{"id":764,"date":"2020-08-21T19:41:44","date_gmt":"2020-08-21T23:41:44","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/4-review\/"},"modified":"2021-03-24T10:54:29","modified_gmt":"2021-03-24T14:54:29","slug":"4-review","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/4-review\/","title":{"raw":"4.5 Chapter Review","rendered":"4.5 Chapter Review"},"content":{"raw":"
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Review Exercises<\/h1>\n
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Write a Ratio as a Fraction<\/h2>\n
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In the following exercises, write each ratio as a fraction. Simplify the answer if possible.<\/p>\n\n\n\n\n\n\n\n
1. \\(56\\) to \\(32\\)<\/td>\n2. \\(28\\) to \\(40\\)<\/td>\n<\/tr>\n
3. \\(1.2\\) to \\(1.8\\)<\/td>\n4. \\(3.5\\) to \\(0.5\\)<\/td>\n<\/tr>\n
5. \\(2\\frac{1}{3}\\phantom{\\rule{0.2em}{0ex}}\\text{to}\\phantom{\\rule{0.2em}{0ex}}5\\frac{1}{4}\\)<\/td>\n6. \\(1\\frac{3}{4}\\phantom{\\rule{0.2em}{0ex}}\\text{to}\\phantom{\\rule{0.2em}{0ex}}1\\frac{5}{8}\\)<\/td>\n<\/tr>\n
\u00a07. \\(28\\) inches to \\(3\\) feet<\/td>\n8. \\(64\\) ounces to \\(30\\) ounces<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Write a Rate as a Fraction<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, write each rate as a fraction. Simplify the answer if possible.<\/p>\n\n\n\n\n\n
9. \\(90\\) pounds per \\(7.5\\) square inches<\/td>\n10. \\(180\\) calories per \\(8\\) ounces<\/td>\n<\/tr>\n
\u00a011.\\(\\text{\\$612.50}\\) for \\(35\\) hours<\/td>\n12. \\(126\\) miles in \\(4\\) hours<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Find Unit Rates<\/h2>\n<\/div>\n<\/div>\n<\/div>\nIn the following exercises, find the unit rate.\n\n\n\n\n
13. \\(90\\) pounds per \\(7.5\\) square inches<\/td>\n14. \\(180\\) calories per \\(8\\) ounces<\/td>\n<\/tr>\n
15. \\(\\text{\\$612.50}\\) for \\(35\\) hours<\/td>\n16. \\(126\\) miles in \\(4\\) hours<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Find Unit Price<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, find the unit price.<\/p>\n\n\n\n\n\n
17.Highlighters: \\(6\\) for \\(\\text{\\$2.52}\\)<\/td>\n18. T-shirts: \\(3\\) for \\(\\text{\\$8.97}\\)<\/td>\n<\/tr>\n
19. Anna bought a pack of \\(8\\) kitchen towels for \\(\\text{\\$13.20}\\). How much did each towel cost? Round to the nearest cent if necessary.<\/td>\n20. An office supply store sells a box of pens for \\(\\text{\\$11}\\). The box contains \\(12\\) pens. How much does each pen cost?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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In the following exercises, find each unit price and then determine the better buy.<\/div>\n
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21.Vitamins: \\(60\\) tablets for \\(\\text{\\$6.49}\\) or \\(100\\) for \\(\\text{\\$11.99}?\\)<\/td>\n22. Shampoo: \\(12\\) ounces for \\(\\text{\\$4.29}\\) or \\(22\\) ounces for \\(\\text{\\$7.29}?\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
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Translate Phrases to Expressions with Fractions<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate the English phrase into an algebraic expression.<\/p>\n\n\n\n\n\n
23. \\(a\\) adults to \\(45\\) children<\/td>\n24. \\(535\\) miles per \\(h\\phantom{\\rule{0.2em}{0ex}}\\text{hours}\\)<\/td>\n<\/tr>\n
25. the ratio of \\(19\\) and the sum of \\(3\\) and \\(n\\)<\/td>\n26. the ratio of \\(4y\\) and the difference of \\(x\\) and \\(10\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nIn the following exercises, write each percent as a ratio.\n\n<\/div>\n
\n\n\n\n
27. \\(\\text{32\\%}\\) admission rate for the university<\/td>\n28. \\(\\text{53.3\\%}\\) rate of college students with student loans<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In the following exercises, write as a ratio and then as a percent.<\/p>\n\n\n\n\n
29. \\(13\\) out of \\(100\\) architects are women.<\/td>\n30. \\(9\\) out of every \\(100\\) nurses are men.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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In the following exercises, convert each percent to a fraction.<\/p>\n\n\n\n\n\n
31. \\(\\text{48\\%}\\)<\/td>\n32. \\(\\text{175\\%}\\)<\/td>\n<\/tr>\n
33. \\(\\text{64.1\\%}\\)<\/td>\n34. \\(8\\frac{1}{4}\\%\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, convert each percent to a decimal.<\/p>\n\n\n\n\n\n
35. \\(\\text{6\\%}\\)<\/td>\n36. \\(\\text{23\\%}\\)<\/td>\n<\/tr>\n
37. \\(\\text{128\\%}\\)<\/td>\n38. 4.9%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, convert each percent to a) a simplified fraction and b) a decimal.<\/p>\n\n\n\n\n\n
39. In \\(2016,\\text{17\\%}\\) of the Canadian population was age \\(65\\) or over. (Source: www12.statcan.gc.ca)<\/td>\n40. In \\(2016,\\text{16.6\\%}\\) of the Canadian population was under \\(15\\) years old. (Source: www12.statcan.gc.ca)<\/td>\n<\/tr>\n
41. When a die is tossed, the probability it will land with an even number of dots on the top side is \\(\\text{50\\%}\\).<\/td>\n42. A couple plans to have three children. The probability they will all be girls is \\(\\text{12.5\\%}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, convert each decimal to a percent.<\/p>\n\n\n\n\n\n\n
43. \\(0.04\\)<\/td>\n44. \\(0.15\\)<\/td>\n<\/tr>\n
45. \\(2.82\\)<\/td>\n46. \\(3\\)<\/td>\n<\/tr>\n
47. \\(0.003\\)<\/td>\n48. \\(1.395\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, convert each fraction to a percent.<\/p>\n\n\n\n\n\n\n
49. \\(\\frac{3}{4}\\)<\/td>\n50. \\(\\frac{11}{5}\\)<\/td>\n<\/tr>\n
51. \\(3\\frac{5}{8}\\)<\/td>\n52. \\(\\frac{2}{9}\\)<\/td>\n<\/tr>\n
53. According to the Centers for Disease Control, \\(\\frac{2}{5}\\) of adults do not take a vitamin or supplement.<\/td>\n54. According to the Centers for Disease Control, among adults who do take a vitamin or supplement, \\(\\frac{3}{4}\\) take a multivitamin.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, translate and solve.<\/p>\n\n\n\n\n\n\n\n
55. What number is \\(\\text{46\\%}\\) of \\(350?\\)<\/td>\n56. \\(\\text{120\\%}\\) of \\(55\\) is what number?<\/td>\n<\/tr>\n
57. \\(84\\) is \\(\\text{35\\%}\\) of what number?<\/td>\n58. \\(15\\) is \\(\\text{8\\%}\\) of what number?<\/td>\n<\/tr>\n
59. \\(\\text{200\\%}\\) of what number is \\(50?\\)<\/td>\n60. \\(\\text{7.9\\%}\\) of what number is \\(\\text{\\$4.74}?\\)<\/td>\n<\/tr>\n
61. What percent of \\(120\\) is \\(81.6?\\)<\/td>\n62. What percent of \\(340\\) is \\(595?\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
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Solve General Applications of Percents<\/h2>\n

In the following exercises, solve.<\/p>\n\n\n\n\n\n
63. When Aurelio and his family ate dinner at a restaurant, the bill was \\(\\text{\\$83.50}\\). Aurelio wants to leave \\(\\text{20\\%}\\) of the total bill as a tip. How much should the tip be?<\/td>\n64. One granola bar has \\(2\\) grams of fiber, which is \\(\\text{8\\%}\\) of the recommended daily amount. What is the total recommended daily amount of fiber?<\/td>\n<\/tr>\n
65. The nutrition label on a package of granola bars says that each granola bar has \\(190\\) calories, and \\(54\\) calories are from fat. What percent of the total calories is from fat?<\/td>\n66. Elsa gets paid \\(\\text{\\$4,600}\\) per month. Her car payment is \\(\\text{\\$253}\\). What percent of her monthly pay goes to her car payment?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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67. Marta got a gift of\u00a0 \\(\\text{\\$1900}\\) from her uncle.\u00a0 She spent \\(\\text{35\\%}\\) of that money for her trip to Victoria. How much money she has left?.<\/td>\n68. Last year Bernard bought a new car for \\(\\text{\\$30,000}\\). If the value of the car depreciated\u00a0 \\(\\text{20\\%}\\) every year , find the value of the car this year.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
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Solve Proportions and their Applications<\/h2>\n<\/div>\n
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In the following exercises, write each sentence as a proportion.<\/p>\n\n\n\n\n\n
69. \\(3\\) is to \\(8\\) as \\(12\\) is to \\(32\\).<\/td>\n70. \\(95\\) miles to \\(3\\) gallons is the same as \\(475\\) miles to \\(15\\) gallons.<\/td>\n<\/tr>\n
71. \\(1\\) teacher to \\(18\\) students is the same as \\(23\\) teachers to \\(414\\) students.<\/td>\n72. \\(\\text{\\$7.35}\\) for \\(15\\) ounces is the same as \\(\\text{\\$2.94}\\) for \\(6\\) ounces.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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In the following exercises, determine whether each equation is a proportion.<\/p>\n\n\n\n\n\n
73. \\(\\frac{5}{13}=\\frac{30}{78}\\)<\/td>\n74. \\(\\frac{16}{7}=\\frac{48}{23}\\)<\/td>\n<\/tr>\n
75. \\(\\frac{12}{18}=\\frac{6.99}{10.99}\\)<\/td>\n76. \\(\\frac{11.6}{9.2}=\\frac{37.12}{29.44}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, solve each proportion.<\/p>\n\n\n\n\n\n
77. \\(\\frac{x}{36}=\\frac{5}{9}\\)<\/td>\n78. \\(\\frac{7}{a}=\\frac{-6}{84}\\)<\/td>\n<\/tr>\n
79. \\(\\frac{1.2}{1.8}=\\frac{d}{6}\\)<\/td>\n80. \\(\\frac{\\frac{1}{2}}{2}=\\frac{m}{20}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, solve the proportion problem.<\/p>\n\n\n\n\n\n\n
81. The children\u2019s dosage of acetaminophen is \\(5\\) millilitre s (ml) for every \\(25\\) pounds of a child\u2019s weight. How many millilitre s of acetaminophen will be prescribed for a \\(60\\) pound child?<\/td>\n82. After a workout, Dennis takes his pulse for \\(10\\) sec and counts \\(21\\) beats. How many beats per minute is this?<\/td>\n<\/tr>\n
83. An \\(8\\) ounce serving of ice cream has \\(272\\) calories. If Lavonne eats \\(10\\) ounces of ice cream, how many calories does she get?<\/td>\n84. Alma is going to Europe and wants to exchange \\(\\text{\\$1,200}\\) into Euros. If each dollar is \\(0.65\\) Euros, how many Euros will Alma get?<\/td>\n<\/tr>\n
85. Zack wants to drive from Abbotsford to Banff, a distance of \\(494\\) miles. If his car gets \\(38\\) miles to the gallon, how many gallons of gas will Zack need to get to Banff?<\/td>\n86. Teresa is planning a party for \\(100\\) people. Each gallon of punch will serve \\(18\\) people. How many gallons of punch will she need?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, translate to a proportion.<\/p>\n\n\n\n\n\n
87. What number is \\(\\text{62\\%}\\) of \\(395?\\)<\/td>\n88. \\(42\\) is \\(\\text{70\\%}\\) of what number?<\/td>\n<\/tr>\n
89. What percent of \\(1,000\\) is \\(15?\\)<\/td>\n90. What percent of \\(140\\) is \\(210?\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, translate and solve using proportions.<\/p>\n\n\n\n\n\n
91. What number is \\(\\text{85\\%}\\) of \\(900?\\)<\/td>\n92. \\(\\text{6\\%}\\) of what number is \\(\\text{\\$24}?\\)<\/td>\n<\/tr>\n
93. \\(\\text{\\$3.51}\\) is \\(\\text{4.5\\%}\\) of what number?<\/td>\n94. What percent of \\(3,100\\) is \\(930?\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, convert each percent to a) a decimal b) a simplified fraction.<\/p>\n\n\n\n\n\n
95. \\(\\text{24\\%}\\)<\/td>\n96. \\(\\text{5\\%}\\)<\/td>\n<\/tr>\n
97. \\(\\text{350\\%}\\)<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In the following exercises, convert each fraction to a percent. (Round to \\(3\\) decimal places if needed.)<\/p>\n\n\n\n\n\n
98. \\(\\frac{7}{8}\\)<\/td>\n99. \\(\\frac{1}{3}\\)<\/td>\n<\/tr>\n
100. \\(\\frac{11}{12}\\)<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
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In the following exercises, solve the percent problem.<\/p>\n\n\n\n\n\n\n
101. \\(65\\) is what percent of \\(260?\\)<\/td>\n102. What number is \\(\\text{27\\%}\\) of \\(3,000?\\)<\/td>\n<\/tr>\n
103. \\(\\text{150\\%}\\) of what number is \\(60?\\)<\/td>\n104. Write as a proportion: \\(4\\) gallons to \\(144\\) miles is the same as \\(10\\) gallons to \\(360\\) miles.<\/td>\n<\/tr>\n
105. Vin read \\(10\\) pages of a book in \\(12\\) minutes. At that rate, how long will it take him to read \\(35\\) pages?<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n

Review Answers<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. \\(\\frac{7}{4}\\)<\/td>\n3. \\(\\frac{2}{3}\\)<\/td>\n5. \\(\\frac{4}{9}\\)<\/td>\n<\/tr>\n
7. \\(\\frac{7}{9}\\)<\/td>\n9. \\(\\frac{90\\phantom{\\rule{0.2em}{0ex}}\\text{pounds}}{7.5\\phantom{\\rule{0.2em}{0ex}}\\text{square inches}}\\)<\/td>\n11. \\(\\frac{\\text{\\$612.50}}{35\\phantom{\\rule{0.2em}{0ex}}\\text{hours}}\\)<\/td>\n<\/tr>\n
13. 12 pounds\/sq.in.<\/td>\n15. \\$17.50\/hour<\/td>\n17. \\$0.42<\/td>\n<\/tr>\n
19. \\$1.65<\/td>\n21. \\$0.11, \\$0.12; 60 tablets for \\$6.49<\/td>\n23. \\(\\frac{a\\phantom{\\rule{0.2em}{0ex}}\\text{adults}}{45\\phantom{\\rule{0.2em}{0ex}}\\text{children}}\\)<\/td>\n<\/tr>\n
25. \\(\\frac{19}{3+n}\\)<\/td>\n27. \\(\\frac{32}{100}\\)<\/td>\n29. \\(\\frac{13}{100},\\text{13\\%}\\)<\/td>\n<\/tr>\n
31. \\(\\frac{12}{25}\\)<\/td>\n33. \\(\\frac{641}{1000}\\)<\/td>\n35. 0.06<\/td>\n<\/tr>\n
37. 1.28<\/td>\n39.\n\na) \\(\\phantom{\\rule{0.2em}{0ex}}\\frac{17}{100}\\)\n\nb) \\(\\phantom{\\rule{0.2em}{0ex}}0.17\\)<\/td>\n41.\n\na) \\(\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\)\n\nb) \\(\\phantom{\\rule{0.2em}{0ex}}0.5\\)<\/td>\n<\/tr>\n
43. 4%<\/td>\n45. 282%<\/td>\n47. 0.3%<\/td>\n<\/tr>\n
49. 75%<\/td>\n51. 362.5%<\/td>\n53. 40%<\/td>\n<\/tr>\n
55. 161<\/td>\n57. 240<\/td>\n59. 25<\/td>\n<\/tr>\n
61. 68%<\/td>\n63. \\$16.70<\/td>\n65. 28.4%<\/td>\n<\/tr>\n
67. 1235<\/td>\n69. \\(\\frac{3}{8}=\\frac{12}{32}\\)<\/td>\n71. \\(\\frac{1}{18}=\\frac{23}{414}\\)<\/td>\n<\/tr>\n
73. yes<\/td>\n75. no<\/td>\n77. 20<\/td>\n<\/tr>\n
79. 4<\/td>\n81. 12<\/td>\n83. 340<\/td>\n<\/tr>\n
87. \\(\\frac{x}{395}=\\frac{62}{100}\\)<\/td>\n89. \\(\\frac{x}{100}=\\frac{15}{1000}\\)<\/td>\n91.765<\/td>\n<\/tr>\n
93. \\$78<\/td>\n95.\\(0.24,\\frac{6}{25}\\)<\/td>\n97. \\(3.5,3\\frac{1}{2}\\)<\/td>\n<\/tr>\n
99. 33.333%<\/td>\n101.25%<\/td>\n103. 40<\/td>\n<\/tr>\n
105. 42<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Chapter Test<\/h1>\n\n\n\n\n\n\n\n\n\n\n
1. Write a ratio as a fraction. Simplify the answer if possible. \\(42\\) to \\(28\\)<\/td>\n\n

2. Write a rate as a fraction. Simplify the answer if possible.\u00a0\\(80\\) pounds per \\(6.5\\) square inches<\/p>\n<\/td>\n<\/tr>\n

3. Find the unit rate.\u00a0\\(\\text{\\$868.80}\\) for \\(24\\) hours<\/td>\n4. Marta bought a pack of \\(6\\) paint brushes for \\(\\text{\\$32.20}\\). How much did each brush cost? Round to the nearest cent if necessary<\/td>\n<\/tr>\n
5. Find each unit price and then the better buy.\nLaundry detergent: \\(64\\) ounces for \\(\\text{\\$10.99}\\) or \\(48\\) ounces for \\(\\text{\\$8.49}\\)<\/td>\n6. Convert a percent to a fraction: \\(\\text{245\\%}\\)<\/td>\n<\/tr>\n
7. Convert a decimal to a percent: \\(0.07\\)<\/td>\n8. Convert a fraction to a percent. (Round to \\(3\\) decimal places if needed.)\u00a0\\(\\frac{11}{8}\\)<\/td>\n<\/tr>\n
9. \u00a0What number is \\(\\text{36\\%}\\) of \\(450?\\)<\/td>\n10. \\(\\text{8\\%}\\) of what number is \\(\\text{\\$34}?\\)<\/td>\n<\/tr>\n
11. \\(57.6\\) is what percent of \\(360?\\)<\/td>\n12. One granola bar has \\(3\\) grams of fiber, which is \\(\\text{12\\%}\\) of the recommended daily amount. What is the total recommended daily amount of fiber?<\/td>\n<\/tr>\n
13. Klaudia is going to Poland and wants to exchange \\(\\text{\\$1,400}\\) into Polish zlotych. If each dollar is \\(2.91\\) zlotych, how many zlotych will Klaudia get?<\/td>\n14. Solve a proportion:\\(\\frac{24}{x}=\\frac{3}{7}\\)<\/td>\n<\/tr>\n
15. Solve a proportion:\\(\\frac{x}{6}=\\frac{9}{24}\\)<\/td>\n16.Solve a proportion:\\(\\frac{2.4}{1.6}=\\frac{t}{6.2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
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Test Answers<\/h1>\n
\n\n\n\n\n\n\n\n\n
1. \\(\\frac{3}{2}\\)<\/td>\n2. \\(\\frac{160}{13}\\)<\/td>\n3. \\$36.20<\/td>\n<\/tr>\n
4. \\$5.37<\/td>\n5. 64 ounces for \\$10.99 is the better buy<\/td>\n6. \\(\\frac{49}{20}\\)<\/td>\n<\/tr>\n
7. 7%<\/td>\n8. 137.5%<\/td>\n9. 162<\/td>\n<\/tr>\n
10. 425<\/td>\n11. 16%<\/td>\n12. 25 grams<\/td>\n<\/tr>\n
13. 4074 zlotych<\/td>\n14. 56<\/td>\n15. 2.25<\/td>\n<\/tr>\n
16. 9.3<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>","rendered":"
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Review Exercises<\/h1>\n
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Write a Ratio as a Fraction<\/h2>\n
\n

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.<\/p>\n\n\n\n\n\n\n
1. \"56\" to \"32\"<\/td>\n2. \"28\" to \"40\"<\/td>\n<\/tr>\n
3. \"1.2\" to \"1.8\"<\/td>\n4. \"3.5\" to \"0.5\"<\/td>\n<\/tr>\n
5. \"2\frac{1}{3}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}5\frac{1}{4}\"<\/td>\n6. \"1\frac{3}{4}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}1\frac{5}{8}\"<\/td>\n<\/tr>\n
\u00a07. \"28\" inches to \"3\" feet<\/td>\n8. \"64\" ounces to \"30\" ounces<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Write a Rate as a Fraction<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, write each rate as a fraction. Simplify the answer if possible.<\/p>\n\n\n\n\n
9. \"90\" pounds per \"7.5\" square inches<\/td>\n10. \"180\" calories per \"8\" ounces<\/td>\n<\/tr>\n
\u00a011.\"\text{\$612.50}\" for \"35\" hours<\/td>\n12. \"126\" miles in \"4\" hours<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Find Unit Rates<\/h2>\n<\/div>\n<\/div>\n<\/div>\n

In the following exercises, find the unit rate.<\/p>\n\n\n\n\n
13. \"90\" pounds per \"7.5\" square inches<\/td>\n14. \"180\" calories per \"8\" ounces<\/td>\n<\/tr>\n
15. \"\text{\$612.50}\" for \"35\" hours<\/td>\n16. \"126\" miles in \"4\" hours<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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Find Unit Price<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, find the unit price.<\/p>\n\n\n\n\n
17.Highlighters: \"6\" for \"\text{\$2.52}\"<\/td>\n18. T-shirts: \"3\" for \"\text{\$8.97}\"<\/td>\n<\/tr>\n
19. Anna bought a pack of \"8\" kitchen towels for \"\text{\$13.20}\". How much did each towel cost? Round to the nearest cent if necessary.<\/td>\n20. An office supply store sells a box of pens for \"\text{\$11}\". The box contains \"12\" pens. How much does each pen cost?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
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In the following exercises, find each unit price and then determine the better buy.<\/div>\n
\n\n\n\n
21.Vitamins: \"60\" tablets for \"\text{\$6.49}\" or \"100\" for \"\text{\$11.99}?\"<\/td>\n22. Shampoo: \"12\" ounces for \"\text{\$4.29}\" or \"22\" ounces for \"\text{\$7.29}?\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n

Translate Phrases to Expressions with Fractions<\/h2>\n<\/div>\n<\/div>\n

In the following exercises, translate the English phrase into an algebraic expression.<\/p>\n\n\n\n\n
23. \"a\" adults to \"45\" children<\/td>\n24. \"535\" miles per \"h\phantom{\rule{0.2em}{0ex}}\text{hours}\"<\/td>\n<\/tr>\n
25. the ratio of \"19\" and the sum of \"3\" and \"n\"<\/td>\n26. the ratio of \"4y\" and the difference of \"x\" and \"10\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In the following exercises, write each percent as a ratio.<\/p>\n<\/div>\n

\n\n\n\n
27. \"\text{32\%}\" admission rate for the university<\/td>\n28. \"\text{53.3\%}\" rate of college students with student loans<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In the following exercises, write as a ratio and then as a percent.<\/p>\n\n\n\n
29. \"13\" out of \"100\" architects are women.<\/td>\n30. \"9\" out of every \"100\" nurses are men.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, convert each percent to a fraction.<\/p>\n\n\n\n\n
31. \"\text{48\%}\"<\/td>\n32. \"\text{175\%}\"<\/td>\n<\/tr>\n
33. \"\text{64.1\%}\"<\/td>\n34. \"8\frac{1}{4}\%\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, convert each percent to a decimal.<\/p>\n\n\n\n\n
35. \"\text{6\%}\"<\/td>\n36. \"\text{23\%}\"<\/td>\n<\/tr>\n
37. \"\text{128\%}\"<\/td>\n38. 4.9%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, convert each percent to a) a simplified fraction and b) a decimal.<\/p>\n\n\n\n\n
39. In \"2016,\text{17\%}\" of the Canadian population was age \"65\" or over. (Source: www12.statcan.gc.ca)<\/td>\n40. In \"2016,\text{16.6\%}\" of the Canadian population was under \"15\" years old. (Source: www12.statcan.gc.ca)<\/td>\n<\/tr>\n
41. When a die is tossed, the probability it will land with an even number of dots on the top side is \"\text{50\%}\".<\/td>\n42. A couple plans to have three children. The probability they will all be girls is \"\text{12.5\%}\".<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, convert each decimal to a percent.<\/p>\n\n\n\n\n\n
43. \"0.04\"<\/td>\n44. \"0.15\"<\/td>\n<\/tr>\n
45. \"2.82\"<\/td>\n46. \"3\"<\/td>\n<\/tr>\n
47. \"0.003\"<\/td>\n48. \"1.395\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, convert each fraction to a percent.<\/p>\n\n\n\n\n\n
49. \"\frac{3}{4}\"<\/td>\n50. \"\frac{11}{5}\"<\/td>\n<\/tr>\n
51. \"3\frac{5}{8}\"<\/td>\n52. \"\frac{2}{9}\"<\/td>\n<\/tr>\n
53. According to the Centers for Disease Control, \"\frac{2}{5}\" of adults do not take a vitamin or supplement.<\/td>\n54. According to the Centers for Disease Control, among adults who do take a vitamin or supplement, \"\frac{3}{4}\" take a multivitamin.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, translate and solve.<\/p>\n\n\n\n\n\n\n
55. What number is \"\text{46\%}\" of \"350?\"<\/td>\n56. \"\text{120\%}\" of \"55\" is what number?<\/td>\n<\/tr>\n
57. \"84\" is \"\text{35\%}\" of what number?<\/td>\n58. \"15\" is \"\text{8\%}\" of what number?<\/td>\n<\/tr>\n
59. \"\text{200\%}\" of what number is \"50?\"<\/td>\n60. \"\text{7.9\%}\" of what number is \"\text{\$4.74}?\"<\/td>\n<\/tr>\n
61. What percent of \"120\" is \"81.6?\"<\/td>\n62. What percent of \"340\" is \"595?\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
\n

Solve General Applications of Percents<\/h2>\n

In the following exercises, solve.<\/p>\n\n\n\n\n
63. When Aurelio and his family ate dinner at a restaurant, the bill was \"\text{\$83.50}\". Aurelio wants to leave \"\text{20\%}\" of the total bill as a tip. How much should the tip be?<\/td>\n64. One granola bar has \"2\" grams of fiber, which is \"\text{8\%}\" of the recommended daily amount. What is the total recommended daily amount of fiber?<\/td>\n<\/tr>\n
65. The nutrition label on a package of granola bars says that each granola bar has \"190\" calories, and \"54\" calories are from fat. What percent of the total calories is from fat?<\/td>\n66. Elsa gets paid \"\text{\$4,600}\" per month. Her car payment is \"\text{\$253}\". What percent of her monthly pay goes to her car payment?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n\n\n\n
67. Marta got a gift of\u00a0 \"\text{\$1900}\" from her uncle.\u00a0 She spent \"\text{35\%}\" of that money for her trip to Victoria. How much money she has left?.<\/td>\n68. Last year Bernard bought a new car for \"\text{\$30,000}\". If the value of the car depreciated\u00a0 \"\text{20\%}\" every year , find the value of the car this year.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
\n

Solve Proportions and their Applications<\/h2>\n<\/div>\n
\n

In the following exercises, write each sentence as a proportion.<\/p>\n\n\n\n\n
69. \"3\" is to \"8\" as \"12\" is to \"32\".<\/td>\n70. \"95\" miles to \"3\" gallons is the same as \"475\" miles to \"15\" gallons.<\/td>\n<\/tr>\n
71. \"1\" teacher to \"18\" students is the same as \"23\" teachers to \"414\" students.<\/td>\n72. \"\text{\$7.35}\" for \"15\" ounces is the same as \"\text{\$2.94}\" for \"6\" ounces.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

In the following exercises, determine whether each equation is a proportion.<\/p>\n\n\n\n\n
73. \"\frac{5}{13}=\frac{30}{78}\"<\/td>\n74. \"\frac{16}{7}=\frac{48}{23}\"<\/td>\n<\/tr>\n
75. \"\frac{12}{18}=\frac{6.99}{10.99}\"<\/td>\n76. \"\frac{11.6}{9.2}=\frac{37.12}{29.44}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, solve each proportion.<\/p>\n\n\n\n\n
77. \"\frac{x}{36}=\frac{5}{9}\"<\/td>\n78. \"\frac{7}{a}=\frac{-6}{84}\"<\/td>\n<\/tr>\n
79. \"\frac{1.2}{1.8}=\frac{d}{6}\"<\/td>\n80. \"\frac{\frac{1}{2}}{2}=\frac{m}{20}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, solve the proportion problem.<\/p>\n\n\n\n\n\n
81. The children\u2019s dosage of acetaminophen is \"5\" millilitre s (ml) for every \"25\" pounds of a child\u2019s weight. How many millilitre s of acetaminophen will be prescribed for a \"60\" pound child?<\/td>\n82. After a workout, Dennis takes his pulse for \"10\" sec and counts \"21\" beats. How many beats per minute is this?<\/td>\n<\/tr>\n
83. An \"8\" ounce serving of ice cream has \"272\" calories. If Lavonne eats \"10\" ounces of ice cream, how many calories does she get?<\/td>\n84. Alma is going to Europe and wants to exchange \"\text{\$1,200}\" into Euros. If each dollar is \"0.65\" Euros, how many Euros will Alma get?<\/td>\n<\/tr>\n
85. Zack wants to drive from Abbotsford to Banff, a distance of \"494\" miles. If his car gets \"38\" miles to the gallon, how many gallons of gas will Zack need to get to Banff?<\/td>\n86. Teresa is planning a party for \"100\" people. Each gallon of punch will serve \"18\" people. How many gallons of punch will she need?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, translate to a proportion.<\/p>\n\n\n\n\n
87. What number is \"\text{62\%}\" of \"395?\"<\/td>\n88. \"42\" is \"\text{70\%}\" of what number?<\/td>\n<\/tr>\n
89. What percent of \"1,000\" is \"15?\"<\/td>\n90. What percent of \"140\" is \"210?\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, translate and solve using proportions.<\/p>\n\n\n\n\n
91. What number is \"\text{85\%}\" of \"900?\"<\/td>\n92. \"\text{6\%}\" of what number is \"\text{\$24}?\"<\/td>\n<\/tr>\n
93. \"\text{\$3.51}\" is \"\text{4.5\%}\" of what number?<\/td>\n94. What percent of \"3,100\" is \"930?\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, convert each percent to a) a decimal b) a simplified fraction.<\/p>\n\n\n\n\n
95. \"\text{24\%}\"<\/td>\n96. \"\text{5\%}\"<\/td>\n<\/tr>\n
97. \"\text{350\%}\"<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n

In the following exercises, convert each fraction to a percent. (Round to \"3\" decimal places if needed.)<\/p>\n\n\n\n\n
98. \"\frac{7}{8}\"<\/td>\n99. \"\frac{1}{3}\"<\/td>\n<\/tr>\n
100. \"\frac{11}{12}\"<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

In the following exercises, solve the percent problem.<\/p>\n\n\n\n\n\n
101. \"65\" is what percent of \"260?\"<\/td>\n102. What number is \"\text{27\%}\" of \"3,000?\"<\/td>\n<\/tr>\n
103. \"\text{150\%}\" of what number is \"60?\"<\/td>\n104. Write as a proportion: \"4\" gallons to \"144\" miles is the same as \"10\" gallons to \"360\" miles.<\/td>\n<\/tr>\n
105. Vin read \"10\" pages of a book in \"12\" minutes. At that rate, how long will it take him to read \"35\" pages?<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n

Review Answers<\/h1>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
1. \"\frac{7}{4}\"<\/td>\n3. \"\frac{2}{3}\"<\/td>\n5. \"\frac{4}{9}\"<\/td>\n<\/tr>\n
7. \"\frac{7}{9}\"<\/td>\n9. \"\frac{90\phantom{\rule{0.2em}{0ex}}\text{pounds}}{7.5\phantom{\rule{0.2em}{0ex}}\text{square inches}}\"<\/td>\n11. \"\frac{\text{\$612.50}}{35\phantom{\rule{0.2em}{0ex}}\text{hours}}\"<\/td>\n<\/tr>\n
13. 12 pounds\/sq.in.<\/td>\n15. $17.50\/hour<\/td>\n17. $0.42<\/td>\n<\/tr>\n
19. $1.65<\/td>\n21. $0.11, $0.12; 60 tablets for $6.49<\/td>\n23. \"\frac{a\phantom{\rule{0.2em}{0ex}}\text{adults}}{45\phantom{\rule{0.2em}{0ex}}\text{children}}\"<\/td>\n<\/tr>\n
25. \"\frac{19}{3+n}\"<\/td>\n27. \"\frac{32}{100}\"<\/td>\n29. \"\frac{13}{100},\text{13\%}\"<\/td>\n<\/tr>\n
31. \"\frac{12}{25}\"<\/td>\n33. \"\frac{641}{1000}\"<\/td>\n35. 0.06<\/td>\n<\/tr>\n
37. 1.28<\/td>\n39.<\/p>\n

a) \"\phantom{\rule{0.2em}{0ex}}\frac{17}{100}\"<\/p>\n

b) \"\phantom{\rule{0.2em}{0ex}}0.17\"<\/td>\n

41.<\/p>\n

a) \"\phantom{\rule{0.2em}{0ex}}\frac{1}{2}\"<\/p>\n

b) \"\phantom{\rule{0.2em}{0ex}}0.5\"<\/td>\n<\/tr>\n

43. 4%<\/td>\n45. 282%<\/td>\n47. 0.3%<\/td>\n<\/tr>\n
49. 75%<\/td>\n51. 362.5%<\/td>\n53. 40%<\/td>\n<\/tr>\n
55. 161<\/td>\n57. 240<\/td>\n59. 25<\/td>\n<\/tr>\n
61. 68%<\/td>\n63. $16.70<\/td>\n65. 28.4%<\/td>\n<\/tr>\n
67. 1235<\/td>\n69. \"\frac{3}{8}=\frac{12}{32}\"<\/td>\n71. \"\frac{1}{18}=\frac{23}{414}\"<\/td>\n<\/tr>\n
73. yes<\/td>\n75. no<\/td>\n77. 20<\/td>\n<\/tr>\n
79. 4<\/td>\n81. 12<\/td>\n83. 340<\/td>\n<\/tr>\n
87. \"\frac{x}{395}=\frac{62}{100}\"<\/td>\n89. \"\frac{x}{100}=\frac{15}{1000}\"<\/td>\n91.765<\/td>\n<\/tr>\n
93. $78<\/td>\n95.\"0.24,\frac{6}{25}\"<\/td>\n97. \"3.5,3\frac{1}{2}\"<\/td>\n<\/tr>\n
99. 33.333%<\/td>\n101.25%<\/td>\n103. 40<\/td>\n<\/tr>\n
105. 42<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Chapter Test<\/h1>\n\n\n\n\n\n\n\n\n\n\n
1. Write a ratio as a fraction. Simplify the answer if possible. \"42\" to \"28\"<\/td>\n\n

2. Write a rate as a fraction. Simplify the answer if possible.\u00a0\"80\" pounds per \"6.5\" square inches<\/p>\n<\/td>\n<\/tr>\n

3. Find the unit rate.\u00a0\"\text{\$868.80}\" for \"24\" hours<\/td>\n4. Marta bought a pack of \"6\" paint brushes for \"\text{\$32.20}\". How much did each brush cost? Round to the nearest cent if necessary<\/td>\n<\/tr>\n
5. Find each unit price and then the better buy.
\nLaundry detergent: \"64\" ounces for \"\text{\$10.99}\" or \"48\" ounces for \"\text{\$8.49}\"<\/td>\n		6. Convert a percent to a fraction: \"\text{245\%}\"<\/td>\n<\/tr>\n
7. Convert a decimal to a percent: \"0.07\"<\/td>\n8. Convert a fraction to a percent. (Round to \"3\" decimal places if needed.)\u00a0\"\frac{11}{8}\"<\/td>\n<\/tr>\n
9. \u00a0What number is \"\text{36\%}\" of \"450?\"<\/td>\n10. \"\text{8\%}\" of what number is \"\text{\$34}?\"<\/td>\n<\/tr>\n
11. \"57.6\" is what percent of \"360?\"<\/td>\n12. One granola bar has \"3\" grams of fiber, which is \"\text{12\%}\" of the recommended daily amount. What is the total recommended daily amount of fiber?<\/td>\n<\/tr>\n
13. Klaudia is going to Poland and wants to exchange \"\text{\$1,400}\" into Polish zlotych. If each dollar is \"2.91\" zlotych, how many zlotych will Klaudia get?<\/td>\n14. Solve a proportion:\"\frac{24}{x}=\frac{3}{7}\"<\/td>\n<\/tr>\n
15. Solve a proportion:\"\frac{x}{6}=\frac{9}{24}\"<\/td>\n16.Solve a proportion:\"\frac{2.4}{1.6}=\frac{t}{6.2}\"<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n

Test Answers<\/h1>\n
\n\n\n\n\n\n\n\n\n
1. \"\frac{3}{2}\"<\/td>\n2. \"\frac{160}{13}\"<\/td>\n3. $36.20<\/td>\n<\/tr>\n
4. $5.37<\/td>\n5. 64 ounces for $10.99 is the better buy<\/td>\n6. \"\frac{49}{20}\"<\/td>\n<\/tr>\n
7. 7%<\/td>\n8. 137.5%<\/td>\n9. 162<\/td>\n<\/tr>\n
10. 425<\/td>\n11. 16%<\/td>\n12. 25 grams<\/td>\n<\/tr>\n
13. 4074 zlotych<\/td>\n14. 56<\/td>\n15. 2.25<\/td>\n<\/tr>\n
16. 9.3<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n","protected":false},"author":90,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-764","chapter","type-chapter","status-publish","hentry"],"part":627,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/764\/revisions"}],"predecessor-version":[{"id":765,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/764\/revisions\/765"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/627"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/764\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=764"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=764"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=764"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}