Writing and Identifying Characteristics of Decimals

Name Decimals

In the following exercises, name each decimal.

1. [latex]5.5[/latex]
2. [latex]5.01[/latex]
3. [latex]8.71[/latex]
4. [latex]0.002[/latex]
5. [latex]0.381[/latex]
6. [latex]-17.9[/latex]

Write Decimals

In the following exercises, translate the name into a decimal number.

7. Eight and three hundredths
8. Twenty-nine and eighty-one hundredths
9. Seven tenths
10. One thousandth
11. Twenty-nine thousandths
12. Negative eleven and nine ten-thousandths
13. Thirteen and three hundred ninety-five ten thousandths

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

14. [latex]1.99[/latex]
15. [latex]15.7[/latex]
16. [latex]0.239[/latex]
17. [latex]0.13[/latex]
18. [latex]0.011[/latex]
19. [latex]-0.00003[/latex]
20. [latex]5.2[/latex]
21. [latex]9.04[/latex]
22. [latex]2.008[/latex]
23. [latex]12.75[/latex]
24. [latex]2.482[/latex]
25. [latex]20.375[/latex]

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

26. [latex]0.8[/latex]
27. [latex]-0.2[/latex]
28. [latex]3.1[/latex]
29. [latex]-2.5[/latex]

Order Decimals

In the following exercises, order each of the following pairs of numbers, using [latex]<[/latex] or [latex]>[/latex].

30. [latex]0.9[/latex]__[latex]0.6[/latex]
31. [latex]0.37[/latex]__[latex]0.63[/latex]
32. [latex]0.6[/latex]__[latex]0.59[/latex]
33. [latex]0.91[/latex]__[latex]0.901[/latex]
34. [latex]−0.5[/latex]__[latex]−0.3[/latex]
35. [latex]−0.62[/latex]__[latex]−0.619[/latex]

Round Decimals

In the following exercises, round each number to the nearest tenth.

36. [latex]0.67[/latex]
37. [latex]2.84[/latex]

In the following exercises, round each number to the nearest hundredth.

38. [latex]0.845[/latex]
39. [latex]5.7932[/latex]
40. [latex]0.697[/latex]
41. [latex]7.096[/latex]

In the following exercises, round each number to the nearest hundreth, tenth, and whole number.

42. [latex]5.781[/latex]
43. [latex]63.479[/latex]

Operations on Decimals

Add and Subtract Decimals

In the following exercises, add or subtract.

44. [latex]16.92 + 7.56[/latex]
45. [latex]256.37 − 85.49[/latex]
46. [latex]21.76− 30.99[/latex]
47. [latex]37.5 + 12.23[/latex]
48. [latex]−16.53 - 24.38[/latex]
49. [latex]−38.69 + 31.47[/latex]
50. [latex]−4.2 + (-9.3)[/latex]
51. [latex]100−64.2[/latex]
52. [latex]72.5−100[/latex]
53. [latex]15 + 0.73[/latex]
54. [latex]2.51 + 40[/latex]
55. [latex]91.75−(−10.462)[/latex]
56. [latex]55.01  3.7[/latex]
57. [latex]2.51 − 7.4[/latex]

Multiply Decimals

In the following exercises, multiply.

58. [latex](0.3)(0.4)[/latex]
59. [latex](0.24)(0.6)[/latex]
60. [latex](5.9)(7.12)[/latex]
61. [latex](8.52)(3.14)[/latex]
62. [latex](-4.3)(2.71)[/latex]
63. [latex](-5.18)(-65.23)[/latex]
64. [latex](0.09)(24.78)[/latex]
65. [latex](0.06)(21.75)[/latex]
66. [latex](9.24)(10)[/latex]
67. [latex](55.2)(1,000)[/latex]

Divide Decimals

In the following exercises, divide.

68. [latex]0.15÷5[/latex]
69. [latex]4.75÷25[/latex]
70. [latex]$8.49÷12[/latex]
71. [latex]$117.25÷48[/latex]
72. [latex]0.6÷0.2[/latex]
73. [latex]1.44÷(−0.3)[/latex]
74. [latex]−1.75÷(−0.05)[/latex]
75. [latex]5.2÷2.5[/latex]
76. [latex]12÷0.08[/latex]
77. [latex]11÷0.55[/latex]

Mixed Practice

In the following exercises, simplify.

78. [latex]6(12.4−9.2)[/latex]
79. [latex]24(0.5)+(0.3)2[/latex]
80. [latex]1.15(26.83+1.61)[/latex]
81. [latex]$45+0.08($45)[/latex]
82. [latex]18÷(0.75+0.15)[/latex]
83. [latex](1.43+0.27)÷(0.9−0.05)[/latex]
84. [latex][$75.42+0.18($75.42)]÷5[/latex]

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

85. Brenda got [latex]$40[/latex] from the ATM. She spent [latex]$15.11[/latex] on a pair of earrings. How much money did she have left?
86. Adam bought a t-shirt for [latex]$18.49[/latex] and a book for [latex]$8.92[/latex] The sales tax was [latex]$1.65[/latex]. How much did Adam spend?
87. Emily bought a box of cereal that cost [latex]$4.29[/latex]. She had a coupon for [latex]$0.55 [/latex] off, and the store doubled the coupon. How much did she pay for the box of cereal?
88. Leo took part in a diet program. He weighed [latex]190[/latex] pounds at the start of the program. During the first week, he lost [latex]4.3[/latex] pounds. During the second week, he had lost [latex]2.8[/latex] pounds. The third week, he gained [latex]0.7[/latex] pounds. The fourth week, he lost [latex]1.9[/latex] pounds. What did Leo weigh at the end of the fourth week?
89. Noriko bought [latex]4[/latex] coffees for herself and her co-workers. Each coffee was [latex]$3.75[/latex]. How much did she pay for all the coffees?
90. Mayra earns [latex]$9.25[/latex] per hour. Last week she worked [latex]32[/latex] hours. How much did she earn?
91. Alan got his first paycheck from his new job. He worked [latex]30[/latex] hours and earned [latex]$382.50[/latex]. How much does he earn per hour?
92. Jeannette and her friends love to order mud pie at their favorite restaurant. They always share just one piece of pie among themselves. With tax and tip, the total cost is [latex]$6.00[/latex]. How much does each girl pay if the total number sharing the mud pie is
    • [latex]2[/latex]?
    • [latex]3[/latex]?
    • [latex]4[/latex]?
    • [latex]5[/latex]?
    • [latex]6[/latex]?
93. At their favorite fast food restaurant, the Carlson family orders [latex]4[/latex] burgers that cost [latex]$3.29[/latex] each and [latex]2[/latex] orders of fries at [latex]$2.74[/latex] each. What is the total cost of the order?
94. The Lewis and Chousmith families are planning to go to the zoo together. Adult tickets cost [latex]$29.95[/latex] and children’s tickets cost [latex]$19.95[/latex]. What will the total cost be for [latex]4[/latex] adults and [latex]7[/latex] children

Convert Fractions to Decimals

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

95. [latex]\frac{2}{5}[/latex]
96. [latex]\frac{−3}{8}[/latex]
97. [latex]\frac{17}{20}[/latex]
98. [latex]\frac{11}{4}[/latex]
99. [latex]\frac{−310}{25}[/latex]
100. [latex]\frac{5}{9}[/latex]
101. [latex]\frac{15}{11}[/latex]
102. [latex]\frac{15}{111}[/latex]

Convert Fractions to Decimals and Simplify

In the following exercises, simplify the expression.

103. [latex]12+6.5[/latex]
104. [latex]2.4+58[/latex]
105. [latex]9.73+1720[/latex]

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using <; or >.

106. [latex]\frac{1}{8}[/latex]___[latex]0.8[/latex]
107. [latex]\frac{2}{5}[/latex]___[latex]0.25[/latex]
108. [latex]0.725[/latex]___[latex]\frac{3}{4}[/latex]
109. [latex]0.66[/latex]___[latex]\frac{2}{3}[/latex]
110. [latex]-0.75[/latex]___[latex]\frac{−4}{5}[/latex]
111. [latex]\frac{−3}{4}[/latex]___[latex]−0.925[/latex]

In the following exercises, write each set of numbers in order from least to greatest.

112. [latex]\frac{3}{5}, \frac{9}{16}, 0.55[/latex]
113. [latex]0.702, \frac{13}{20}, \frac{5}{8}[/latex]
114. [latex]−0.3, \frac{−1}{3}, \frac{−7}{20}[/latex]
115. [latex]\frac{−3}{4}, \frac{−7}{9}, −0.7[/latex]

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

116. [latex]10(25.1−43.8)[/latex]
117. [latex]62(9.75−4.99)[/latex]
118. [latex]\frac{3}{4}(12.4−4.2)[/latex]
119. [latex]\frac{5}{12}(30.58+17.9)[/latex]
120. [latex]10÷0.1+(1.8)4−(0.3)[/latex]
121. [latex](37.1+52.7)÷(12.5÷62.5)[/latex]
122. [latex](\frac{1}{5})2+(1.4)(6.5)[/latex]
123. [latex]\frac{−9}{10}⋅\frac{8}{15}+0.25[/latex]

Mixed Practice

In the following exercises, simplify. Give the answer as a decimal.

124. [latex]3 \frac{1}{4}−6.5[/latex]
125. [latex]10.86÷2/3[/latex]
126. [latex]\frac{7}{8}(103.48)+1 \frac{1}{2}(361)[/latex]
127. [latex]3.6(\frac{9}{8}−2.72)[/latex]

Find the Circumference and Area of Circles

In the following exercises, approximate the circumference and area of each circle. If measurements are given in fractions, leave answers in fraction form.

128. radius [latex]= 5[/latex] in.
129. radius [latex]= 9[/latex] ft.
130. radius [latex]= 46[/latex] cm
131. radius [latex]= 18.6[/latex] m
132. radius [latex]= \frac{7}{10}[/latex] mile
133. radius [latex]= \frac{3}{8}[/latex] yard
134. diameter [latex]= \frac{5}{6}[/latex] m

Solving Equations with Decimals

Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether each number is a solution of the given equation.

135. [latex]x−0.8 = 2.3[/latex]
     1. [latex]x = 2[/latex]
     2. [latex]x = -1.5[/latex]
     3. [latex]x = 3.1[/latex]
136. [latex]1.5h = −4.3[/latex]
     1. [latex]h = 6.45[/latex]
     2. [latex]h = -6.45[/latex]
     3. [latex]h = -2.1[/latex]

Solve Equations with Decimals

In the following exercises, solve the equation.

137. [latex]y+2.9 = 5.7[/latex]
138. [latex]f+3.45 = 2.6[/latex]
139. [latex]a+6.2 = −1.7[/latex]
140. [latex]c+1.15 = −3.5[/latex]
141. [latex]n−2.6 = 1.8[/latex]
142. [latex]x−0.4 = −3.9[/latex]
143. [latex]j−1.82 = −6.5[/latex]
144. [latex]m−0.25 = −1.67[/latex]
145. [latex]0.5x = 3.5[/latex]
146. [latex]−1.7c = 8.5[/latex]
147. [latex]−1.4p = −4.2[/latex]
148. [latex]−120 = 1.5q[/latex]
149. [latex]0.24x = 4.8[/latex]
150. [latex]−3.4z = −9.18[/latex]
151. [latex]\frac{a}{0.4} = −20[/latex]
152. [latex]\frac{x}{0.7} = −0.4[/latex]
153. [latex]\frac{p}{−5} = −1.65[/latex]
154. [latex]\frac{r}{−1.2} = −6[/latex]

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

155. [latex]x−5[/latex] = [latex]−11[/latex]
156. [latex]p+8[/latex] = [latex]−2[/latex]
157. [latex]−4.2m[/latex] = [latex]−33.6[/latex]
158. [latex]q + \frac{5}{6} = \frac{1}{12}[/latex]

Translate to an Equation and Solve

In the following exercises, translate and solve.

159. The difference of [latex]n[/latex] and [latex]1.9[/latex] is [latex]3.4[/latex]
160. The product of [latex]−6.2[/latex] and [latex]x[/latex] is [latex]−4.96[/latex]
161. The quotient of [latex]y[/latex] and [latex]−1.7[/latex] is [latex]−5[/latex].
162. The sum of nand [latex]−7.3[/latex] is [latex]2.4[/latex].

Chapter Review Exercises

Decimals

Name Decimals

In the following exercises, name each decimal.

163. [latex]0.8[/latex]
164. [latex]0.007[/latex]
165. [latex]−12.5632[/latex]

Write Decimals

In the following exercises, write as a decimal.

166. three tenths
167. twenty-seven hundredths
168. negative twenty and three tenths

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

169. [latex]0.43[/latex]
170. [latex]9.7[/latex]

Locate Decimals on the Number Line

171. [latex]0.6[/latex]
172. [latex]2.2[/latex]

Order Decimals

In the following exercises, order each of the following pairs of numbers, using [latex]<[/latex] or [latex]>[/latex].

173. [latex]0.6[/latex]___[latex]0.8[/latex]
174. [latex]0.803[/latex]____[latex]0.83[/latex]

Round Decimals

In the following exercises, round each number to the nearest: ⓐ hundredth ⓑ tenth ⓒ whole number.

175. [latex]12.529[/latex]
176. [latex]5.897[/latex]

Decimal Operations

Add and Subtract Decimals

In the following exercises, add or subtract.

177. [latex]5.75+8.46[/latex]
178. [latex]24−19.31[/latex]
179. [latex]−6.4+(−2.9)[/latex]

Multiply Decimals

In the following exercises, multiply.

180. [latex](0.3)[/latex][latex](0.7)[/latex]
181. [latex](−3.35)[/latex][latex](−12.7)[/latex]

Divide Decimals

In the following exercises, divide.

182. [latex]0.48÷6[/latex]
183. [latex]$6.29÷12[/latex]
184. [latex]1.65÷0.15[/latex]

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

185. Miranda got [latex]$40[/latex] from her ATM. She spent [latex]$9.32[/latex] on lunch and [latex]$16.99[/latex] on a book. How much money did she have left? Round to the nearest cent if necessary.
186. A pack of [latex]16[/latex] water bottles cost [latex]$6.72[/latex]. How much did each bottle cost?

Decimals and Fractions

Convert Fractions to Decimals

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

187. [latex]\frac{3}{5}[/latex]
188. [latex]\frac{−19}{20}[/latex]
189. [latex]\frac{1}{3}[/latex]

In the following exercises, order each pair of numbers, using [latex]<[/latex] or [latex]>[/latex].

190. [latex]\frac{1}{2}[/latex]___[latex]0.2[/latex]
191. [latex]\frac{−7}{8}[/latex]___[latex]−0.84[/latex]
192. [latex]0.625[/latex]___[latex]\frac{13}{20}[/latex]
193. [latex]\frac{2}{3}, \frac{17}{20}, 0.65[/latex]

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

194. [latex]4(10.3−5.8)[/latex]
195. [latex]1.6+\frac{3}{8}[/latex]
196. [latex]\frac{−2}{5}⋅\frac{9}{10}+0.14[/latex]

Find the Circumference and Area of Circles in the following exercises, approximate the circumference and area of each circle.

197. radius = [latex]6[/latex] in.
198. radius = [latex]\frac{7}{33}[/latex] m

Problem Set: Percents

Writing Percents Using Words, Ratios, and Fractions

Use the Definition of Percents

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

199. In 2014, the unemployment rate for those with only a high school degree was [latex]6.0\%[/latex].
200. The unemployment rate for those with Bachelor’s degrees was [latex]3.2\%[/latex] in 2014.

Show Solution

Show Solution

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

201. [latex]57[/latex] out of [latex]100[/latex] nursing candidates received their degree at a community college.
202. [latex]42[/latex] out of [latex]100[/latex] first-time freshmen students attend a community college.

Convert Percents to Fractions and Decimals

In the following exercises, convert each percent to a fraction and simplify all fractions.

203. [latex]4\%[/latex]
204. [latex]17\%[/latex]
205. [latex]52\%[/latex]
206. [latex]125\%[/latex]
207. [latex]37.5\%[/latex]
208. [latex]18.4\%[/latex]

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

209. [latex]5\%[/latex]
210. [latex]1\%[/latex]
211. [latex]63\%[/latex]
212. [latex]40\%[/latex]
213. [latex]115\%[/latex]
214. [latex]150\%[/latex]
215. [latex]21.4\%[/latex]
216. [latex]7.8\%[/latex]

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

217. In 2010, [latex]1.5\%[/latex] of home sales had owner financing. (Source:Bloomberg Businessweek, 5/23–29/2011)
218. According to government data, in 2013 the number of cell phones in India was [latex]70.23\%[/latex] of the population.
219. A couple plans to have two children. The probability they will have two girls is [latex]25\%[/latex].
220. According to the local weather report, the probability of thunderstorms in New York City on July [latex]15[/latex] is [latex]60\%[/latex].

Convert Decimals and Fractions to Percents

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

221. [latex]0.01[/latex]
222. [latex]0.18[/latex]
223. [latex]1.35[/latex]
224. [latex]33[/latex]
225. [latex]0.009[/latex]
226. [latex]0.0875[/latex]
227. [latex]1.5[/latex]
228. [latex]2.254[/latex]

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

229. [latex]\frac{1}{4}[/latex]
230. [latex]\frac{3}{8}[/latex]
231. [latex]\frac{7}{4}[/latex]
232. [latex]6 \frac{4}{5}[/latex]
233. [latex]\frac{5}{12}[/latex]
234. [latex]2 \frac{2}{3}[/latex]
235. [latex]\frac{3}{7}[/latex]
236. [latex]\frac{5}{9}[/latex]

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

237. [latex]14[/latex] of washing machines needed repair.
238. According to the National Center for Health Statistics, in 2012, [latex]720[/latex] of American adults were obese.

Solving General Applications of Percent

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

239. What number is [latex]45\%[/latex] of [latex]120[/latex]?
240. What number is [latex]24\%[/latex] of [latex]112[/latex]?
241. [latex]250\%[/latex] of [latex]65[/latex] is what number?
242. [latex]800\%[/latex] of [latex]2,250[/latex] is what number?
243. [latex]28[/latex] is [latex]25\%[/latex] of what number?
244. [latex]81[/latex] is [latex]75\%[/latex] of what number?
245. [latex]8.2\%[/latex] of what number is [latex]$2.87[/latex]?
246. [latex]11.5\%[/latex] of what number is [latex]$108.10[/latex]?
247. What percent of [latex]260[/latex] is [latex]78[/latex]?
248. What percent of [latex]1,500[/latex] is [latex]540[/latex]?
249. [latex]30[/latex] is what percent of [latex]20[/latex]?
250. [latex]840[/latex] is what percent of [latex]480[/latex]?

Solve Applications of Percents

In the following exercises, solve the applications of percents.

251. Geneva treated her parents to dinner at their favorite restaurant. The bill was [latex]$74.25[/latex]. She wants to leave [latex]16\%[/latex] of the total bill as a tip. How much should the tip be?
252. Trong has [latex]12\%[/latex] of each paycheck automatically deposited to his savings account. His last paycheck was [latex]$2,165[/latex]. How much money was deposited to Trong’s savings account?
253. One serving of oatmeal has [latex]8[/latex] grams of fiber, which is [latex]33\%[/latex] of the recommended daily amount. What is the total recommended daily amount of fiber?
254. A bacon cheeseburger at a popular fast-food restaurant contains [latex]2,070[/latex] milligrams (mg) of sodium, which is [latex]86\%[/latex] of the recommended daily amount. What is the total recommended daily amount of sodium?
255. The nutrition fact sheet at a fast food restaurant says the fish sandwich has [latex]380[/latex] calories, and [latex]171[/latex] calories are from fat. What percent of the total calories is from fat?
256. Emma gets paid [latex]$3,000[/latex] per month. She pays [latex]$750[/latex] a month for rent. What percent of her monthly pay goes to rent?

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

257. Tamanika got a raise in her hourly pay, from [latex]$15.50[/latex] to [latex]$17.55[/latex]. Find the percent increase.
258. Annual student fees at the University of California rose from about [latex]$4,000[/latex] in [latex]2000[/latex] to about [latex]$9,000[/latex] in [latex]2014[/latex]. Find the percent increase.
259. According to Time magazine (7/19/2011) annual global seafood consumption rose from [latex]22[/latex] pounds per person in [latex]1960[/latex] to [latex]38[/latex] pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)
260. A grocery store reduced the price of a loaf of bread from [latex]$2.80[/latex] to [latex]$2.73[/latex]. Find the percent decrease.
261. Hernando’s salary was [latex]$49,500[/latex] last year. This year his salary was cut to [latex]$44,055[/latex]. Find the percent decrease.
262. In one month, the median home price in the West fell from [latex]$203,400[/latex] to [latex]$192,300[/latex]. Find the percent decrease. (Round to the nearest tenth of a percent.)

Solving Sales Tax, Commission, and Discount Applications

In the following exercises, find ⓐ the sales tax and ⓑ the total cost.

263. The cost of a pair of boots was [latex]$84[/latex]. The sales tax rate is [latex]5\%[/latex] of the purchase price.
264. The cost of a microwave oven was [latex]$129[/latex]. The sales tax rate is [latex]7.5\%[/latex] of the purchase price.
265. The cost of a file cabinet is [latex]$250[/latex]. The sales tax rate is [latex]6.85\%[/latex] of the purchase price.
266. The cost of a [latex]6[/latex]-drawer dresser [latex]$1,199[/latex]. The sales tax rate is [latex]5.125\%[/latex] of the purchase price.

In the following exercises, find the sales tax rate.

267. Shawna bought a mixer for [latex]$300[/latex]. The sales tax on the purchase was [latex]$19.50[/latex].
268. Bopha bought a bedroom set for [latex]$3,600[/latex]. The sales tax on the purchase was [latex]$246.60[/latex].

Solve Commission Applications

In the following exercises, find the commission.

269. Christopher sold his dinette set for [latex]$225[/latex] through an online site, which charged him [latex]9\%[/latex] of the selling price as commission. How much was the commission?
270. Farrah works in a jewelry store and receives [latex]12\%[/latex] commission when she makes a sale. How much commission will she receive for selling an [latex]$8,125[/latex]?
271. Hector receives [latex]17.5\%[/latex] commission when he sells an insurance policy. How much commission will he receive for selling a policy for [latex]$4,910[/latex]?

Show Solution

In the following exercises, find the rate of commission.

272. Dontay is a realtor and earned [latex]$11,250[/latex] commission on the sale of a [latex]$375,000[/latex] house. What is his rate of commission?
273. As a waitress, Emily earned [latex]$420[/latex] in tips on sales of [latex]$2,625[/latex] last Saturday night. What was her rate of commission?
274. Maureen earned [latex]$7,052.50[/latex] commission when she sold a [latex]$45,500[/latex] car. What was the rate of commission?

Solve Discount Applications

In the following exercises, find the sale price.

275. Perla bought a cellphone that was on sale for [latex]$50[/latex] off. The original price of the cellphone was [latex]$189[/latex].
276. Rick wants to buy a tool set with original price [latex]$165[/latex]. Next week the tool set will be on sale for [latex]40\%[/latex] off.

In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.

277. Janelle bought a beach chair on sale at [latex]60\%[/latex] off. The original price was [latex]$44.95[/latex].
278. Kathy wants to buy a camera that lists for [latex]$389[/latex]. The camera is on sale with a [latex]33\%[/latex] discount.
279. Erys bought a treadmill on sale at [latex]35\%[/latex] off. The original price was [latex]$949.95[/latex].

In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

280. Larry and Donna bought a sofa at the sale price of [latex]$1,344[/latex]. The original price of the sofa was [latex]$1,920[/latex].
281. Patty bought a baby stroller on sale for [latex]$301.75[/latex]. The original price of the stroller was [latex]$355[/latex].
282. Nikki bought a patio set on sale for [latex]$480[/latex]. The original price was [latex]$850[/latex].

Solve Mark-up Applications

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

283. Daria bought a bracelet at wholesale cost [latex]$16[/latex] to sell in her handicraft store. She marked the price up [latex]45\%[/latex].
284. Tom paid [latex]$0.60[/latex] a pound for tomatoes to sell at his produce store. He added a [latex]33\%[/latex] mark-up.
285. Alan bought a used bicycle for [latex]$115[/latex]. After re-conditioning it, he added [latex]225\%[/latex] mark-up and then advertised it for sale.

In the following exercises, solve the problem using the simple interest formula.

286. Find the simple interest earned after [latex]5[/latex] years on [latex]$600[/latex] at an interest rate of [latex]3\%[/latex].
287. Find the simple interest earned after [latex]2[/latex] years on [latex]$8,950[/latex] at an interest rate of [latex]3.24\%[/latex].
288. Find the simple interest earned after [latex]8[/latex] years on [latex]$15,500[/latex] at an interest rate of [latex]11.425\%[/latex].
289. Find the principal invested if [latex]$656[/latex] interest was earned in 5years at an interest rate of [latex]4\%[/latex].
290. Find the principal invested if [latex]$70.95[/latex] interest was earned in [latex]3[/latex] years at an interest rate of [latex]2.75\%[/latex].
291. Find the principal invested if [latex]$15,222.57[/latex] interest was earned in [latex]6[/latex] years at an interest rate of [latex]10.28\%[/latex].
292. Find the rate if a principal of [latex]$5,400[/latex] earned [latex]$432[/latex] interest in [latex]2[/latex] years.
293. Find the rate if a principal of [latex]$11,000[/latex] earned [latex]$1,815[/latex] interest in [latex]3[/latex] years.

Solve Simple Interest Applications

In the following exercises, solve the problem using the simple interest formula.

294. Casey deposited [latex]$1,450[/latex] in a bank account with interest rate [latex]4\%[/latex]. How much interest was earned in [latex]2[/latex] years?
295. Robin deposited [latex]$31,000[/latex] in a bank account with interest rate [latex]5.2\%[/latex]. How much interest was earned in [latex]3[/latex] years?
296. Hilaria borrowed [latex]$8,000[/latex] from her grandfather to pay for college. Five years later, she paid him back the [latex]$8,000[/latex], plus [latex]$1,200[/latex] interest. What was the rate of interest?
297. Lebron lent his daughter [latex]$20,000[/latex] to help her buy a condominium. When she sold the condominium four years later, she paid him the [latex]$20,000[/latex], plus [latex]$3,000[/latex] interest. What was the rate of interest?
298. In [latex]10[/latex] years, a bank account that paid [latex]5.25\%[/latex] earned [latex]$18,375[/latex] interest. What was the principal of the account?
299. Joshua’s computer loan statement said he would pay [latex]$1,244.34[/latex] in interest for a [latex]3[/latex] year loan at [latex]12.4\%[/latex]. How much did Joshua borrow to buy the computer?
300. Caitlin invested [latex]$8,200[/latex] in an [latex]18[/latex]-month certificate of deposit paying [latex]2.7\%[/latex] interest. How much interest did she earn form this investment?
301. Airin borrowed [latex]$3,900[/latex] from her parents for the down payment on a car and promised to pay them back in [latex]15[/latex] months at a [latex]4\%[/latex] rate of interest. How much interest did she owe her parents?

Solving Proportions and their Applications

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

302. [latex]4[/latex] is to [latex]15[/latex] as [latex]36[/latex] is to [latex]135[/latex].
303. [latex]12[/latex] is to [latex]5[/latex] as [latex]96[/latex] is to [latex]40[/latex].
304. [latex]5[/latex] wins in [latex]7[/latex] games is the same as [latex]115[/latex] wins in [latex]161[/latex] games.
305. [latex]8[/latex] campers to [latex]1[/latex] counselor is the same as [latex]48[/latex] campers to [latex]6[/latex] counselors.
306. [latex]$9.36[/latex] for [latex]18[/latex] ounces is the same as [latex]$2.60[/latex] for [latex]5[/latex] ounces.
307. [latex]$18.04[/latex] for [latex]11[/latex] pounds is the same as [latex]$4.92[/latex] for [latex]3[/latex] pounds.

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

308. [latex]\frac{7}{15} = \frac{56}{120}[/latex]
309. [latex]\frac{11}{6} = \frac{21}{16}[/latex]
310. [latex]\frac{12}{18} = \frac{4.99}{7.56}[/latex]
311. [latex]\frac{13.5}{8.5} = \frac{31.05}{19.55}[/latex]

Solve Proportions

In the following exercises, solve each proportion.

312. [latex]\frac{x}{56} = \frac{7}{8}[/latex]
313. [latex]\frac{49}{63} = \frac{z}{9}[/latex]
314. [latex]\frac{5}{a} = \frac{65}{117}[/latex]
315. [latex]\frac{98}{154} = \frac{-7}{p}[/latex]
316. [latex]\frac{a}{-8} = \frac{-42}{48}[/latex]
317. [latex]\frac{2.6}{3.9} = \frac{c}{3}[/latex]
318. [latex]\frac{2.7}{j} = \frac{0.9}{0.2}[/latex]
319. [latex]\frac{\frac{1}{2}}{1} = \frac{m}{8}[/latex]

Solve Applications Using Proportions

In the following exercises, solve the proportion problem.

320. Pediatricians prescribe [latex]5[/latex] milliliters (ml) of acetaminophen for every [latex]25[/latex] pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs [latex]45[/latex] pounds?
321. At the gym, Carol takes her pulse for [latex]10[/latex] sec and counts [latex]19[/latex] beats. How many beats per minute is this? Has Carol met her target heart rate of [latex]140[/latex] beats per minute?
322. A new energy drink advertises [latex]106[/latex] calories for [latex]8[/latex] ounces. How many calories are in [latex]12[/latex] ounces of the drink?
323. Karen eats [latex]12[/latex] cup of oatmeal that counts for [latex]2[/latex] points on her weight loss program. Her husband, Joe, can have [latex]3[/latex] points of oatmeal for breakfast. How much oatmeal can he have?
324. Janice is traveling to Canada and will change [latex]$250[/latex] US dollars into Canadian dollars. At the current exchange rate, [latex]$1[/latex] US is equal to [latex]$1.01[/latex] Canadian. How many Canadian dollars will she get for her trip?
325. Steve changed [latex]$600[/latex] into [latex]480[/latex] Euros. How many Euros did he receive per US dollar?
326. At the laundromat, Lucy changed [latex]$12.00[/latex] into quarters. How many quarters did she get?
327. Jesse’s car gets [latex]30[/latex] miles per gallon of gas. If Las Vegas is [latex]285[/latex] miles away, how many gallons of gas are needed to get there and then home? If gas is [latex]$3.09[/latex] per gallon, what is the total cost of the gas for the trip?
328. Hugh leaves early one morning to drive from his home in Chicago to go to Mount Rushmore, [latex]812[/latex] miles away. After [latex]3[/latex] hours, he has gone [latex]190[/latex] miles. At that rate, how long will the whole drive take?
329. Phil wants to fertilize his lawn. Each bag of fertilizer covers about [latex]4,000[/latex] square feet of lawn. Phil’s lawn is approximately [latex]13,500[/latex] square feet. How many bags of fertilizer will he have to buy?

Write Percent Equations as Proportions

In the following exercises, translate to a proportion.

330. What number is [latex]35\%[/latex] of [latex]250[/latex]?
331. What number is [latex]110\%[/latex] of [latex]47[/latex]?
332. [latex]45[/latex] is [latex]30\%[/latex] of what number?
333. [latex]90[/latex] is [latex]150\%[/latex] of what number?
334. What percent of [latex]85[/latex] is [latex]17[/latex]?
335. What percent of [latex]260[/latex] is [latex]340[/latex]?

Translate and Solve Percent Proportions

In the following exercises, translate and solve using proportions.

336. What number is [latex]65\%[/latex] of [latex]180[/latex]?
337. [latex]18\%[/latex] of [latex]92[/latex] is what number?
338. [latex]175\%[/latex] of [latex]26[/latex] is what number?
339. What is [latex]300\%[/latex] of [latex]488[/latex]?
340. [latex]17\%[/latex] of what number is [latex]$7.65[/latex]?
341. [latex]$13.53[/latex] is [latex]8.25\%[/latex] of what number?
342. What percent of [latex]56[/latex] is [latex]14[/latex]?
343. What percent of [latex]96[/latex] is [latex]12[/latex]?

Problem Set: The Language of Algebra

Using the Language of Algebra

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

344. [latex]16−9[/latex]
345. [latex]5⋅6[/latex]
346. [latex]28÷4[/latex]
347. [latex]x+8[/latex]
348. [latex](2)(7)[/latex]
349. [latex]14<21[/latex]
350. [latex]36≥19[/latex]
351. [latex]3n=243[/latex]
352. [latex]y−1>6[/latex]
353. [latex]2≤18÷6[/latex]
354. [latex]a≠7⋅4[/latex]

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

355. [latex]9⋅6=54[/latex]
356. [latex]5⋅4+3[/latex]
357. [latex]x+7[/latex]
358. [latex]y−5=25[/latex]

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

359. [latex]3⋅3⋅3⋅3⋅3⋅3⋅3[/latex]
360. [latex]x⋅x⋅x⋅x⋅x[/latex]

Simplify Expressions with Exponents

In the following exercises, write in expanded form.

361. [latex]5^{3}[/latex]
362. [latex]2^{8}[/latex]

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

363. [latex]3+8⋅5[/latex]
364. [latex]2+6⋅32+6⋅3[/latex]
365. [latex]2^{3} - 12÷(9-5)[/latex]
366. [latex]3⋅8+5⋅2[/latex]
367. [latex]2+8(6+1)[/latex]
368. [latex]4⋅\frac{12}{8}[/latex]
369. [latex]6+\frac{10}{2}+2[/latex]
370. [latex](6+10)÷(2+2)[/latex]
371. [latex]20÷4+6⋅5[/latex]
372. [latex]20÷(4+6)⋅5[/latex]
373. [latex]4^{2}+5{2}[/latex]
374. [latex](4+5)^{2}[/latex]
375. [latex]3(1+9⋅6)-4^{2}[/latex]
376. [latex]2[1+3(10-2)][/latex]
377. [latex]5[2+4(3−2)][/latex]

Evaluating, Simplifying, and Translating Algebraic Expressions

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

378. [latex]7x+8[/latex] when [latex]x=2[/latex]
379. [latex]5x-4[/latex] when [latex]x=6[/latex]
380. [latex]2x[/latex] when [latex]x=12[/latex]
381. [latex]5x[/latex] when [latex]x=2[/latex]
382. [latex]3x[/latex] when [latex]x=3[/latex]
383. [latex]2x+3x−7[/latex] when [latex]x=4[/latex]
384. [latex]2x+4y−5[/latex] when [latex]x=7[/latex], [latex]y=8[/latex]
385. [latex](x+y)^{2}[/latex] when [latex]x=6, y=9[/latex]
386. [latex]r^{2}-s^{2}[/latex] when [latex]r=12, s=5[/latex]
387. [latex]2l+2w[/latex] when [latex]l=15, w=12[/latex]

Identify Terms, Coefficients, and Like Terms

In the following exercises, list the terms in the given expression.

388. [latex]15x^{2}+6x+2[/latex]
389. [latex]10y^{3}+y+2[/latex]

In the following exercises, identify the coefficient of the given term.

390. [latex]8a[/latex]
391. [latex]5r^{2}[/latex]
392. [latex]x^{3}, 8x, 14, 8y, 5, 8x^{3}[/latex]
393. [latex]9a, a^{2}, 16ab, 16b^{2}, 4ab, 9b^{2}[/latex]

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

394. [latex]10x+3x[/latex]
395. [latex]17a+9a[/latex]
396. [latex]4c+2c+c[/latex]
397. [latex]9x+3x+8[/latex]
398. [latex]7u+2+3u+1[/latex]
399. [latex]7p+6+5p+4[/latex]
400. [latex]10a+7+5a−2+7a−4[/latex]
401. [latex]3x^{2}+12x+11+14x^{2}+8x+5[/latex]

Translate English Phrases into Algebraic Expressions

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

402. The sum of [latex]8[/latex] and [latex]12[/latex]
403. The difference of [latex]14[/latex] and [latex]9[/latex]
404. The product of [latex]9[/latex] and [latex]7[/latex]
405. The quotient of [latex]36[/latex] and [latex]9[/latex]
406. The difference of [latex]x[/latex] and [latex]4[/latex]
407. The product of [latex]6[/latex] and [latex]y[/latex]

Show Solution

408. The sum of [latex]8x[/latex] and [latex]3x[/latex]
409. The quotient of [latex]y[/latex] and [latex]3[/latex]
410. Eight times the difference of [latex]y[/latex] and nine
411. Five times the sum of [latex]x[/latex] and [latex]y[/latex]

Translate English Phrases into Algebraic Expressions

In the following exercises, write an algebraic expression.

412. Adele bought a skirt and a blouse. The skirt cost [latex]$15[/latex] more than the blouse. Let [latex]b[/latex] represent the cost of the blouse. Write an expression for the cost of the skirt.
413. The number of girls in a second-grade class is [latex]4[/latex] less than the number of boys. Let [latex]b[/latex] represent the number of boys. Write an expression for the number of girls.
414. Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.