3.5 Chapter Review

Pooja Gupta

3.5 Chapter Review

Review Exercises

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

1. $56$ to $32$	2. $28$ to $40$
3. $1.2$ to $1.8$	4. $3.5$ to $0.5$
5. $2\frac{1}{3}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}5\frac{1}{4}$	6. $1\frac{3}{4}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}1\frac{5}{8}$
7. $28$ inches to $3$ feet	8. $64$ ounces to $30$ ounces

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

9. $90$ pounds per $7.5$ square inches	10. $180$ calories per $8$ ounces
11. $\text{\$612.50}$ for $35$ hours	12. $126$ miles in $4$ hours

Find Unit Rates

In the following exercises, find the unit rate.

13. $90$ pounds per $7.5$ square inches	14. $180$ calories per $8$ ounces
15. $\text{\$612.50}$ for $35$ hours	16. $126$ miles in $4$ hours

Find Unit Price

In the following exercises, find the unit price.

17.Highlighters: $6$ for $\text{\$2.52}$	18. T-shirts: $3$ for $\text{\$8.97}$
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.	20. An office supply store sells a box of pens for $\text{\$11}$ . The box contains $12$ pens. How much does each pen cost?

In the following exercises, find each unit price and then determine the better buy.

21.Vitamins: $60$ tablets for $\text{\$6.49}$ or $100$ for $\text{\$11.99}?$

22. Shampoo: $12$ ounces for $\text{\$4.29}$ or $22$ ounces for $\text{\$7.29}?$

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

23. $a$ adults to $45$ children	24. $535$ miles per $h\phantom{\rule{0.2em}{0ex}}\text{hours}$
25. the ratio of $19$ and the sum of $3$ and $n$	26. the ratio of $4y$ and the difference of $x$ and $10$

In the following exercises, write each percent as a ratio.

27. $\text{32\%}$ admission rate for the university

28. $\text{53.3\%}$ rate of college students with student loans

In the following exercises, write as a ratio and then as a percent.

29. $13$ out of $100$ architects are women.

30. $9$ out of every $100$ nurses are men.

In the following exercises, convert each percent to a fraction.

31. $\text{48\%}$	32. $\text{175\%}$
33. $\text{64.1\%}$	34. $8\frac{1}{4}\%$

In the following exercises, convert each percent to a decimal.

35. $\text{6\%}$	36. $\text{23\%}$
37. $\text{128\%}$	38. 4.9%

In the following exercises, convert each percent to a) a simplified fraction and b) a decimal.

39. In $2016,\text{17\%}$ of the Canadian population was age $65$ or over. (Source: www12.statcan.gc.ca)	40. In $2016,\text{16.6\%}$ of the Canadian population was under $15$ years old. (Source: www12.statcan.gc.ca)
41. When a die is tossed, the probability it will land with an even number of dots on the top side is $\text{50\%}$ .	42. A couple plans to have three children. The probability they will all be girls is $\text{12.5\%}$ .

In the following exercises, convert each decimal to a percent.

43. $0.04$	44. $0.15$
45. $2.82$	46. $3$
47. $0.003$	48. $1.395$

In the following exercises, convert each fraction to a percent.

49. $\frac{3}{4}$	50. $\frac{11}{5}$
51. $3\frac{5}{8}$	52. $\frac{2}{9}$
53. According to the Centers for Disease Control, $\frac{2}{5}$ of adults do not take a vitamin or supplement.	54. According to the Centers for Disease Control, among adults who do take a vitamin or supplement, $\frac{3}{4}$ take a multivitamin.

In the following exercises, translate and solve.

55. What number is $\text{46\%}$ of $350?$	56. $\text{120\%}$ of $55$ is what number?
57. $84$ is $\text{35\%}$ of what number?	58. $15$ is $\text{8\%}$ of what number?
59. $\text{200\%}$ of what number is $50?$	60. $\text{7.9\%}$ of what number is $\text{\$4.74}?$
61. What percent of $120$ is $81.6?$	62. What percent of $340$ is $595?$

Solve General Applications of Percents

In the following exercises, solve.

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?	64. 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?
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?	66. 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?

67. Marta got a gift of $\text{\$1900}$ from her uncle. She spent $\text{35\%}$ of that money for her trip to Victoria. How much money she has left?.

68. Last year Bernard bought a new car for $\text{\$30,000}$ . If the value of the car depreciated $\text{20\%}$ every year , find the value of the car this year.

Solve Proportions and their Applications

In the following exercises, write each sentence as a proportion.

69. $3$ is to $8$ as $12$ is to $32$ .	70. $95$ miles to $3$ gallons is the same as $475$ miles to $15$ gallons.
71. $1$ teacher to $18$ students is the same as $23$ teachers to $414$ students.	72. $\text{\$7.35}$ for $15$ ounces is the same as $\text{\$2.94}$ for $6$ ounces.

In the following exercises, determine whether each equation is a proportion.

73. $\frac{5}{13}=\frac{30}{78}$	74. $\frac{16}{7}=\frac{48}{23}$
75. $\frac{12}{18}=\frac{6.99}{10.99}$	76. $\frac{11.6}{9.2}=\frac{37.12}{29.44}$

In the following exercises, solve each proportion.

77. $\frac{x}{36}=\frac{5}{9}$	78. $\frac{7}{a}=\frac{-6}{84}$
79. $\frac{1.2}{1.8}=\frac{d}{6}$	80. $\frac{\frac{1}{2}}{2}=\frac{m}{20}$

In the following exercises, solve the proportion problem.

81. The children’s dosage of acetaminophen is $5$ millilitre s (ml) for every $25$ pounds of a child’s weight. How many millilitre s of acetaminophen will be prescribed for a $60$ pound child?	82. After a workout, Dennis takes his pulse for $10$ sec and counts $21$ beats. How many beats per minute is this?
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?	84. 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?
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?	86. Teresa is planning a party for $100$ people. Each gallon of punch will serve $18$ people. How many gallons of punch will she need?

In the following exercises, translate to a proportion.

87. What number is $\text{62\%}$ of $395?$	88. $42$ is $\text{70\%}$ of what number?
89. What percent of $1,000$ is $15?$	90. What percent of $140$ is $210?$

In the following exercises, translate and solve using proportions.

91. What number is $\text{85\%}$ of $900?$	92. $\text{6\%}$ of what number is $\text{\$24}?$
93. $\text{\$3.51}$ is $\text{4.5\%}$ of what number?	94. What percent of $3,100$ is $930?$

In the following exercises, convert each percent to a) a decimal b) a simplified fraction.

95. $\text{24\%}$	96. $\text{5\%}$
97. $\text{350\%}$

In the following exercises, convert each fraction to a percent. (Round to $3$ decimal places if needed.)

98. $\frac{7}{8}$	99. $\frac{1}{3}$
100. $\frac{11}{12}$

In the following exercises, solve the percent problem.

101. $65$ is what percent of $260?$	102. What number is $\text{27\%}$ of $3,000?$
103. $\text{150\%}$ of what number is $60?$	104. Write as a proportion: $4$ gallons to $144$ miles is the same as $10$ gallons to $360$ miles.
105. Vin read $10$ pages of a book in $12$ minutes. At that rate, how long will it take him to read $35$ pages?

Review Answers

1. $\frac{7}{4}$	3. $\frac{2}{3}$	5. $\frac{4}{9}$
7. $\frac{7}{9}$	9. $\frac{90\phantom{\rule{0.2em}{0ex}}\text{pounds}}{7.5\phantom{\rule{0.2em}{0ex}}\text{square inches}}$	11. $\frac{\text{\$612.50}}{35\phantom{\rule{0.2em}{0ex}}\text{hours}}$
13. 12 pounds/sq.in.	15. $17.50/hour	17. $0.42
19. $1.65	21. $0.11, $0.12; 60 tablets for $6.49	23. $\frac{a\phantom{\rule{0.2em}{0ex}}\text{adults}}{45\phantom{\rule{0.2em}{0ex}}\text{children}}$
25. $\frac{19}{3+n}$	27. $\frac{32}{100}$	29. $\frac{13}{100},\text{13\%}$
31. $\frac{12}{25}$	33. $\frac{641}{1000}$	35. 0.06
37. 1.28	39. a) $\phantom{\rule{0.2em}{0ex}}\frac{17}{100}$ b) $\phantom{\rule{0.2em}{0ex}}0.17$	41. a) $\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ b) $\phantom{\rule{0.2em}{0ex}}0.5$
43. 4%	45. 282%	47. 0.3%
49. 75%	51. 362.5%	53. 40%
55. 161	57. 240	59. 25
61. 68%	63. $16.70	65. 28.4%
67. 1235	69. $\frac{3}{8}=\frac{12}{32}$	71. $\frac{1}{18}=\frac{23}{414}$
73. yes	75. no	77. 20
79. 4	81. 12	83. 340
87. $\frac{x}{395}=\frac{62}{100}$	89. $\frac{x}{100}=\frac{15}{1000}$	91.765
93. $78	95. $0.24,\frac{6}{25}$	97. $3.5,3\frac{1}{2}$
99. 33.333%	101.25%	103. 40
105. 42

Chapter Test

1. Write a ratio as a fraction. Simplify the answer if possible. $42$ to $28$	2. Write a rate as a fraction. Simplify the answer if possible. $80$ pounds per $6.5$ square inches
3. Find the unit rate. $\text{\$868.80}$ for $24$ hours	4. 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
5. Find each unit price and then the better buy. Laundry detergent: $64$ ounces for $\text{\$10.99}$ or $48$ ounces for $\text{\$8.49}$	6. Convert a percent to a fraction: $\text{245\%}$
7. Convert a decimal to a percent: $0.07$	8. Convert a fraction to a percent. (Round to $3$ decimal places if needed.) $\frac{11}{8}$
9. What number is $\text{36\%}$ of $450?$	10. $\text{8\%}$ of what number is $\text{\$34}?$
11. $57.6$ is what percent of $360?$	12. 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?
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?	14. Solve a proportion: $\frac{24}{x}=\frac{3}{7}$
15. Solve a proportion: $\frac{x}{6}=\frac{9}{24}$	16.Solve a proportion: $\frac{2.4}{1.6}=\frac{t}{6.2}$

Test Answers

1. $\frac{3}{2}$	2. $\frac{160}{13}$	3. $36.20
4. $5.37	5. 64 ounces for $10.99 is the better buy	6. $\frac{49}{20}$
7. 7%	8. 137.5%	9. 162
10. 425	11. 16%	12. 25 grams
13. 4074 zlotych	14. 56	15. 2.25
16. 9.3

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