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All Textbook Solutions for PREALGEBRA
TRY IT:: 4.57 Find the reciprocal: a. 57 b. 18 c. 114 d. 14TRY IT:: 4.58 Find the reciprocal: a. 37 b. 112 c. 149 d. 21TRY IT:: 4.59 Fill in the chart for each number given:TRY IT:: 4.60 Fill in the chart for each number given:TRY IT:: 4.61 Model: 1316 .TRY IT:: 4.62 Model: 1214 .TRY IT:: 4.63 Model: 213 .TRY IT:: 4.64 Model: 312 .TRY IT:: 4.65 Divide, and write the answer in simplified form: 37(23) .TRY IT:: 4.66 Divide, and write the answer in simplified form: 23(75) .TRY IT:: 4.67 Divide, and write the answer in simplified form: 35p7 .TRY IT:: 4.68 Divide, and write the answer in simplified form: 58q3 .TRY IT:: 4.69 Divide, and write the answer in simplified form: 23(56) .TRY IT:: 4.70 Divide, and write the answer in simplified form: 56(23) .TRY IT:: 4.71 Divide, and write the answer in simplified form: 7273536 .TRY IT:: 4.72 Divide, and write the answer in simplified form: 5141528 .In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 77. 721In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 78. 824In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 79. 1520In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 80. 1218In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 81. 4088In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 82. 6399In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 83. 10863In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 84. 10448In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 85. 120252In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 86. 182294In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 87. 168192In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 88. 140224In the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 89. 11x11yIn the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 15a15bIn the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 91. 3x12yIn the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 92. 4x32yIn the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 93. 14x221yIn the following exercises, simplify each fraction. Do not convert any improper fractions to mixed numbers. 94. 24a32b2In the following exercises, use a diagram to model. 1223In the following exercises, use a diagram to model. 1258In the following exercises, use a diagram to model. 1356In the following exercises, use a diagram to model. 1325In the following exercises, multiply, and write the answer in simplified form. 2513In the following exercises, multiply, and write the answer in simplified form. 1238In the following exercises, multiply, and write the answer in simplified form. 34910In the following exercises, multiply, and write the answer in simplified form. 4527In the following exercises, multiply, and write the answer in simplified form. 23(38)In the following exercises, multiply, and write the answer in simplified form. 34(49)In the following exercises, multiply, and write the answer in simplified form. 59310In the following exercises, multiply, and write the answer in simplified form. 38415In the following exercises, multiply, and write the answer in simplified form. 712(821)In the following exercises, multiply, and write the answer in simplified form. 512(815)In the following exercises, multiply, and write the answer in simplified form. (1415)(920)In the following exercises, multiply, and write the answer in simplified form. (920)(2533)In the following exercises, multiply, and write the answer in simplified form. (6384)(4490)In the following exercises, multiply, and write the answer in simplified form. (3360)(4088)In the following exercises, multiply, and write the answer in simplified form. 4511In the following exercises, multiply, and write the answer in simplified form. 583In the following exercises, multiply, and write the answer in simplified form. 3721nIn the following exercises, multiply, and write the answer in simplified form. 5630mIn the following exercises, multiply, and write the answer in simplified form. 28p(14)In the following exercises, multiply, and write the answer in simplified form. 51q(13)In the following exercises, multiply, and write the answer in simplified form. 8(174)In the following exercises, multiply, and write the answer in simplified form. 145(15)In the following exercises, multiply, and write the answer in simplified form. 1(38)In the following exercises, multiply, and write the answer in simplified form. (1)(67)In the following exercises, multiply, and write the answer in simplified form. (23)3In the following exercises, multiply, and write the answer in simplified form. (45)2In the following exercises, multiply, and write the answer in simplified form. (65)4In the following exercises, multiply, and write the answer in simplified form. (47)4In the following exercises, find the reciprocal. 34In the following exercises, find the reciprocal. 23In the following exercises, find the reciprocal. 517In the following exercises, find the reciprocal. 619In the following exercises, find the reciprocal. 118In the following exercises, find the reciprocal. 13In the following exercises, find the reciprocal. 19In the following exercises, find the reciprocal. 1In the following exercises, find the reciprocal. 1In the following exercises, find the reciprocal. Fill in the chart.In the following exercises, find the reciprocal. Fill in the chart.In the following exercises, model each fraction division. 1214In the following exercises, model each fraction division. 1218In the following exercises, model each fraction division. 215In the following exercises, model each fraction division. 314In the following exercises, divide, and write the answer in simplified form. 1214In the following exercises, divide, and write the answer in simplified form. 1218In the following exercises, divide, and write the answer in simplified form. 3423In the following exercises, divide, and write the answer in simplified form. 4534In the following exercises, divide, and write the answer in simplified form. 4547In the following exercises, divide, and write the answer in simplified form. 3435In the following exercises, divide, and write the answer in simplified form. 79(79)In the following exercises, divide, and write the answer in simplified form. 56(56)In the following exercises, divide, and write the answer in simplified form. 34x11In the following exercises, divide, and write the answer in simplified form. 25y9In the following exercises, divide, and write the answer in simplified form. 58a10In the following exercises, divide, and write the answer in simplified form. 56c15In the following exercises, divide, and write the answer in simplified form. 518(1524)In the following exercises, divide, and write the answer in simplified form. 718(1427)In the following exercises, divide, and write the answer in simplified form. 7p1221p8SIn the following exercises, divide, and write the answer in simplified form. 5q1215q8In the following exercises, divide, and write the answer in simplified form. 8u1512v25In the following exercises, divide, and write the answer in simplified form. 12r2518s35In the following exercises, divide, and write the answer in simplified form. 512In the following exercises, divide, and write the answer in simplified form. 314In the following exercises, divide, and write the answer in simplified form. 34(12)In the following exercises, divide, and write the answer in simplified form. 25(10)In the following exercises, divide, and write the answer in simplified form. 18(92)In the following exercises, divide, and write the answer in simplified form. 15(53)In the following exercises, divide, and write the answer in simplified form. 12(34)78In the following exercises, divide, and write the answer in simplified form. 11278211Baking A recipe for chocolate chip cookies calls for 34 cup brown sugar. Imelda wants to double the recipe. a. How much brown sugar will Imelda need? Show your calculation. Write your result as an improper fraction and as a mixed number. b. Measuring cups usually come in sets of 18,14,13,12 , and 1 cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the recipe.Baking Nina is making 4 pans of fudge to serve after a music recital. For each pan, she needs 23 cup of condensed milk. a. How much condensed milk will Nina need? Show your calculation. Write your result as an improper fraction and as a mixed number. b. Measuring cups usually come in sets of 18,14,13,12 , and 1 cup. Draw a diagram to show two different ways that Nina could measure the condensed milk she needs.Portions Don purchased a bulk package of candy that weighs 5 pounds. He wants to sell the candy in little bags that hold 14 pound. How many little bags of candy can he fill from the bulk package?Portions Kristen has 34 yards of ribbon. She wants to cut it into equal parts to make hair ribbons for her daughter’s 6 dolls. How long will each doll’s hair ribbon be?Explain how you find the reciprocal of a fraction.Explain how you find the reciprocal of a negative fraction.Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into 6 or 8 slices. Would he prefer 3 out of 6 slices or 4 out of 8 slices? Rafael replied that since he wasn’t very hungry, he would prefer 3 out of 6 slices. Explain what is wrong with Rafael’s reasoning.Give an example from everyday life that demonstrates how 1223 is 13 .TRY IT:: 4.73 Multiply, and write your answer in simplified form: 523617 .TRY IT:: 4.74 Multiply, and write your answer in simplified form: 37514 .TRY IT:: 4.75 Multiply, and write your answer in simplified form: 557(258) .TRY IT:: 4.76 Multiply, and write your answer in simplified form: 325416 .TRY IT:: 4.77 Divide, and write your answer in simplified form: 4387 .TRY IT:: 4.78 Divide, and write your answer in simplified form: 2583 .TRY IT:: 4.79 Divide, and write your answer in simplified form: 223113 .TRY IT:: 4.80 Divide, and write your answer in simplified form: 334112 .TRY IT:: 4.81 Translate the phrase into an algebraic expression: the quotient of 9s and 14.TRY IT:: 4.82 Translate the phrase into an algebraic expression: the quotient of 5y and 6.TRY IT:: 4.83 Translate the phrase into an algebraic expression: the quotient of the difference of a and b, and cd.TRY IT:: 4.84 Translate the phrase into an algebraic expression: the quotient of the sum of p and q, and r.TRY IT:: 4.85 Simplify: 2356 .TRY IT:: 4.86 Simplify: 37611 .TRY IT:: 4.87 Simplify: 874 .TRY IT:: 4.88 Simplify: 3910 .TRY IT:: 4.89 Simplify: a8ab6 .TRY IT:: 4.90 Simplify: p2pq8 .TRY IT:: 4.91 Simplify: 57125 .TRY IT:: 4.92 Simplify: 85315 .TRY IT:: 4.93 Which of the following fractions are equivalent to 35 ? 35,35,35,35TRY IT:: 4.94 Which of the following fractions are equivalent to 27 ? 27,27,27,27TRY IT:: 4.95 Simplify: 4+6112 .TRY IT:: 4.96 Simplify: 3+5182 .TRY IT:: 4.97 Simplify: 63(5)32+3 .TRY IT:: 4.98 Simplify: 44(6)33+3 .TRY IT:: 4.99 Simplify: ( 117)211272 .TRY IT:: 4.100 Simplify: ( 6+2)262+22 .TRY IT:: 4.101 Simplify: 8(2)+4(3)5(2)+3 .TRY IT:: 4.102 Simplify: 7(1)+9(3)5(3)2 .In the following exercises, multiply and write the answer in simplified form. 438710In the following exercises, multiply and write the answer in simplified form. 24967In the following exercises, multiply and write the answer in simplified form. 1522335In the following exercises, multiply and write the answer in simplified form. 25366310In the following exercises, multiply and write the answer in simplified form. 423(118)In the following exercises, multiply and write the answer in simplified form. 225(229)In the following exercises, multiply and write the answer in simplified form. 44951316In the following exercises, multiply and write the answer in simplified form. 172021112In the following exercises, divide, and write your answer in simplified form. 5134In the following exercises, divide, and write your answer in simplified form. 13129In the following exercises, divide, and write your answer in simplified form. 123311In the following exercises, divide, and write your answer in simplified form. 7514In the following exercises, divide, and write your answer in simplified form. 638218In the following exercises, divide, and write your answer in simplified form. 2151110In the following exercises, divide, and write your answer in simplified form. 935(135)In the following exercises, divide, and write your answer in simplified form. 1834(334)In the following exercises, translate each English phrase into an algebraic expression. the quotient of 5u and 11In the following exercises, translate each English phrase into an algebraic expression. the quotient of 7v and 13In the following exercises, translate each English phrase into an algebraic expression. the quotient of p and qIn the following exercises, translate each English phrase into an algebraic expression. the quotient of a and bIn the following exercises, translate each English phrase into an algebraic expression. the quotient of r and the sum of s and 10In the following exercises, translate each English phrase into an algebraic expression. the quotient of A and the difference of 3 and BIn the following exercises, simplify the complex fraction. 2389In the following exercises, simplify the complex fraction. 45815In the following exercises, simplify the complex fraction. 8211235In the following exercises, simplify the complex fraction. 9163340In the following exercises, simplify the complex fraction. 452In the following exercises, simplify the complex fraction. 9103In the following exercises, simplify the complex fraction. 258In the following exercises, simplify the complex fraction. 5310In the following exercises, simplify the complex fraction. m3n2In the following exercises, simplify the complex fraction. r5s3In the following exercises, simplify the complex fraction. x689In the following exercises, simplify the complex fraction. 38y12In the following exercises, simplify the complex fraction. 245110In the following exercises, simplify the complex fraction. 42316In the following exercises, simplify the complex fraction. 79245In the following exercises, simplify the complex fraction. 38634In the following exercises, identify the equivalent fractions. Which of the following fractions are equivalent to 511 ? 511,511,511,511In the following exercises, identify the equivalent fractions. Which of the following fractions are equivalent to 49 ? 49,49,49,49In the following exercises, identify the equivalent fractions. Which of the following fractions are equivalent to 113 ? 113,113,113,113In the following exercises, identify the equivalent fractions. Which of the following fractions are equivalent to 136 ? 136,136,136,136In the following exercises, simplify. 4+118In the following exercises, simplify. 9+37In the following exercises, simplify. 22+310In the following exercises, simplify. 1946In the following exercises, simplify. 482415In the following exercises, simplify. 464+4In the following exercises, simplify. 6+68+4In the following exercises, simplify. 6+3178In the following exercises, simplify. 22141913In the following exercises, simplify. 15+918+12In the following exercises, simplify. 5810In the following exercises, simplify. 3424In the following exercises, simplify. 4366In the following exercises, simplify. 6692In the following exercises, simplify. 42125In the following exercises, simplify. 72+160In the following exercises, simplify. 83+2914+3In the following exercises, simplify. 964722+3In the following exercises, simplify. 15552210In the following exercises, simplify. 12932318In the following exercises, simplify. 56344523In the following exercises, simplify. 89765692In the following exercises, simplify. 523235In the following exercises, simplify. 624246In the following exercises, simplify. 2+4(3)322In the following exercises, simplify. 7+3(5)232In the following exercises, simplify. 742(85)9.33.5In the following exercises, simplify. 973(128)8.76.6In the following exercises, simplify. 9(82)3(157)6(71)3(179)In the following exercises, simplify. 8(92)4(149)7(83)3(169)Baking A recipe for chocolate chip cookies calls for 214 cups of flour. Graciela wants to double the recipe. a. How much flour will Graciela need? Show your calculation. Write your result as an improper fraction and as a mixed number. b. Measuring cups usually come in sets with cups for 18,14,13,12 , and 1 cup. Draw a diagram to show two different ways that Graciela could measure out the flour needed to double the recipe.Baking A booth at the county fair sells fudge by the pound. Their award winning “Chocolate Overdose” fudge contains 223 cups of chocolate chips per pound. a. How many cups of chocolate chips are in a half-pound of the fudge? b. The owners of the booth make the fudge in 10 -pound batches. How many chocolate chips do they need to make a 10 -pound batch? Write your results as improper fractions and as a mixed numbers.Explain how to find the reciprocal of a mixed number.Explain how to multiply mixed numbers.Randy thinks that 312514 is 1518 . Explain what is wrong with Randy’s thinking.Explain why 12,12 , and 12 are equivalent.TRY IT:: 4.103 Use a model to find each sum. Show a diagram to illustrate your model. 18+48TRY IT:: 4.104 Use a model to find each sum. Show a diagram to illustrate your model. 16+46TRY IT:: 4.105 Find each sum: 36+26 .TRY IT:: 4.106 Find each sum: 310+710 .TRY IT:: 4.107 Find the sum: x4+34 .TRY IT:: 4.108 Find the sum: y8+58 .TRY IT:: 4.109 Find the sum: 7d+8d .TRY IT:: 4.110 Find the sum: 6m+9m .TRY IT:: 4.111 Find the sum: 3p8+6p8 .TRY IT:: 4.112 Find the sum: 2q5+7q5 .TRY IT:: 4.113 Find each sum: 415+(615) .TRY IT:: 4.114 Find each sum: 521+(921) .TRY IT:: 4.115 Use a model to find each difference. Show a diagram to illustrate your model. 7848TRY IT:: 4.116 Use a model to find each difference. Show a diagram to illustrate your model. 5646TRY IT:: 4.117 Find the difference: 1928728 .TRY IT:: 4.118 Find the difference: 27321132 .TRY IT:: 4.119 Find the difference: x727 .TRY IT:: 4.120 Find the difference: y141314 .TRY IT:: 4.121 Find the difference: 9x7x .TRY IT:: 4.122 Find the difference: 17a5a .TRY IT:: 4.123 Simplify: 25+(45)35 .TRY IT:: 4.124 Simplify: 59+(49)79 .In the following exercises, use a model to add the fractions. Show a diagram to illustrate your model. 254. 25+15In the following exercises, use a model to add the fractions. Show a diagram to illustrate your model. 255. 310+410In the following exercises, use a model to add the fractions. Show a diagram to illustrate your model. 256. 16+36In the following exercises, use a model to add the fractions. Show a diagram to illustrate your model. 257. 38+38In the following exercises, find each sum. 49+19In the following exercises, find each sum. 29+59In the following exercises, find each sum. 613+713In the following exercises, find each sum. 915+715In the following exercises, find each sum. x4+34In the following exercises, find each sum. y3+23In the following exercises, find each sum. 7p+9pIn the following exercises, find each sum. 8q+6qIn the following exercises, find each sum. 8b9+3b9In the following exercises, find each sum. 5a7+4a7In the following exercises, find each sum. 12y8+3y8In the following exercises, find each sum. 11x5+7x5In the following exercises, find each sum. 18+(38)In the following exercises, find each sum. 18+(58)In the following exercises, find each sum. 316+(716)In the following exercises, find each sum. 516+(916)In the following exercises, find each sum. 817+1517In the following exercises, find each sum. 919+1719In the following exercises, find each sum. 613+(1013)+(1213)In the following exercises, find each sum. 512+(712)+(1112)In the following exercises, use a model to subtract the fractions. Show a diagram to illustrate your model. 278. 5828In the following exercises, use a model to subtract the fractions. Show a diagram to illustrate your model. 279. 5626In the following exercises, find the difference. 4515In the following exercises, find the difference. 4535In the following exercises, find the difference. 1115715In the following exercises, find the difference. 913413In the following exercises, find the difference. 1112512In the following exercises, find the difference. 712512In the following exercises, find the difference. 4211921In the following exercises, find the difference. 89169In the following exercises, find the difference. y17917In the following exercises, find the difference. x19819In the following exercises, find the difference. 5y878In the following exercises, find the difference. 11z13813In the following exercises, find the difference. 8d3dIn the following exercises, find the difference. 7c7cIn the following exercises, find the difference. 23u15uIn the following exercises, find the difference. 29v26vIn the following exercises, find the difference. 6c75c7In the following exercises, find the difference. 12d119d11In the following exercises, find the difference. 4r135r13In the following exercises, find the difference. 7s37s3In the following exercises, find the difference. 35(45)In the following exercises, find the difference. 37(57)In the following exercises, find the difference. 79(59)In the following exercises, find the difference. 811(511)In the following exercises, perform the indicated operation and write your answers in simplified form. 518910In the following exercises, perform the indicated operation and write your answers in simplified form. 314712In the following exercises, perform the indicated operation and write your answers in simplified form. n545In the following exercises, perform the indicated operation and write your answers in simplified form. 611s11In the following exercises, perform the indicated operation and write your answers in simplified form. 724+224