Chapter Fractions and Mixed Numbers: Multiplication and Division Chapter Opener Puzzle Section 2.1 Introduction to Fractions and Mixed Numbers Section 2.1 Practice Exercises Answers will vary ÷ 1; (a) A fraction is a part of a whole unit (b) The numerator of a fraction denotes the number of pieces of the whole being considered (c) The denominator of a fraction denotes the number of equal pieces into which a whole unit is divided (d) A fraction is a proper fraction if the numerator is less than the denominator (e) An improper fraction is a fraction in which the numerator is greater than or equal to the denominator (f) A mixed number is a sum of a whole number and a fractional part of a whole ÷ 1; 9 ÷ 2; 10 ÷ 8; 11 ÷ 3; 12 ÷ 7; 13 ÷ 0; undefined 14 11 ÷ 0; undefined Numerator: 2; denominator: 15 16 17 Numerator: 8; denominator: Numerator: 12; denominator: 11 Numerator 1; denominator: 51 Chapter 18 Fractions and Mixed Numbers: Multiplication and Division 37 Proper 38 Proper 19 39 20 40 21 41 12 22 42 27 23 43 ;1 4 24 44 13 ;3 4 25 45 13 ;1 8 26 or 46 ;2 2 27 41 103 !1 + 47 = = 4 28 43 103 ! + 19 48 = = 3 29 10 21 ! + 38 49 = = 9 30 10 63 ! + 16 50 = = 5 31 Proper 3 ! + 24 51 = = 7 32 Proper ! + 26 52 = = 3 33 Improper 34 Improper 53 35 Improper 36 Improper 52 ! + 29 = = 4 Section 2.1 10 ! + 53 54 10 = = 5 67 10 27 !20 11 ! 12 + 137 = = 12 12 12 55 11 68 18 43 !36 12 ! + 73 56 12 = = 6 21 ! + 171 57 21 = = 8 69 52 !45 15 ! + 31 58 15 = = 2 70 12 67 !60 ! + 19 59 = = 8 19 eighths ! + 13 60 = = 5 13 fifths 12 71 11 133 !11 23 !22 1! + 61 = = 4 fourths ! + 17 62 = = 3 17 thirds 63 37 !32 64 13 !7 65 39 !35 4 66 19 !16 Introduction to Fractions and Mixed Numbers 72 10 51 !50 73 23 !18 7 16 74 115 !7 45 !42 44 75 309 !28 29 !28 53 10 18 5 12 12 11 10 16 44 Chapter Fractions and Mixed Numbers: Multiplication and Division 230 921 76 !8 12 !12 !0 1056 77 5281 !5 !0 28 !25 31 !30 901 78 7213 !72 !0 13 !8 810 79 11 8913 !88 11 !11 !0 185 80 23 4257 !23 195 !184 117 !115 12 81 15 187 !15 37 !30 230 1056 20 34 695 82 !68 15 !0 15 12 15 20 15 34 83 Divide the distance between and into equal parts 84 Divide the distance between and into equal parts 901 85 Divide the distance between and into equal parts 810 11 86 Divide the distance between and into equal parts 87 Divide the distance between and into equal parts 185 23 88 Divide the distance between and into equal parts 54 Section 2.2 89 90 =1 6 Divide the distance between and into equal parts 92 =1 5 Divide the distance between and into equal parts Prime Numbers and Factorization =1 2 Divide the distance between and into equal parts 93 False; whole numbers cannot be written as proper fractions 94 True 95 True 96 True 91 =1 3 Divide the distance between and into equal parts Section 2.2 Prime Numbers and Factorization Section 2.2 Practice Exercises Answers will vary (a) A factor of a number n is a nonzero whole number that divides evenly into n (b) A factorization of a number n is a product of factors that equals n (c) A prime number is a whole number greater than that has only two factors (itself and 1) (d) A composite number is a whole number greater than that is not prime (e) The prime factorization of a number is the factorization in which every factor is a prime number ; 12 12 ; 2 5 ; 4 6 ; improper 7 ; proper 12 ; improper 23 !20 ! + 44 10 = = 7 11 For example: ⋅ and ⋅ 55 Chapter Fractions and Mixed Numbers: Multiplication and Division 12 For example: ⋅ 10 and ⋅ 24 241 (a) No; 241 is not even (b) No; + + = is not divisible by (c) No; the ones-place digit is not or (d) No; the ones-place digit is not 13 For example: ⋅ and ⋅ ⋅ ⋅ 14 For example: ⋅ 14 and ⋅ 15 16 Product 42 30 15 81 Factor 30 15 27 Factor 1 Sum 13 31 16 30 Product 42 45 72 24 Factor 15 18 Factor Sum 12 14 25 108 (a) Yes; 108 is even (b) Yes; + + = is divisible by (c) No; the ones-place digit is not or (d) No; the ones-place digit is not 26 1040 (a) Yes; 1040 is even (b) No; + + + = is not divisible by (c) Yes; the ones-place digit is (d) Yes; the ones-place digit is 27 3140 (a) Yes; 3140 is even (b) No; + + + = is not divisible by (c) Yes; the ones-place digit is (d) Yes; the ones-place digit is 17 A whole number is divisible by if it is an even number 18 A whole number is divisible by 10 if its ones-place digit is 28 2115 (a) No; 2115 is not even (b) Yes; + + + = is divisible by (c) Yes; the ones-place digit is (d) No; the ones-place digit is not 19 A whole number is divisible by if the sum of its digits is divisible by 20 A whole number is divisible by if its ones-place digit is or 21 45 (a) (b) (c) (d) 29 28 84 !84 Yes, 84 is divisible by 28 No; 45 is not even Yes; + = is divisible by Yes; the ones-place digit is No; the ones-place digit is not 22 100 (a) Yes; 100 is even (b) No; + + = is not divisible by (c) Yes; the ones-place digit is (d) Yes; the ones-place digit is 30 22 110 !110 Yes, 110 is divisible by 22 23 137 (a) No; 137 is not even (b) No; + + = 11 is not divisible by (c) No; the ones-place digit is not or (d) No; the ones-place digit is not 31 Prime 32 Prime 56 33 Composite ⋅ = 10 34 Composite ⋅ = 21 Section 2.2 35 Composite ⋅ 17 = 51 36 Composite ⋅ 19 = 57 Prime Numbers and Factorization 11 55 58 165 495 37 Prime 38 Prime 13 59 65 130 260 39 Neither 40 Neither 41 Composite 11 ⋅ 11 = 121 42 Composite ⋅ 23 = 69 43 Prime 44 Prime 45 Composite ⋅ 13 = 39 46 Composite ⋅ = 49 47 There are two whole numbers that are neither prime nor composite, and 48 False; the square of any prime number is divisible by that prime number 49 False; is not prime 50 False; is not composite 51 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 52 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79 54 No, is not a prime number ! ! ! 13 = 22 ! ! 13 = 260 60 35 175 ! ! = 52 ! = 175 61 49 147 ! ! = ! = 147 17 51 62 102 ⋅ ⋅ 17 = 51 23 63 69 138 ⋅ ⋅ 23 = 138 11 64 77 231 ⋅ ⋅ 11 = 231 65 2 53 No, is not a prime number ! ! ! 11 = 32 ! ! 11 = 495 11 77 154 308 616 ! ! ! ! 11 = 23 ! ! 11 = 616 55 Yes 13 91 66 182 364 56 Yes 57 35 70 ⋅ ⋅ = 70 67 47 is prime 68 41 is prime 57 ! ! ! 13 = 22 ! ! 13 = 364 Chapter Fractions and Mixed Numbers: Multiplication and Division 69 1, 2, 3, 4, 6, 12 82 Yes; 520 is divisible by 70 1, 2, 3, 6, 9, 18 83 No; 126 is not divisible by 71 1, 2, 4, 8, 16, 32 84 No; 58 is not divisible by 72 1, 5, 11, 55 85 Yes; + + = 18 is divisible by 73 1, 3, 9, 27, 81 86 Yes; + + = is divisible by 74 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 87 No; + + + = 20 is not divisible by 75 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 88 No; + + + = 21 is not divisible by 76 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 77 No; 30 is not divisible by 89 Yes; 522 is even and + + = is divisible by 78 No; 46 is not divisible by 79 Yes; 16 is divisible by 90 Yes; 546 is even and + + = 15 is divisible by 80 Yes; 64 is divisible by 91 No; 5917 is not even 81 Yes; 32 is divisible by 92 No; + + + = 22 is not divisible by Section 2.3 Simplifying Fractions to Lowest Terms Section 2.3 Practice Exercises Answers will vary (a) A fraction is said to be in lowest terms if the numerator and denominator share no common factor other than (b) The largest number that divides evenly into the numerator and denominator is call their greatest common factor 29 145 19 57 114 23 46 92 ! ! 23 = 22 ! 23 = 92 17 51 153 ! ! 17 = 32 ! 17 = 153 17 85 ⋅ 29 = 145 2 2 ⋅ ⋅ 19 = 114 58 15 30 60 120 ⋅ 17 = 85 ! ! ! ! = 23 ! ! = 120 Section 2.3 13 65 195 15 10 Simplifying Fractions to Lowest Terms 19 1! ! ! 6=6 = ⋅ ⋅ 13 = 195 20 ! ! 16 ! 48 = 48 = 16 ! ! 3! 3!5 = 22 ! 32 !5 = 180 45 90 180 21 12 ! ! 16 ! 48 = 48 12 = 11 22 ! 15 ! ! 12 60 = 60 12 = 15 12 23 ! 27 ! ! 20 216 " 180 20 ! 27 13 24 ! 18 ! ! 12 90 " 72 12 ! 18 14 25 12 2!2!3 = = 24 ! ! ! 26 15 !5 = = 18 ! ! 27 2!3 = = 18 ! ! 3 28 21 !7 = = 24 ! ! ! 29 36 ! ! ! = = 20 ! !5 30 49 !7 = = 42 ! ! 15 False; × ≠ × 16 Two fractions are equivalent if they both represent the same part of a whole 17 ! ! ! 10 " ! 18 1! ! ! 9"8 ! 59 Chapter Fractions and Mixed Numbers: Multiplication and Division 31 15 !5 = = 12 ! ! 47 130 ! ! 13 13 = = 150 ! ! ! 15 32 30 ! ! = = 25 !5 48 70 ! !7 = = 120 ! ! ! ! 12 33 20 ! ! = = 25 !5 49 385 ! ! 11 77 = = 195 ! ! 13 39 34 8 = = 16 ! 50 39 ! 13 = = 130 ! ! 13 10 35 14 =1 14 51 34 ! 17 = = 85 ! 17 36 =1 52 69 ! 23 = = 92 ! ! 23 37 50 ! 25 = =2 25 25 53 6!2 "2 = = = 10 + 14 " 7 38 24 ! = =4 6 54 !1 "2"2 = = = 15 + 18 " 3" 39 =1 55 5!5 = =0 7!2 40 =1 56 41 105 3! ! = = 140 ! ! ! 11 ! 11 = =0 + 11 57 7!2 = = undefined 5!5 42 84 ! ! ! = = 126 ! ! ! 58 + 11 = = undefined 11 ! 11 43 33 ! 11 = =3 11 11 59 8!2 "3 = = = + 10 " 5 44 65 ! 13 = = 13 5 60 15 + 18 " 3 = = = 15 ! 12 " 2 45 77 ! 11 = = 110 10 ! 11 10 61 120 12 ! !3 = = = 160 16 ! ! ! 46 85 ! 17 = = 153 ! ! 17 62 720 72 ! 9 = = = 800 80 ! 10 10 60 Problem Recognition Exercises: Multiplication and Division of Fractions 12 3! 27 (a) 12 ! = ! = ! = 8 2! (a) (b) 9 12 3! 27 !12 = ! = ! = 8 2! (b) (c) 12 ÷ (d) 9 !3 ÷ 12 = ! = ! = 8 12 ! 32 12 ! 32 = ! = ! = !3 3 15 3! !15 = ! = ! = =9 5 1 (c) 15 !5 25 15 ÷ = ! = ! = = 25 3 (d) 3 1 ÷ 15 = ! = ! = 5 15 !5 25 (a) (b) 16 ! !2 ÷ ! = ! ! 12 21 ! 21 = 21 16 21 ÷ ÷ = ! ! (d) 12 21 12 16 21 21 = ! ! = ! 16 128 (a) 5 25 ! = 6 36 ! = =1 (c) 5 ÷ = ! = =1 6 (d) 5 25 ÷ = ! = 6 36 16 21 ! ÷ = ! ! 12 21 12 16 !7 = ! ! = 12 !8 96 (c) 15 3! (a) 15! = ! = ! = =9 5 (b) 16 !4 ! ! = ! ! = 12 21 3! 21 189 (b) 7 7 ! ÷ = ! ! = ! ! = 9 2 ! 12 (c) !3 ÷ ! = ! ! = ! ! = 7 (d) 27 ÷ ÷ = ! ! = 28 (a) (b) !0 = (b) ! = (c) ÷ = Undefined (d) ÷ = ! = (a) (c) (d) 73 7 ! ! = 27 9 !6! = ! ! 10 10 !3 27 = ! ! = 10 ! 20 9 !6 ÷ = ! ! 10 10 1 ! 108 = ! ! = !5 1 9 1 ÷ 6! = ! ! 10 10 3! 1 = ! ! = 10 ! 80 9 ÷6÷ = ! ! 10 10 3! 2!2 = ! ! = !5 ! Chapter 10 (a) (b) (c) (d) Fractions and Mixed Numbers: Multiplication and Division 2! 10 ! !10 = ! ! = 20 ! 10 14 (a) 4 1 ! ÷ 10 = ! ! = 20 !5 10 250 (b) 4 20 ! 160 ÷ !10 = ! ! = 20 1 = 160 4 20 ÷ ÷ 10 = ! ! 20 10 2! 4! = ! ! = !5 5 (c) (d) 1 !8 42 ! = ! ! = 16 ! = ! 6 !3 = 1 (b) 42 ÷ = ! ÷ = 16 ! = 16 ! = 96 6 15 (a) 2 !1 = 3 2 (b) 1! = 3 2 (c) ÷1= 3 3 (d) ÷ = 1! = 2 11 (a) 12 (a) ÷ 10 = 1 1 ÷2= ! = 7 14 1 2 !2 = ! = 7 1 ! = 14 1 2 ÷ = ! = 7 (c) " 1% 1 4 4!$ ' = ! ! = = = 6 36 ! 9 # 6& (d) !3 ! = ! = 10 !5 ! 1$ ! 1$ ! $ 4÷# & = ÷# ' & = ÷# & " 6 % " 36 % " 6% 36 = ' = 144 1 16 (a) 10 !5 (b) 10 ÷ = ! = ! = !3 (c) !10 = 60 (d) 10 ! = 60 ! 1$ 1 #" &% ' = ' ' = 2 ! 1$ 1 3 (b) # & ÷ = ' ' = 2 " 2% 13 (a) ÷ = ! = 32 (b) ! = = 4 (c) ÷ = (d) ! = 32 (c) " 2% 2 !$ ' = ! ! = # 3& 3 (d) 74 ! 2$ ! 2$ ÷# & = ÷# ' & = ÷ " 3% " 3% 9 = ' = Section 2.6 Section 2.6 Multiplication and Division of Mixed Numbers Multiplication and Division of Mixed Numbers Section 2.6 Practice Exercises ! + 11 11 = = 7 Chapter Review Exercises, pages 157−160 Chapter Test, pages 160−161 Cumulative Review Exercises, pages 161−162 Answers will vary ! + 33 12 = = 8 5 ! = 27 13 13 10 26 ! = 9 20 10 20 ÷ = ! = 9 10 42 42 12 ÷ = ! = 11 11 11 15 39 !36 15 15 31 !2 11 !10 11 52 52 ÷ 13 = ! = = 18 18 13 18 ! "! " 12 37 37 ' = 17 # $# $ = % &% 12 & 12 1 37 !35 Multiply the whole number by the denominator Add the result to the numerator Write the result from step over the denominator ! + 17 = = 5 10 16 12 14 11 57 !55 32 32 ÷4= ! = 15 15 15 12 77 !6 17 !12 ! 10 + 27 = = 10 10 10 75 =7 Chapter Fractions and Mixed Numbers: Multiplication and Division 13 19 39 !2 19 !18 = 19 1 2 5 19 ! = ! = 7 =1 = 72 1 =3 72 145 !14 !4 ! 2" 26 $ % # = # = & 3' 49 20 ! = ! = 8 7 !6 ! 1$ 29 10 145 25 # & '10 = ' = " 4% 1 !3 2 ! $ ! $ 26 27 24 # & # & = ' = 18 13 " % " 13 % ! "! " 26 15 39 ' = 18 # $# $ = % &% & 5 27 ! = 1 28 ! =0 10 ! $ ! $ 15 15 29 # & # & = ' = = 2 " 2% " 7% 38 21 ! = ! = 38 9 1 1 ! $ ! $ 13 13 30 # & # & = ' = =1 " 10 % " % 10 10 22 ! = ! = 20 3 1 ! $ ! $ ! $ 27 54 31 # & # & # & = ' ' = =2 25 " % " % " % 25 ! $ ! $ 83 16 83 23 # & # & = ' = " 16 % " % 16 1 27 83 !6 23 !21 = 27 1 ! $ ! $ ! $ 49 11 77 32 # & # & # & = ' ' = = 19 4 " 8% " 4% " % 76 Section 2.6 Multiplication and Division of Mixed Numbers 1 13 13 44 ÷ = ÷ = ! = 13 2 2 17 11 17 34 ! = 33 ÷ = ÷ = 10 10 10 11 55 34 17 2 4 14 45 ÷ = ÷ = ! = = 7 3 3 51 51 34 ÷ = ÷ = ! = =6 10 10 10 5 1 15 15 13 39 ! = =5 46 ÷ = ÷ = 13 13 7 53 53 53 35 ÷ = ÷ = ! = =4 9 12 12 7 47 ÷ = ÷ = ! = = 2 2 4 64 13 64 64 12 36 12 ÷ = ÷ = ! = =4 5 5 13 13 13 14 14 14 48 ÷ = ÷ = ! = = 3 3 9 1 17 16 40 = =2 37 ÷ = ÷ = ! 16 16 17 17 17 19 49 ! = ! = 38 4 1 38 19 38 12 24 ÷ = ! = =4 38 ÷ = 12 12 19 5 Tabitha earned $38 1 3500 10,500 50 ! 10,500 = ! = 28,000 3 1 9 39 ÷ = ÷ = ! = 2 4 1 The land will cost Kurt $28,000 257 25 1285 ! = = 642 51 25 ! 25 = 10 2 10 35 35 ÷ = ! = =2 40 ÷ = 6 2 2 41 ÷ = 12 Average Americans consume 642 42 ÷ = 11 21 20 63 105 ! = = 105 52 !15 = 4 1 17 17 43 ÷ = ÷ = ! = 17 6 6 1 Kayla is paid $105 77 lb Chapter Fractions and Mixed Numbers: Multiplication and Division 16 59 ÷ = ÷ = ! = = 8 3 7 53 (a) ÷ = ÷ = ! = weeks old 4 4 1 17 ÷ (b) ÷ = 8 8 24 60 ÷ = ÷ = ! = =3 3 7 17 17 = ! = = weeks old 2 27 !2 = ! = =1 61 10 10 5 1 7 54 ÷ = ÷ = ! = 4 12 Each child will inherit $ million 12 4 41 41 62 !5 = ! = =6 8 6 17 28 41 28 24 672 = ÷ = ! = 24 24 41 41 16 = 16 41 16 The roll is 16 ft long 41 55 28 ÷ 63 !0 = 12 16 64 ! = ! = 32 3 1 7 71 14 56 (a) Lucy: 35 ! 14 = " = 497 2 1 21 21 ! = =1 65 10 ÷ = ÷ = 2 6 85 10 Ricky: 42 ! 10 = " = 425 2 66 497 − 425 = 72 Lucy earned $72 more than Ricky 67 ÷ = (b) 497 + 425 = 922 Together they earned $922 1 3 3 68 ÷2 = ÷ = ! = 8 20 1 11 11 11 10 ! =2 57 ÷ = ÷ = 10 10 11 17 34 !1 = ! = 9 63 12 ! = =1 69 12 ! = 8 2 5 15 11 55 ! = =6 58 ! = 6 8 20 ! = =2 70 20 ! = 15 15 3 78 Section 2.6 Multiplication and Division of Mixed Numbers 71 ÷ is undefined 1 72 ! = 2 1 79 12 ! 25 = 318 =2 1 80 38 ÷ 12 = 3 15 18 81 56 ÷ = 17 6 19 74 ! $ ! $ ! 14 $ 31 11 14 #" &% #" &% #" 33 &% = ' ' 33 62 31 = =3 18 9 1 82 25 !18 = 466 5 1 57 ÷ ÷ 75 ÷ ÷ = 8 19 1 83 32 57 19 = ! ! = =2 8 = 1 85 11 ! 41 = 480 25 16 10 ! ! = = 40 21 24 12 99 ÷ 12 = 12 146 404 84 106 ÷ 41 = 753 5 25 40 21 76 ÷ ÷ = ÷ ÷ 16 16 It takes gallons of gas for Sara to get to and from work × $5 = $15 It costs Sara $15 each day 73 ! $ ! $ ! $ 17 15 21 ' = #" &% #" 34 &% #" &% = ' 34 = 1 129 43 129 ÷ = ! =3 78 64 ÷ 21 = 2 2 43 86 ! 28 = 280 27 77 The perimeter of the garden is 2(20) + 2(15) = 40 + 30 = 70 ft 14 70 70 70 ÷ = ÷ = ! = 56 4 56 bricks will be needed 56 × $3 = $168 The total cost is $168 79 Chapter Fractions and Mixed Numbers: Multiplication and Division Chapter Review Exercises 134 16 941 !7 24 !21 31 !28 Section 2.1 1 2 (b) Improper (a) (b) Proper 18 21, 51, 1200 23 or 8 19 55, 140, 260, 1200 20 58, 124, 140, 260, 1200 7 or 6 21 Prime ! + 43 = = 7 22 Composite 44 = × 11 11 ! + 57 11 = = 5 23 Neither 24 Neither 1 17 17 10 ÷ = ÷ = ! = 17 4 4 25 2 2 12 60 Section 2.2 15 11 47 !45 60 17 26 1582 !156 22 !0 22 (a) 134 16 32 64 ! ! ! ! ! = 26 = 64 23 =1 21 21 11 26 55 165 330 13−15 ⋅ ⋅ ⋅ 11 = 330 80 22 11 = 60 26 13 Chapter 27 5 2 45 225 450 900 40 42 ! 14 14 = = 45 ! 15 15 45 − 42 = 3 = = 45 ! 15 15 ! ! ! ! ! = 22 ! 32 ! 52 = 900 28 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 41 (a) !3 = = 10 ! 5 (b) 2! = = 15 ! 5 29 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 Section 2.3 Section 2.4 30 ! ! ! 18 " 30 ! 31 15 ! 14 ! 21! 10 210 = 210 15 10 = 21 14 32 Review Exercises 42 ! = 35 43 32 ! = 3 9 14 44 14 ! = ! = 63 2 5 = = 20 ! 33 34 35 33 ! = 15 45 33 ! = 11 11 14 ! = = 49 ! 7 24 ! = = 16 ! 17 36 =1 17 39 1400 14 !7 = = = 2000 20 ! 10 10 5 45 28 12 47 ! ! = 10 63 42 ! 21 = =2 37 21 21 120 12 ! 4 = = = 150 15 ! 5 36 46 ! ! = 25 63 ! 7 = = 27 ! 3 38 41 1 1 !1" 48 $ % = # # # = & 10 ' 10 10 10 10 10,000 81 Chapter Fractions and Mixed Numbers: Multiplication and Division 900 !2" ! " !2 2" ! 1 " 49 $ % # $ % = $ # % # $ # % & ' & 10 ' & 5 ' & 10 10 ' 1 3600 ! 3600 = ! = 900 58 4 1 = # 25 100 There are 900 African American students 25 300 1 3600 ! 3600 = ! = 300 59 12 12 = 625 1 There are 300 Asian American students ! 2" ! 1" 1 1 50 $ # % =$ % = # # = & 20 ' & 10 ' 10 10 10 1000 10 60 1 1000 ! " ! 1000 " ' = 51 # $ # $= 17 % 10 & % 17 & 1000 17 1 1 3600 3600 ! ! 3600 = ! ! = = 300 6 12 There are 300 Hispanic female students 300 5 3600 1500 ! ! 3600 = ! ! = = 750 61 12 12 1 52 A = bh There are 750 Caucasian male students Section 2.5 53 A = lw 1 1 62 ! =1 3 17 17 ! 17 " 54 A = (12) $ % = # = # = 51 ft 2 2 & 2' 1 1 12 ! 12 = ! =1 63 12 12 55 A = lw = 10 ! = or m 3 1 20 20 !3+ ! !6 56 A = 3 10 20 20 = ! + ! ! 3 1 1 65 67 68 7 = ! = or 8 2 69 Multiplying Maximus requires 66 Reciprocal does not exist = 20 + 20 = 40 yd 57 ! 64 or yd of lumber 2 70 82 28 21 28 20 ! ! 16 ÷ = ! = ! = 15 20 15 21 ! ! Chapter 71 35 63 7 ! ÷ = ! = ! = 63 35 ! 5 4 20 ! 20 = ! = 16 80 5 1 6 1 ÷ 18 = ! = 72 7 18 21 18 81 18 ÷ = ! = 27 3 1 3 ÷ = ! = 73 10 10 12 24 82 24 ÷ = ! = 36 74 1 200 25 200 17 25 ! 17 ÷ = ! = ! = 51 17 51 25 17 ! 25 36 bags of candy 4 40 83 ! 40 = ! = 32 hr 5 12 ! = 14 75 12 ÷ = 32 × $18 = $576 Amelia earned $576 1 3 ! $ 76 ! ÷ $ = ' 19 = ! $ # & #" 19 19 &% #" &% " 19 % = 84 4 16 ! = 3 16 16 10 12 640 ! 10 ! 12 = ! ! = 9 1 1 1 ' ' = 4 64 The area is ! 12 $ 36 144 36 144 77 # & ÷ = ÷ = ' 25 25 36 " 5% 1 27 Yes, he will have 24 pieces, which is more than enough for his class Section 2.6 81 3 81 11 18 ÷ ÷ = ! ! = 55 11 55 3 5 ! "! " 11 32 352 86 $ %$ % = # = 15 & '& ' 23 15 352 = 23 15 !30 52 !45 1 " % 79 ! ÷ = ! ÷ = ÷ 13 $# '& 13 26 = 640 or 213 ft 3 85 ÷ = ! = 24 36 ' = ' = '5 36 78 Review Exercises 1 ! = 26 52 83 Chapter Fractions and Mixed Numbers: Multiplication and Division 1 14 9 = =4 93 ÷ = ÷ = ! 9 14 2 ! "! " 34 71 71 ' = = 23 87 #11 $# $ = 3 % &% 34 & 34 1 1 25 50 50 25 94 ÷ = ÷ = ! = =2 11 11 11 11 11 13 16 ! =8 88 ! = 13 13 1 51 17 51 ! = 95 10 ÷ 17 = ÷ = 5 17 ! " 45 45 = = 22 89 # $ % = # 8 2 & ' 90 45 !0 = 13 96 ÷ 3 1 5 25 97 ! = ! = =3 4 8 It will take gal 69 23 69 ÷ = ! = =1 91 ÷ = 16 16 16 23 2 =0 12 5 38 19 38 10 ÷ = ! = 92 ÷ = 11 11 11 19 11 1 There will be 10 pieces Chapter Test (b) Proper (a) 12 44 !36 (a) (b) Improper (a) 1 25 25 ÷ = ! = 10 98 12 ÷ = 4 =3 12 ! + 34 (b) = = 9 11 ;5 2 7 is an improper fraction because the numerator is greater than or equal to the denominator 84 Chapter 10 (a) (b) (c) (d) (e) (f) Composite Neither Prime Neither Prime Composite 15 = × (b) Brad has the greater fractional part completed since > 5 19 39 = × 13 11 (a) 1, 3, 5, 9, 15, 45 (b) 57 ! 19 19 " = ! = 46 ! ! 23 69 75 75 ' 25 20 ! 75 $ ' = = #" 24 &% ' = '2 24 39 45 = 3! 3!5 = 32 !5 = 45 12 (a) Add the digits of the number If the sum is divisible by 3, then the original number is divisible by 21 (b) Yes; + + + + + + = 21 and 21 is divisible by 25 or 12 2 28 21 28 ÷ = ! 24 24 21 ! ! !2!2 = ! = ! ! ! 3! 21 105 105 21 ÷5 = ! = = 22 42 42 42 13 (a) No; 1155 is not even (b) Yes; + + + = 12 is divisible by (c) Yes; the digit in the ones-place is a (d) No; the digit in the ones-place is not 23 14 15 ! ! 12 ! 60 = 60 15 = 12 40 ! !2!2! " " = ! ! 18 25 ! ! !5 !3 = 15 24 600 ÷ 50 ÷ 13 = ÷ !10 ÷ 13 1200 65 15 !13 15 15 ! 25 ! ! 50 " 20 ! 25 16 Test 1 13 15 = ! ! = 10 13 150 ! ! ! 10 = = or 105 ! !7 7 25 1, 200 , 000 12 ! 6 = = = 17 1, 400 , 000 14 ! 7 15 ! = = 25 ! 5 16 ! 4 = = Brad: 20 ! 5 18 (a) Christine: 85 10 10 25 ÷4 = ÷ 21 21 10 = ! 21 25 2! 2! = ! !7 !5 = 35 Chapter Fractions and Mixed Numbers: Multiplication and Division 26 4 ! = 72 ! 34 = 144 = ! 48 17 15 17 15 15 !5 20 29 20 ! = ! =5 4 1 = 20 20 = ÷ = ! = 80 4 1 20 ÷ is greater 48 =9 5 20 ÷ 2 ( + 27 52 ÷ *! $ ' - = 52 ÷ ( ' + = 52 ÷ * 72 *#" &% - 72 ) , 72 ) , 12 12 = ÷ = ! = 48 4 1 48 quarter-pounders 30 12 ÷ 26 1 52 26 13 = ' = = 72 24 12 24 32 11 44 = ' ' = or 14 cm 2 3 4 ! = = 10 They can build on a maximum of Cumulative Review Exercises 24 16 384 !32 64 !64 17,000; nineteen thousand, three hundred forty; 22,047; fifteen thousand, seven hundred seventy-one 432 + 998 1430 572 ! 433 139 4122 52 244 206 100 214,344 dogs are female pure breeds 1 ! 11$ 28 A = bh = (8) # & 2 " 3% Chapters 1–2 15 5 120 15 ! ! 120 = ! ! = =5 31 15 15 ! 23 ! 81 23 1840 1863 18 R 74 !4 34 !32 86 acre Chapters 1–2 3,000,000 ! 40,000 120,000,000,000 23 35 51 ! ! 17 119 ! = ! = 27 95 ! ! ! 19 171 17 34 17 5 24 ÷ = ÷ = ! = 5 34 1007 ! 823 184 10 Cumulative Review Exercises 48 =6 1 5 25 Yes; and ! = ! = 13 16 26 16 13 26 11 + ⋅ = + 16 = 22 12 52 ! 32 = 25 ! = 16 !1 2" 5 26 Yes; $ # % # = # = and & ' 27 13 (5 ! 3) = 22 = ! " 10 #$ # % = # = & ' 27 27 14 d 15 c 16 b 17 e 18 a = ! = 25 25 1 11 11 28 A = lw = ! = or m 9 20 (a) Proper (b) Improper (c) Improper 1 bh ! 25 $ 25 ' ' = # & (8) = ' ' = 50 ft 2" % 2 29 A = 21 (a) 1, 2, 3, 5, 6, 10, 15, 30 (b) 15 30 ⋅ ⋅ = 30 (b) 2 19 (a) 7 (b) or 3 22 (a) 27 " ! 12 % ÷ = " % ÷ = ÷ $ ' $# '& 25 # 25 & 30 144 ! ! ! ! ! 12 = = or 84 ! ! !7 7 60 , 000 2! = = = 150 , 000 15 ! 87 3 ! = 10 40 of the students are males from out of 40 state ... to Fractions and Mixed Numbers 72 10 51 !50 73 23 !18 7 16 74 115 !7 45 !42 44 75 309 !28 29 !28 53 10 18 5 12 12 11 10 16 44 Chapter Fractions and Mixed Numbers: Multiplication and Division... by , and ÷ ! multiplies 3 2 2 multiplies by So ! = ! = 3 55 16 16 ÷8 = ! = 5 1 2 1 and ÷ = ! = 3 69 Chapter Fractions and Mixed Numbers: Multiplication and Division 2 multiplies by , and ÷... factorization of a number n is a product of factors that equals n (c) A prime number is a whole number greater than that has only two factors (itself and 1) (d) A composite number is a whole number greater