tussy NOT FOR SALE Full file at https://TestbankDirect.eu/ 24 Perform the operation: 1 1 − − (− ) = − + = − 4 4 Study Set 1.5 38 Perform