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Study Guides > Prealgebra

Problem Set 5: Decimals

Practice Makes Perfect

Name Decimals In the following exercises, name each decimal. 5.55.5 five and five tenths 7.87.8 5.015.01 five and one hundredth 14.0214.02 8.718.71 eight and seventy-one hundredths 2.642.64 0.0020.002 two thousandths 0.0050.005 0.3810.381 three hundred eighty-one thousandths 0.4790.479 −17.9-17.9 negative seventeen and nine tenths −31.4-31.4 Write Decimals In the following exercises, translate the name into a decimal number. Eight and three hundredths 8.03 Nine and seven hundredths Twenty-nine and eighty-one hundredths 29.81 Sixty-one and seventy-four hundredths Seven tenths 0.7 Six tenths One thousandth 0.001 Nine thousandths Twenty-nine thousandths 0.029 Thirty-five thousandths Negative eleven and nine ten-thousandths −11.0009 Negative fifty-nine and two ten-thousandths Thirteen and three hundred ninety-five ten thousandths 13.0395 Thirty and two hundred seventy-nine thousandths Convert Decimals to Fractions or Mixed Numbers In the following exercises, convert each decimal to a fraction or mixed number. 1.991.99 1991001\frac{99}{100} 5.835.83 15.715.7 1571015\frac{7}{10} 18.118.1 0.2390.239 2391000\frac{239}{1000} 0.3730.373 0.130.13 13100\frac{13}{100} 0.190.19 0.0110.011 111000\frac{11}{1000} 0.0490.049 −0.00007-0.00007 −7100000-\frac{7}{100000} −0.00003-0.00003 6.46.4 6256\frac{2}{5} 5.25.2 7.057.05 71207\frac{1}{20} 9.049.04 4.0064.006 435004\frac{3}{500} 2.0082.008 10.2510.25 101410\frac{1}{4} 12.7512.75 1.3241.324 1812501\frac{81}{250} 2.4822.482 14.12514.125 141814\frac{1}{8} 20.37520.375 Locate Decimals on the Number Line In the following exercises, locate each number on a number line. 0.80.8 There is a number line shown with integers from negative 4 to 4. There is a red dot between 0 and 1 labeled 0.8. 0.30.3 −0.2-0.2 There is a number line shown with integers from negative 4 to 4. There is a red dot between negative 1 and 0 labeled negative 0.2. −0.9-0.9 3.13.1 This is an image of a number line. It spans from negative 5 on the left to 5 on the right. To the right of 0 are tick marks with the numbers 1, 2, 3, 4, 5 on the number line. To the left of the zero are tick marks with the numbers negative 1, negative 2, negative 3, negative 4, and negative 5. A point is plotted at 3.1. 2.72.7 −2.5-2.5 There is a number line shown with integers from negative 4 to 4. There is a red dot between negative 3 and negative 2 labeled negative 2.5. −1.6-1.6 Order Decimals In the following exercises, order each of the following pairs of numbers, using <or><\text{or}>;. 0.9__0.6 > 0.7__0.8 0.37__0.63 < 0.86__0.69 0.6__0.59 > 0.27__0.3 0.91__0.901 > 0.415__0.41 -0.5__ - 0.3 < −0.1−0.4-0.1_ - 0.4 −0.62−0.619-0.62_ - 0.619 < −7.31−7.3-7.31_ - 7.3 Round Decimals In the following exercises, round each number to the nearest tenth. 0.670.67 0.7 0.490.49 2.842.84 2.8 4.634.63 In the following exercises, round each number to the nearest hundredth. 0.8450.845 0.85 0.7610.761 5.79325.7932 5.79 3.62843.6284 0.2990.299 0.30 0.6970.697 4.0984.098 4.10 7.0967.096 In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number. 5.7815.781 ⓐ 5.78 ⓑ 5.8 ⓒ 6 1.6381.638 63.47963.479 ⓐ 63.48 ⓑ 63.5 ⓒ 63 84.28184.281

Everyday Math

Salary Increase Danny got a raise and now makes \text{$58,965.95} a year. Round this number to the nearest: ⓐ dollar ⓑ thousand dollars ⓒ ten thousand dollars. ⓐ $58,966 ⓑ $59,000 ⓒ $60,000 New Car Purchase Selena’s new car cost \text{$23,795.95}. Round this number to the nearest: ⓐ dollar ⓑ thousand dollars ⓒ ten thousand dollars. Sales Tax Hyo Jin lives in San Diego. She bought a refrigerator for \text{$1624.99} and when the clerk calculated the sales tax it came out to exactly \text{$142.186625}. Round the sales tax to the nearest ⓐ penny ⓑ dollar. ⓐ $142.19 ⓑ $142 Sales Tax Jennifer bought a \text{$1,038.99} dining room set for her home in Cincinnati. She calculated the sales tax to be exactly \text{$67.53435}. Round the sales tax to the nearest ⓐ penny ⓑ dollar.

Writing Exercises

How does your knowledge of money help you learn about decimals? Answers will vary. Explain how you write "three and nine hundredths" as a decimal. Jim ran a 100−meter100-meter race in 12.32 seconds\text{12.32 seconds}. Tim ran the same race in 12.3 seconds\text{12.3 seconds}. Who had the faster time, Jim or Tim? How do you know? Tim had the faster time. 12.3 is less than 12.32, so Tim had the faster time. Gerry saw a sign advertising postcards marked for sale at "10for0.99\textcent.""10\text{for}0.99\text{\textcent ."} What is wrong with the advertised price?

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ If most of your checks were: …confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific. …with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved? …no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.    

Practice Makes Perfect

Add and Subtract Decimals In the following exercises, add or subtract. 16.92+7.5616.92+7.56 24.48 18.37+9.3618.37+9.36 256.37−85.49256.37 - 85.49 170.88 248.25−91.29248.25 - 91.29 21.76−30.9921.76 - 30.99 −9.23 15.35−20.8815.35 - 20.88 37.5+12.2337.5+12.23 49.73 38.6+13.6738.6+13.67 −16.53−24.38-16.53 - 24.38 −40.91 −19.47−32.58-19.47 - 32.58 −38.69+31.47-38.69+31.47 −7.22 −29.83+19.76-29.83+19.76 −4.2+(−9.3)-4.2+\left(-9.3\right) −13.5 −8.6+(−8.6)-8.6+\left(-8.6\right) 100−64.2100 - 64.2 35.8 100−65.83100 - 65.83 72.5−10072.5 - 100 −27.5 86.2−10086.2 - 100 15+0.7315+0.73 15.73 27+0.8727+0.87 2.51+402.51+40 42.51 9.38+609.38+60 91.75−(−10.462)91.75-\left(-10.462\right) 102.212 94.69−(−12.678)94.69-\left(-12.678\right) 55.01−3.755.01 - 3.7 51.31 59.08−4.659.08 - 4.6 2.51−7.42.51 - 7.4 −4.89 3.84−6.13.84 - 6.1 Multiply Decimals In the following exercises, multiply. (0.3)(0.4)\left(0.3\right)\left(0.4\right) 0.12 (0.6)(0.7)\left(0.6\right)\left(0.7\right) (0.24)(0.6)\left(0.24\right)\left(0.6\right) 0.144 (0.81)(0.3)\left(0.81\right)\left(0.3\right) (5.9)(7.12)\left(5.9\right)\left(7.12\right) 42.008 (2.3)(9.41)\left(2.3\right)\left(9.41\right) (8.52)(3.14)\left(8.52\right)\left(3.14\right) 26.7528 (5.32)(4.86)\left(5.32\right)\left(4.86\right) (-4.3)(2.71)\text{(-4.3)(2.71)} −11.653 (−8.5)(1.69)\left(-8.5\right)\left(1.69\right) (-5.18)(-65.23)\text{(-5.18)(-65.23)} 337.8914 (−9.16)(−68.34)\left(-9.16\right)\left(-68.34\right) (0.09)(24.78)\left(0.09\right)\left(24.78\right) 2.2302 (0.04)(36.89)\left(0.04\right)\left(36.89\right) (0.06)(21.75)\left(0.06\right)\left(21.75\right) 1.305 (0.08)(52.45)\left(0.08\right)\left(52.45\right) (9.24)(10)\left(9.24\right)\left(10\right) 92.4 (6.531)(10)\left(6.531\right)\left(10\right) (55.2)(1,000)\left(55.2\right)\left(1,000\right) 55,200 (99.4)(1,000)\left(99.4\right)\left(1,000\right) Divide Decimals In the following exercises, divide. 0.15÷50.15\div 5 0.03 0.27÷30.27\div 3 4.75÷254.75\div 25 0.19 12.04÷4312.04\div 43 \text{$8.49}\div 12 $0.71 \text{$16.99}\div 9 \text{$117.25}\div 48 $2.44 \text{$109.24}\div 36 0.6÷0.20.6\div 0.2 3 0.8÷0.40.8\div 0.4 1.44÷(−0.3)1.44\div \left(-0.3\right) −4.8 1.25÷(−0.5)1.25\div \left(-0.5\right) −1.75÷(−0.05)-1.75\div \left(-0.05\right) 35 −1.15÷(−0.05)-1.15\div \left(-0.05\right) 5.2÷2.55.2\div 2.5 2.08 6.5÷3.256.5\div 3.25 12÷0.0812\div 0.08 150 5÷0.045\div 0.04 11÷0.5511\div 0.55 20 14÷0.3514\div 0.35 Mixed Practice In the following exercises, simplify. 6(12.4−9.2)6\left(12.4 - 9.2\right) 19.2 3(15.7−8.6)3\left(15.7 - 8.6\right) 24(0.5)+(0.3)224\left(0.5\right)+{\left(0.3\right)}^{2} 12.09 35(0.2)+(0.9)235\left(0.2\right)+{\left(0.9\right)}^{2} 1.15(26.83+1.61)1.15\left(26.83+1.61\right) 32.706 1.18(46.22+3.71)1.18\left(46.22+3.71\right) \text{$45}+0.08\left(\text{$45}\right) $48.60 \text{$63}+0.18\left(\text{$63}\right) 18÷(0.75+0.15)18\div \left(0.75+0.15\right) 20 27÷(0.55+0.35)27\div \left(0.55+0.35\right) (1.43+0.27)÷(0.9−0.05)\left(1.43+0.27\right)\div \left(0.9 - 0.05\right) 2 (1.5−0.06)÷(0.12+0.24)\left(1.5 - 0.06\right)\div \left(0.12+0.24\right) \left[\text{$75.42}+0.18\left(\text{$75.42}\right)\right]\div 5 $17.80 \left[\text{$56.31}+0.22\left(\text{$56.31}\right)\right]\div 4 Use Decimals in Money Applications In the following exercises, use the strategy for applications to solve. Spending money Brenda got \text{$40} from the ATM. She spent \text{$15.11} on a pair of earrings. How much money did she have left? $24.89 Spending money Marissa found \text{$20} in her pocket. She spent \text{$4.82} on a smoothie. How much of the \text{$20} did she have left? Shopping Adam bought a t-shirt for \text{$18.49} and a book for \text{$8.92} The sales tax was \text{$1.65}. How much did Adam spend? $29.06 Restaurant Roberto’s restaurant bill was \text{$20.45} for the entrée and \text{$3.15} for the drink. He left a \text{$4.40} tip. How much did Roberto spend? Coupon Emily bought a box of cereal that cost \text{$4.29}. She had a coupon for \text{$0.55} off, and the store doubled the coupon. How much did she pay for the box of cereal? $3.19 Coupon Diana bought a can of coffee that cost \text{$7.99}. She had a coupon for \text{$0.75} off, and the store doubled the coupon. How much did she pay for the can of coffee? Diet Leo took part in a diet program. He weighed 190190 pounds at the start of the program. During the first week, he lost 4.34.3 pounds. During the second week, he had lost 2.82.8 pounds. The third week, he gained 0.70.7 pounds. The fourth week, he lost 1.91.9 pounds. What did Leo weigh at the end of the fourth week? 181.7 pounds Snowpack On April 11, the snowpack at the ski resort was 44 meters deep, but the next few days were very warm. By April 55, the snow depth was 1.61.6 meters less. On April 88, it snowed and added 2.12.1 meters of snow. What was the total depth of the snow? Coffee Noriko bought 44 coffees for herself and her co-workers. Each coffee was \text{$3.75}. How much did she pay for all the coffees? $15.00 Subway Fare Arianna spends \text{$4.50} per day on subway fare. Last week she rode the subway 66 days. How much did she spend for the subway fares? Income Mayra earns \text{$9.25} per hour. Last week she worked 3232 hours. How much did she earn? $296.00 Income Peter earns \text{$8.75} per hour. Last week he worked 1919 hours. How much did he earn? Hourly Wage Alan got his first paycheck from his new job. He worked 3030 hours and earned \text{$382.50}. How much does he earn per hour? $12.75 Hourly Wage Maria got her first paycheck from her new job. She worked 2525 hours and earned \text{$362.50}. How much does she earn per hour? Restaurant 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 \text{$6.00}. How much does each girl pay if the total number sharing the mud pie is ⓐ 2?2? ⓑ 3?3? ⓒ 4?4? ⓓ 5?5? ⓔ 6?6? ⓐ $3 ⓑ $2 ⓒ $1.50 ⓓ $1.20 ⓔ $1 Pizza Alex and his friends go out for pizza and video games once a week. They share the cost of a \text{$15.60} pizza equally. How much does each person pay if the total number sharing the pizza is ⓐ 2?2? ⓑ 3?3? ⓒ 4?4? ⓓ 5?5? ⓔ 6?6? Fast Food At their favorite fast food restaurant, the Carlson family orders 44 burgers that cost \text{$3.29} each and 22 orders of fries at \text{$2.74} each. What is the total cost of the order? $18.64 Home Goods Chelsea needs towels to take with her to college. She buys 22 bath towels that cost \text{$9.99} each and 66 washcloths that cost \text{$2.99} each. What is the total cost for the bath towels and washcloths? Zoo The Lewis and Chousmith families are planning to go to the zoo together. Adult tickets cost \text{$29.95} and children’s tickets cost \text{$19.95}. What will the total cost be for 44 adults and 77 children? $259.45 Ice Skating Jasmine wants to have her birthday party at the local ice skating rink. It will cost \text{$8.25} per child and \text{$12.95} per adult. What will the total cost be for 1212 children and 33 adults?

Everyday Math

Paycheck Annie has two jobs. She gets paid \text{$14.04} per hour for tutoring at City College and \text{$8.75} per hour at a coffee shop. Last week she tutored for 88 hours and worked at the coffee shop for 1515 hours. ⓐ How much did she earn? ⓑ If she had worked all 2323 hours as a tutor instead of working both jobs, how much more would she have earned? ⓐ $243.57 ⓑ $79.35 Paycheck Jake has two jobs. He gets paid \text{$7.95} per hour at the college cafeteria and \text{$20.25} at the art gallery. Last week he worked 1212 hours at the cafeteria and 55 hours at the art gallery. ⓐ How much did he earn? ⓑ If he had worked all 1717 hours at the art gallery instead of working both jobs, how much more would he have earned?

Writing Exercises

In the 2010 winter Olympics, two skiers took the silver and bronze medals in the Men's Super-G ski event. The silver medalist's time was 11 minute 30.6230.62 seconds and bronze medalist's time was 11 minute 30.6530.65 seconds. Whose time was faster? Find the difference in their times and then write the name of that decimal. The difference: 0.03 seconds. Three hundredths of a second. Find the quotient of 0.12÷0.040.12\div 0.04 and explain in words all the steps taken.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ After reviewing this checklist, what will you do to become confident for all objectives?

Practice Makes Perfect

Convert Fractions to Decimals In the following exercises, convert each fraction to a decimal. 25\frac{2}{5} 0.4 45\frac{4}{5} −38-\frac{3}{8} −0.375 −58-\frac{5}{8} 1720\frac{17}{20} 0.85 1320\frac{13}{20} 114\frac{11}{4} 2.75 174\frac{17}{4} −31025-\frac{310}{25} −12.4 −28425-\frac{284}{25} 59\frac{5}{9} 0.5−0.\stackrel{-}{5} 29\frac{2}{9} 1511\frac{15}{11} 1.36-1.\stackrel{\text{-}}{36} 1811\frac{18}{11} 15111\frac{15}{111} 0.135-0.\stackrel{\text{-}}{135} 25111\frac{25}{111} In the following exercises, simplify the expression. 12+6.5\frac{1}{2}+6.5 7 14+10.75\frac{1}{4}+10.75 2.4+582.4+\frac{5}{8} 3.025 3.9+9203.9+\frac{9}{20} 9.73+17209.73+\frac{17}{20} 10.58 6.29+21406.29+\frac{21}{40} Order Decimals and Fractions In the following exercises, order each pair of numbers, using <<; or >.\text{>.} \frac{1}{8}___0.8 < \frac{1}{4}___0.4 \frac{2}{5}___0.25 > \frac{3}{5}___0.35 0.725___\frac{3}{4} < 0.92___\frac{7}{8} 0.66___\frac{2}{3} < 0.83___\frac{5}{6} -0.75___-\frac{4}{5} > -0.44___-\frac{9}{20} -\frac{3}{4}___ - 0.925 > -\frac{2}{3}___ - 0.632 In the following exercises, write each set of numbers in order from least to greatest. 35,916,0.55\frac{3}{5},\frac{9}{16},0.55 0.55,916,350.55,\frac{9}{16},\frac{3}{5} 38,720,0.36\frac{3}{8},\frac{7}{20},0.36 0.702,1320,580.702,\frac{13}{20},\frac{5}{8} 58,1320,0.702\frac{5}{8},\frac{13}{20},0.702 0.15,316,150.15,\frac{3}{16},\frac{1}{5} −0.3,−13,−720-0.3,-\frac{1}{3},-\frac{7}{20} −720,−13,−0.3-\frac{7}{20},-\frac{1}{3},-0.3 −0.2,−320,−16-0.2,-\frac{3}{20},-\frac{1}{6} −34,−79,−0.7-\frac{3}{4},-\frac{7}{9},-0.7 −79,−34,−0.7-\frac{7}{9},-\frac{3}{4},-0.7 −89,−45,−0.9-\frac{8}{9},-\frac{4}{5},-0.9 Simplify Expressions Using the Order of Operations In the following exercises, simplify. 10(25.1−43.8)10\left(25.1 - 43.8\right) −187 30(18.1−32.5)30\left(18.1 - 32.5\right) 62(9.75−4.99)62\left(9.75 - 4.99\right) 295.12 42(8.45−5.97)42\left(8.45 - 5.97\right) 34(12.4−4.2)\frac{3}{4}\left(12.4 - 4.2\right) 6.15 45(8.6+3.9)\frac{4}{5}\left(8.6+3.9\right) 512(30.58+17.9)\frac{5}{12}\left(30.58+17.9\right) 20.2 916(21.96−9.8)\frac{9}{16}\left(21.96 - 9.8\right) 10÷0.1+(1.8)4−(0.3)210\div 0.1+\left(1.8\right)4-{\left(0.3\right)}^{2} 107.11 5÷0.5+(3.9)6−(0.7)25\div 0.5+\left(3.9\right)6-{\left(0.7\right)}^{2} (37.1+52.7)÷(12.5÷62.5)\left(37.1+52.7\right)\div \left(12.5\div 62.5\right) 449 (11.4+16.2)÷(18÷60)\left(11.4+16.2\right)\div \left(18\div 60\right) (15)2+(1.4)(6.5){\left(\frac{1}{5}\right)}^{2}+\left(1.4\right)\left(6.5\right) 9.14 (12)2+(2.1)(8.3){\left(\frac{1}{2}\right)}^{2}+\left(2.1\right)\left(8.3\right) −910⋅815+0.25-\frac{9}{10}\cdot \frac{8}{15}+0.25 −0.23 −38⋅1415+0.72-\frac{3}{8}\cdot \frac{14}{15}+0.72 Mixed Practice In the following exercises, simplify. Give the answer as a decimal. 314−6.53\frac{1}{4}-6.5 −3.25 525−8.755\frac{2}{5}-8.75 10.86÷2310.86\div \frac{2}{3} 16.29 5.79÷345.79\div \frac{3}{4} 78(103.48)+112(361)\frac{7}{8}\left(103.48\right)+1\frac{1}{2}\left(361\right) 632.045 516(117.6)+213(699)\frac{5}{16}\left(117.6\right)+2\frac{1}{3}\left(699\right) 3.6(98−2.72)3.6\left(\frac{9}{8}-2.72\right) −5.742 5.1(125−3.91)5.1\left(\frac{12}{5}-3.91\right) 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. radius=5 in.\text{radius}=\text{5 in.} ⓐ 31.4 in ⓑ 78.5 sq.in. radius=20 in.\text{radius}=\text{20 in.} radius=9 ft.\text{radius}=\text{9 ft.} ⓐ 56.52.ft. ⓑ 254.34 sq.ft. radius=4 ft.\text{radius}=\text{4 ft.} radius=46 cm\text{radius}=\text{46 cm} ⓐ 288.88 cm ⓑ 6644.24 sq.cm radius=38 cm\text{radius}=\text{38 cm} radius=18.6 m\text{radius}=\text{18.6 m} ⓐ 116.808 m ⓑ 1086.3144 sq.m radius=57.3 m\text{radius}=\text{57.3 m} radius=710mile\text{radius}=\frac{7}{10}\text{mile} ⓐ 225mile\frac{22}{5}\text{mile} ⓑ 7750sq.mile\frac{77}{50}\text{sq.mile} radius=711mile\text{radius}=\frac{7}{11}\text{mile} radius=38yard\text{radius}=\frac{3}{8}\text{yard} ⓐ 3314yard\frac{33}{14}\text{yard} ⓑ 99224sq.yard\frac{99}{224}\text{sq.yard} radius=512yard\text{radius}=\frac{5}{12}\text{yard} diameter=56m\text{diameter}=\frac{5}{6}\text{m} ⓐ 5521m\frac{55}{21}\text{m} ⓑ 275504sq.m\frac{275}{504}\text{sq.m} diameter=34m\text{diameter}=\frac{3}{4}\text{m}

Everyday Math

Kelly wants to buy a pair of boots that are on sale for 23\frac{2}{3} of the original price. The original price of the boots is \text{$84.99}. What is the sale price of the shoes? $56.66 An architect is planning to put a circular mosaic in the entry of a new building. The mosaic will be in the shape of a circle with radius of 66 feet. How many square feet of tile will be needed for the mosaic? (Round your answer up to the next whole number.)

Writing Exercises

Is it easier for you to convert a decimal to a fraction or a fraction to a decimal? Explain. Answers will vary. Describe a situation in your life in which you might need to find the area or circumference of a circle.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?  

Practice Makes Perfect

Calculate the Mean of a Set of Numbers In the following exercises, find the mean. 3[/latex],[latex]8[/latex],[latex]2[/latex],[latex]2[/latex],[latex]53[/latex] , [latex]8[/latex] , [latex]2[/latex] , [latex]2[/latex] , [latex]5 4 6[/latex],[latex]1[/latex],[latex]9[/latex],[latex]3[/latex],[latex]4[/latex],[latex]76[/latex] , [latex]1[/latex] , [latex]9[/latex] , [latex]3[/latex] , [latex]4[/latex] , [latex]7 65[/latex],[latex]13[/latex],[latex]48[/latex],[latex]32[/latex],[latex]19[/latex],[latex]3365[/latex] , [latex]13[/latex] , [latex]48[/latex] , [latex]32[/latex] , [latex]19[/latex] , [latex]33 35 34[/latex],[latex]45[/latex],[latex]29[/latex],[latex]61[/latex],and[latex]4134[/latex] , [latex]45[/latex] , [latex]29[/latex] , [latex]61[/latex] , and [latex]41 202[/latex],[latex]241[/latex],[latex]265[/latex],[latex]274202[/latex] , [latex]241[/latex] , [latex]265[/latex] , [latex]274 245.5 525[/latex],[latex]532[/latex],[latex]558[/latex],[latex]574525[/latex] , [latex]532[/latex] , [latex]558[/latex] , [latex]574 12.45[/latex],[latex]12.99[/latex],[latex]10.50[/latex],[latex]11.25[/latex],[latex]9.99[/latex],[latex]12.7212.45[/latex] , [latex]12.99[/latex] , [latex]10.50[/latex] , [latex]11.25[/latex] , [latex]9.99[/latex] , [latex]12.72 11.65 28.8[/latex],[latex]32.9[/latex],[latex]32.5[/latex],[latex]27.9[/latex],[latex]30.4[/latex],[latex]32.5[/latex],[latex]31.6[/latex],[latex]32.728.8[/latex] , [latex]32.9[/latex] , [latex]32.5[/latex] , [latex]27.9[/latex] , [latex]30.4[/latex] , [latex]32.5[/latex] , [latex]31.6[/latex] , [latex]32.7 Four girls leaving a mall were asked how much money they had just spent. The amounts were \text{$0} , \text{$14.95} , \text{$35.25} , and \text{$25.16} . Find the mean amount of money spent. $18.84 Juan bought 55 shirts to wear to his new job. The costs of the shirts were \text{$32.95} , \text{$38.50} , \text{$30.00} , \text{$17.45} , and \text{$24.25} . Find the mean cost. The number of minutes it took Jim to ride his bike to school for each of the past six days was 2121 , 1818 , 1616 , 1919 , 2424 , and 1919 . Find the mean number of minutes. 19.5 minutes Norris bought six books for his classes this semester. The costs of the books were \text{$74.28} , \text{$120.95} , \text{$52.40} , \text{$10.59} , \text{$35.89} , and \text{$59.24} . Find the mean cost. The top eight hitters in a softball league have batting averages of .373.373 , .360.360 , .321.321 , .321.321 , .320.320 , .312.312 , .311.311 , and .311.311 . Find the mean of the batting averages. Round your answer to the nearest thousandth. 0.329 The monthly snowfall at a ski resort over a six-month period was 60.360.3, 79.779.7, 50.950.9, 28.028.0, 47.447.4, and 46.146.1 inches. Find the mean snowfall. Find the Median of a Set of Numbers In the following exercises, find the median. 24[/latex],[latex]19[/latex],[latex]18[/latex],[latex]29[/latex],[latex]2124[/latex] , [latex]19[/latex] , [latex]18[/latex] , [latex]29[/latex] , [latex]21 21 48[/latex],[latex]51[/latex],[latex]46[/latex],[latex]42[/latex],[latex]5048[/latex] , [latex]51[/latex] , [latex]46[/latex] , [latex]42[/latex] , [latex]50 65[/latex],[latex]56[/latex],[latex]35[/latex],[latex]34[/latex],[latex]44[/latex],[latex]39[/latex],[latex]55[/latex],[latex]52[/latex],[latex]4565[/latex] , [latex]56[/latex] , [latex]35[/latex] , [latex]34[/latex] , [latex]44[/latex] , [latex]39[/latex] , [latex]55[/latex] , [latex]52[/latex] , [latex]45 45 121[/latex],[latex]115[/latex],[latex]135[/latex],[latex]109[/latex],[latex]136[/latex],[latex]147[/latex],[latex]127[/latex],[latex]119[/latex],[latex]110121[/latex] , [latex]115[/latex] , [latex]135[/latex] , [latex]109[/latex] , [latex]136[/latex] , [latex]147[/latex] , [latex]127[/latex] , [latex]119[/latex] , [latex]110 4[/latex],[latex]8[/latex],[latex]1[/latex],[latex]5[/latex],[latex]14[/latex],[latex]3[/latex],[latex]1[/latex],[latex]124[/latex] , [latex]8[/latex] , [latex]1[/latex] , [latex]5[/latex] , [latex]14[/latex] , [latex]3[/latex] , [latex]1[/latex] , [latex]12 4.5 3[/latex],[latex]9[/latex],[latex]2[/latex],[latex]6[/latex],[latex]20[/latex],[latex]3[/latex],[latex]3[/latex],[latex]103[/latex] , [latex]9[/latex] , [latex]2[/latex] , [latex]6[/latex] , [latex]20[/latex] , [latex]3[/latex] , [latex]3[/latex] , [latex]10 99.2[/latex],[latex]101.9[/latex],[latex]98.6[/latex],[latex]99.5[/latex],[latex]100.8[/latex],[latex]99.899.2[/latex] , [latex]101.9[/latex] , [latex]98.6[/latex] , [latex]99.5[/latex] , [latex]100.8[/latex] , [latex]99.8 99.65 28.8[/latex],[latex]32.9[/latex],[latex]32.5[/latex],[latex]27.9[/latex],[latex]30.4[/latex],[latex]32.5[/latex],[latex]31.6[/latex],[latex]32.728.8[/latex] , [latex]32.9[/latex] , [latex]32.5[/latex] , [latex]27.9[/latex] , [latex]30.4[/latex] , [latex]32.5[/latex] , [latex]31.6[/latex] , [latex]32.7 Last week Ray recorded how much he spent for lunch each workday. He spent \text{$6.50} , \text{$7.25} , \text{$4.90} , \text{$5.30} , and \text{$12.00} . Find the median. $6.50 Michaela is in charge of 6 two-year olds at a daycare center. Their ages, in months, are 2525 , 2424 , 2828 , 3232 , 2929 , and 3131 . Find the median age. Brian is teaching a swim class for 66 three-year olds. Their ages, in months, are 38,41,45,36,40,and4238,41,45,36,40,\text{and}42. Find the median age. 40.5 months Sal recorded the amount he spent for gas each week for the past 88 weeks. The amounts were \text{$38.65}, \text{$32.18}, \text{$40.23}, \text{$51.50}, \text{$43.68}, \text{$30.96}, \text{$41.37}, and \text{$44.72}. Find the median amount. Identify the Mode of a Set of Numbers In the following exercises, identify the mode. 2[/latex],[latex]5[/latex],[latex]1[/latex],[latex]5[/latex],[latex]2[/latex],[latex]1[/latex],[latex]2[/latex],[latex]3[/latex],[latex]2[/latex],[latex]3[/latex],[latex]12[/latex] , [latex]5[/latex] , [latex]1[/latex] , [latex]5[/latex] , [latex]2[/latex] , [latex]1[/latex] , [latex]2[/latex] , [latex]3[/latex] , [latex]2[/latex] , [latex]3[/latex] , [latex]1 2 8[/latex],[latex]5[/latex],[latex]1[/latex],[latex]3[/latex],[latex]7[/latex],[latex]1[/latex],[latex]1[/latex],[latex]7[/latex],[latex]1[/latex],[latex]8[/latex],[latex]78[/latex] , [latex]5[/latex] , [latex]1[/latex] , [latex]3[/latex] , [latex]7[/latex] , [latex]1[/latex] , [latex]1[/latex] , [latex]7[/latex] , [latex]1[/latex] , [latex]8[/latex] , [latex]7 18[/latex],[latex]22[/latex],[latex]17[/latex],[latex]20[/latex],[latex]19[/latex],[latex]20[/latex],[latex]22[/latex],[latex]19[/latex],[latex]29[/latex],[latex]18[/latex],[latex]23[/latex],[latex]25[/latex],[latex]22[/latex],[latex]24[/latex],[latex]23[/latex],[latex]22[/latex],[latex]18[/latex],[latex]20[/latex],[latex]22[/latex],[latex]2018[/latex] , [latex]22[/latex] , [latex]17[/latex] , [latex]20[/latex] , [latex]19[/latex] , [latex]20[/latex] , [latex]22[/latex] , [latex]19[/latex] , [latex]29[/latex] , [latex]18[/latex] , [latex]23[/latex] , [latex]25[/latex] , [latex]22[/latex] , [latex]24[/latex] , [latex]23[/latex] , [latex]22[/latex] , [latex]18[/latex] , [latex]20[/latex] , [latex]22[/latex] , [latex]20 22 42[/latex],[latex]28[/latex],[latex]32[/latex],[latex]35[/latex],[latex]24[/latex],[latex]32[/latex],[latex]48[/latex],[latex]32[/latex],[latex]32[/latex],[latex]24[/latex],[latex]35[/latex],[latex]28[/latex],[latex]30[/latex],[latex]35[/latex],[latex]45[/latex],[latex]32[/latex],[latex]28[/latex],[latex]32[/latex],[latex]42[/latex],[latex]42[/latex],[latex]3042[/latex] , [latex]28[/latex] , [latex]32[/latex] , [latex]35[/latex] , [latex]24[/latex] , [latex]32[/latex] , [latex]48[/latex] , [latex]32[/latex] , [latex]32[/latex] , [latex]24[/latex] , [latex]35[/latex] , [latex]28[/latex] , [latex]30[/latex] , [latex]35[/latex] , [latex]45[/latex] , [latex]32[/latex] , [latex]28[/latex] , [latex]32[/latex] , [latex]42[/latex] , [latex]42[/latex] , [latex]30 The number of children per house on one block: 11 , 44 , 22 , 33 , 33 , 22 , 66 , 22 , 44 , 22 , 00 , 33 , 00. 2 children The number of movies watched each month last year: 22 , 00 , 33 , 00 , 00 , 88 , 66 , 55 , 00 , 11 , 22 , 33. The number of units being taken by students in one class: 1212 , 55 , 1111 , 1010 , 1010 , 1111 , 55 , 1111 , 1111 , 1111 , 1010 , 1212 . 11 units The number of hours of sleep per night for the past two weeks: 88 , 55 , 77 , 88 , 88 ,   66 , 66 , 66 , 66 , 99 , 77 , 88 , 88 , 88 . Use the Basic Definition of Probability In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.) Josue is in a book club with 2020 members. One member is chosen at random each month to select the next month’s book. Find the probability that Josue will be chosen next month. 120,0.05\frac{1}{20},0.05 Jessica is one of eight kindergarten teachers at Mandela Elementary School. One of the kindergarten teachers will be selected at random to attend a summer workshop. Find the probability that Jessica will be selected. There are 2424 people who work in Dane’s department. Next week, one person will be selected at random to bring in doughnuts. Find the probability that Dane will be selected. Round your answer to the nearest thousandth. 124,0.0416−≈0.042\frac{1}{24},0.041\stackrel{-}{6}\approx 0.042 Monica has two strawberry yogurts and six banana yogurts in her refrigerator. She will choose one yogurt at random to take to work. Find the probability Monica will choose a strawberry yogurt. Michel has four rock CDs and six country CDs in his car. He will pick one CD to play on his way to work. Find the probability Michel will pick a rock CD. 410,0.4\frac{4}{10},0.4 Noah is planning his summer camping trip. He can’t decide among six campgrounds at the beach and twelve campgrounds in the mountains, so he will choose one campground at random. Find the probability that Noah will choose a campground at the beach. Donovan is considering transferring to a 4-year college\text{4-year college}. He is considering 1010 out-of state colleges and 44 colleges in his state. He will choose one college at random to visit during spring break. Find the probability that Donovan will choose an out-of-state college. 1014,0.714285—≈0.714\frac{10}{14},0.\stackrel{\text{---}}{714285}\approx 0.714 There are 258,890,850258,890,850 number combinations possible in the Mega Millions lottery. One winning jackpot ticket will be chosen at random. Brent chooses his favorite number combination and buys one ticket. Find the probability Brent will win the jackpot. Round the decimal to the first digit that is not zero, then write the name of the decimal.

Everyday Math

Joaquin gets paid every Friday. His paychecks for the past 88 Fridays were \text{$315}, \text{$236.25}, \text{$236.25}, \text{$236.25}\text{$315}, \text{$315}, \text{$236.25}, \text{$393.75}. Find the ⓐ mean, ⓑ median, and ⓒ mode. ⓐ $285.47 ⓑ $275.63 ⓒ $236.25 The cash register receipts each day last week at a coffee shop were \text{$1,845}, \text{$1,520}, \text{$1,438}, \text{$1,682}, \text{$1,850}, \text{$2,721}, \text{$2,539}. Find the ⓐ mean, ⓑ median, and ⓒ mode.

Writing Exercises

Explain in your own words the difference between the mean, median, and mode of a set of numbers. Answers will vary. Make an example of probability that relates to your life. Write your answer as a fraction and explain what the numerator and denominator represent.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ After looking at the checklist, do you think you are well prepared for the next section? Why or why not?  

Practice Makes Perfect

Write a Ratio as a Fraction In the following exercises, write each ratio as a fraction. 20[/latex]to[latex]3620[/latex] to [latex]36 59\frac{5}{9} 20[/latex]to[latex]3220[/latex] to [latex]32 42[/latex]to[latex]4842[/latex] to [latex]48 78\frac{7}{8} 45[/latex]to[latex]5445[/latex] to [latex]54 49[/latex]to[latex]2149[/latex] to [latex]21 73\frac{7}{3} 56[/latex]to[latex]1656[/latex] to [latex]16 84[/latex]to[latex]3684[/latex] to [latex]36 73\frac{7}{3} 6.4[/latex]to[latex]0.86.4[/latex] to [latex]0.8 0.56[/latex]to[latex]2.80.56[/latex] to [latex]2.8 15\frac{1}{5} 1.26[/latex]to[latex]4.21.26[/latex] to [latex]4.2 123[/latex]to[latex]2561\frac{2}{3}[/latex] to [latex]2\frac{5}{6} 1017\frac{10}{17} 134[/latex]to[latex]2581\frac{3}{4}[/latex] to [latex]2\frac{5}{8} 416[/latex]to[latex]3134\frac{1}{6}[/latex] to [latex]3\frac{1}{3} 54\frac{5}{4} 535[/latex]to[latex]3355\frac{3}{5}[/latex] to [latex]3\frac{3}{5} \text{$18}[/latex] to [latex]\text{$63} 27\frac{2}{7} \text{$16}[/latex] to [latex]\text{$72} \text{$1.21}[/latex] to [latex]\text{$0.44} 114\frac{11}{4} \text{$1.38}[/latex] to [latex]\text{$0.69} 2828 ounces to 8484 ounces 13\frac{1}{3} 3232 ounces to 128128 ounces 1212 feet to 4646 feet 623\frac{6}{23} 1515 feet to 5757 feet 246246 milligrams to 4545 milligrams 8215\frac{82}{15} 304304 milligrams to 4848 milligrams total cholesterol of 175175 to HDL cholesterol of 4545 359\frac{35}{9} total cholesterol of 215215 to HDL cholesterol of 5555 2727 inches to 11 foot 94\frac{9}{4} 2828 inches to 11 foot Write a Rate as a Fraction In the following exercises, write each rate as a fraction. 140140 calories per 1212 ounces 35 calories3 ounces\frac{\text{35 calories}}{\text{3 ounces}} 180180 calories per 1616 ounces 8.28.2 pounds per 33 square inches 41 lbs15 sq. in.\frac{\text{41 lbs}}{\text{15 sq. in}.} 9.59.5 pounds per 44 square inches 488488 miles in 77 hours 488 miles7 hours\frac{\text{488 miles}}{\text{7 hours}} 527527 miles in 99 hours \text{$595} for 4040 hours \frac{\text{$119}}{\text{8 hours}} \text{$798} for 4040 hours Find Unit Rates In the following exercises, find the unit rate. Round to two decimal places, if necessary. 140140 calories per 1212 ounces 11.67 calories/ounce 180180 calories per 1616 ounces 8.28.2 pounds per 33 square inches 2.73 lbs./sq. in. 9.59.5 pounds per 44 square inches 488488 miles in 77 hours 69.71 mph 527527 miles in 99 hours \text{$595} for 4040 hours $14.88/hour \text{$798} for 4040 hours 576576 miles on 1818 gallons of gas 32 mpg 435435 miles on 1515 gallons of gas 4343 pounds in 1616 weeks 2.69 lbs./week 5757 pounds in 2424 weeks 4646 beats in 0.50.5 minute 92 beats/minute 5454 beats in 0.50.5 minute The bindery at a printing plant assembles 96,00096,000 magazines in 1212 hours. How many magazines are assembled in one hour? 8,000 The pressroom at a printing plant prints 540,000540,000 sections in 1212 hours. How many sections are printed per hour? Find Unit Price In the following exercises, find the unit price. Round to the nearest cent. Soap bars at 88 for \text{$8.69} $1.09/bar Soap bars at 44 for \text{$3.39} Women’s sports socks at 66 pairs for \text{$7.99} $1.33/pair Men’s dress socks at 33 pairs for \text{$8.49} Snack packs of cookies at 1212 for \text{$5.79} $0.48/pack Granola bars at 55 for \text{$3.69} CD-RW discs at 2525 for \text{$14.99} $0.60/disc CDs at 5050 for \text{$4.49} The grocery store has a special on macaroni and cheese. The price is \text{$3.87} for 33 boxes. How much does each box cost? $1.29/box The pet store has a special on cat food. The price is \text{$4.32} for 1212 cans. How much does each can cost? In the following exercises, find each unit price and then identify the better buy. Round to three decimal places. Mouthwash, 50.7-ounce\text{50.7-ounce} size for \text{$6.99} or 33.8-ounce\text{33.8-ounce} size for \text{$4.79} The 50.7-ounce size costs $0.138 per ounce. The 33.8-ounce size costs $0.142 per ounce. The 50.7-ounce size is the better buy. Toothpaste, 66 ounce size for \text{$3.19} or 7.8−ounce7.8-ounce size for \text{$5.19} Breakfast cereal, 1818 ounces for \text{$3.99} or 1414 ounces for \text{$3.29} The 18-ounce size costs $0.222 per ounce. The 14-ounce size costs $0.235 per ounce. The 18-ounce size is a better buy. Breakfast Cereal, 10.710.7 ounces for \text{$2.69} or 14.814.8 ounces for \text{$3.69} Ketchup, 40-ounce\text{40-ounce} regular bottle for \text{$2.99} or 64-ounce\text{64-ounce} squeeze bottle for \text{$4.39} The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy. Mayonnaise 15-ounce\text{15-ounce} regular bottle for \text{$3.49} or 22-ounce\text{22-ounce} squeeze bottle for \text{$4.99} Cheese \text{$6.49} for 11 lb. block or \text{$3.39} for 12\frac{1}{2} lb. block The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy. Candy \text{$10.99} for a 11 lb. bag or \text{$2.89} for 14\frac{1}{4} lb. of loose candy Translate Phrases to Expressions with Fractions In the following exercises, translate the English phrase into an algebraic expression. 793793 miles per pp hours 793 milesphours\frac{\text{793 miles}}{p\text{hours}} 7878 feet per rr seconds \text{$3} for 0.50.5 lbs. \frac{\text{$3}}{\text{0.5 lbs}.} jj beats in 0.50.5 minutes 105105 calories in xx ounces 105 caloriesxounces\frac{\text{105 calories}}{x\text{ounces}} 400400 minutes for mm dollars the ratio of yy and 5x5x y5x\frac{y}{5x} the ratio of 12x12x and yy

Everyday Math

One elementary school in Ohio has 684684 students and 4545 teachers. Write the student-to-teacher ratio as a unit rate. 15.2 students per teacher The average American produces about 1,6001,600 pounds of paper trash per year (365 days). How many pounds of paper trash does the average American produce each day? (Round to the nearest tenth of a pound.) A popular fast food burger weighs 7.57.5 ounces and contains 540540 calories, 2929 grams of fat, 4343 grams of carbohydrates, and 2525 grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce. Round to two decimal places. ⓐ 72 calories/ounce ⓑ 3.87 grams of fat/ounce ⓒ 5.73 grams carbs/once ⓓ 3.33 grams protein/ounce A 16−ounce16-ounce chocolate mocha coffee with whipped cream contains 470470 calories, 1818 grams of fat, 6363 grams of carbohydrates, and 1515 grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce.

Writing Exercises

Would you prefer the ratio of your income to your friend’s income to be 3/1\text{3/1} or 1/3?1/3? Explain your reasoning. Answers will vary. The parking lot at the airport charges \text{$0.75} for every 1515 minutes. ⓐ How much does it cost to park for 11 hour? ⓑ Explain how you got your answer to part ⓐ. Was your reasoning based on the unit cost or did you use another method? Kathryn ate a 4−ounce4-ounce cup of frozen yogurt and then went for a swim. The frozen yogurt had 115115 calories. Swimming burns 422422 calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning. Answers will vary. Mollie had a 16−ounce16-ounce cappuccino at her neighborhood coffee shop. The cappuccino had 110110 calories. If Mollie walks for one hour, she burns 246246 calories. For how many minutes must Mollie walk to burn off the calories in the cappuccino? Explain your reasoning.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ After reviewing this checklist, what will you do to become confident for all objectives?  

Practice Makes Perfect

Simplify Expressions with Square Roots In the following exercises, simplify. 36\sqrt{36} 6 4\sqrt{4} 64\sqrt{64} 8 144\sqrt{144} −4-\sqrt{4} −2 −100-\sqrt{100} −1-\sqrt{1} −1 −121-\sqrt{121} −121\sqrt{-121} not a real number −36\sqrt{-36} −9\sqrt{-9} not a real number −49\sqrt{-49} 9+16\sqrt{9+16} 5 25+144\sqrt{25+144} 9+16\sqrt{9}+\sqrt{16} 7 25+144\sqrt{25}+\sqrt{144} Estimate Square Roots In the following exercises, estimate each square root between two consecutive whole numbers. 70\sqrt{70} 8<70<98<\sqrt{70}<9 55\sqrt{55} 200\sqrt{200} 14<200<1514<\sqrt{200}<15 172\sqrt{172} Approximate Square Roots with a Calculator In the following exercises, use a calculator to approximate each square root and round to two decimal places. 19\sqrt{19} 4.36 21\sqrt{21} 53\sqrt{53} 7.28 47\sqrt{47} Simplify Variable Expressions with Square Roots In the following exercises, simplify. (Assume all variables are greater than or equal to zero.) y2\sqrt{{y}^{2}} y b2\sqrt{{b}^{2}} 49x2\sqrt{49{x}^{2}} 7x 100y2\sqrt{100{y}^{2}} −64a2-\sqrt{64{a}^{2}} −8a −25x2-\sqrt{25{x}^{2}} 144x2y2\sqrt{144{x}^{2}{y}^{2}} 12xy 196a2b2\sqrt{196{a}^{2}{b}^{2}} Use Square Roots in Applications In the following exercises, solve. Round to one decimal place. Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 7575 square feet. How long can a side of his garden be? 8.7 feet Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130130 square feet. How long can a side of his patio be? Gravity An airplane dropped a flare from a height of 1,0241,024 feet above a lake. How many seconds did it take for the flare to reach the water? 8 seconds Gravity A hang glider dropped his cell phone from a height of 350350 feet. How many seconds did it take for the cell phone to reach the ground? Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, 4,0004,000 feet above the Colorado River. How many seconds did it take for the hammer to reach the river? 15.8 seconds Accident investigation The skid marks from a car involved in an accident measured 5454 feet. What was the speed of the car before the brakes were applied? Accident investigation The skid marks from a car involved in an accident measured 216216 feet. What was the speed of the car before the brakes were applied? 72 mph Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175175 feet. What was the speed of the vehicle before the brakes were applied? Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 117117 feet. What was the speed of the vehicle before the brakes were applied? 53.0 mph

Everyday Math

Decorating Denise wants to install a square accent of designer tiles in her new shower. She can afford to buy 625625 square centimeters of the designer tiles. How long can a side of the accent be? Decorating Morris wants to have a square mosaic inlaid in his new patio. His budget allows for 2,0252,025 tiles. Each tile is square with an area of one square inch. How long can a side of the mosaic be? 45 inches

Writing Exercises

Why is there no real number equal to −64?\sqrt{-64}? What is the difference between 92{9}^{2} and 9?\sqrt{9}? Answers will vary. 92 reads: "nine squared" and means nine times itself. The expression 9\sqrt{9} reads: "the square root of nine" which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section. . ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

Chapter Review Exercises

Decimals

Name Decimals In the following exercises, name each decimal. 0.80.8 0.3750.375 three hundred seventy-five thousandths 0.0070.007 5.245.24 five and twenty-four hundredths −12.5632-12.5632 −4.09-4.09 negative four and nine hundredths Write Decimals In the following exercises, write as a decimal. three tenths nine hundredths 0.09 twenty-seven hundredths ten and thirty-five thousandths 10.035 negative twenty and three tenths negative five hundredths −0.05 Convert Decimals to Fractions or Mixed Numbers In the following exercises, convert each decimal to a fraction. Simplify the answer if possible. 0.430.43 0.8250.825 3340\frac{33}{40} 9.79.7 3.643.64 316253\frac{16}{25} Locate Decimals on the Number Line ⓐ 0.60.6 ⓑ −0.9-0.9 ⓒ 2.22.2 ⓓ −1.3-1.3 Order Decimals In the following exercises, order each of the following pairs of numbers, using <<; or >.\text{>.} 0.6___0.8 < 0.2___0.15 0.803____0.83 < -0.56____ - 0.562 Round Decimals In the following exercises, round each number to the nearest: ⓐ hundredth ⓑ tenth ⓒ whole number. 12.52912.529 ⓐ 12.53 ⓑ 12.5 ⓒ 13 4.84474.8447 5.8975.897 ⓐ 5.90 ⓑ 5.9 ⓒ 6

Decimal Operations

Add and Subtract Decimals In the following exercises, add or subtract. 5.75+8.465.75+8.46 32.89−8.2232.89 - 8.22 24.67 24−19.3124 - 19.31 10.2+14.63110.2+14.631 24.831 −6.4+(−2.9)-6.4+\left(-2.9\right) 1.83−4.21.83 - 4.2 −2.37 Multiply Decimals In the following exercises, multiply. (0.3)(0.7)\left(0.3\right)\left(0.7\right) (−6.4)(0.25)\left(-6.4\right)\left(0.25\right) −1.6 (−3.35)(−12.7)\left(-3.35\right)\left(-12.7\right) (15.4)(1000)\left(15.4\right)\left(1000\right) 15,400 Divide Decimals In the following exercises, divide. 0.48÷60.48\div 6 4.32÷244.32\div 24 0.18 \text{$6.29}\div 12 (−0.8)÷(−0.2)\left(-0.8\right)\div \left(-0.2\right) 4 1.65÷0.151.65\div 0.15 9÷0.0459\div 0.045 200 Use Decimals in Money Applications In the following exercises, use the strategy for applications to solve. Miranda got \text{$40} from her ATM. She spent \text{$9.32} on lunch and \text{$16.99} on a book. How much money did she have left? Round to the nearest cent if necessary. Jessie put 88 gallons of gas in her car. One gallon of gas costs \text{$3.528.} How much did Jessie owe for all the gas? $28.22 A pack of 1616 water bottles cost \text{$6.72.} How much did each bottle cost? Alice bought a roll of paper towels that cost \text{$2.49.} She had a coupon for \text{$0.35} off, and the store doubled the coupon. How much did Alice pay for the paper towels? $1.79

Decimals and Fractions

Convert Fractions to Decimals In the following exercises, convert each fraction to a decimal. 35\frac{3}{5} 78\frac{7}{8} 0.875 −1920-\frac{19}{20} −214-\frac{21}{4} −5.25 13\frac{1}{3} 611\frac{6}{11} 0.54-0.\stackrel{\text{-}}{54} Order Decimals and Fractions In the following exercises, order each pair of numbers, using <<; or >.\text{>.} \frac{1}{2}___0.2 \frac{3}{5}___0. > -\frac{7}{8}___ - 0.84 -\frac{5}{12}___ - 0.42 > 0.625___\frac{13}{20} 0.33___\frac{5}{16} > In the following exercises, write each set of numbers in order from least to greatest. 23,1720,0.65\frac{2}{3},\frac{17}{20},0.65 79,0.75,1115\frac{7}{9},0.75,\frac{11}{15} 1115,0.75,79\frac{11}{15},0.75,\frac{7}{9} Simplify Expressions Using the Order of Operations In the following exercises, simplify 4(10.3−5.8)4\left(10.3 - 5.8\right) 34(15.44−7.4)\frac{3}{4}\left(15.44 - 7.4\right) 6.03 30÷(0.45+0.15)30\div \left(0.45+0.15\right) 1.6+381.6+\frac{3}{8} 1.975 52(0.5)+(0.4)252\left(0.5\right)+{\left(0.4\right)}^{2} −25⋅910+0.14-\frac{2}{5}\cdot \frac{9}{10}+0.14 −0.22 Find the Circumference and Area of Circles In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. radius=6 in.\text{radius}=\text{6 in.} radius=3.5 ft.\text{radius}=\text{3.5 ft.} ⓐ 21.98 ft. ⓑ 38.465 sq.ft. radius=733m\text{radius}=\frac{7}{33}\text{m} diameter=11 cm\text{diameter}=\text{11 cm} ⓐ 34.54 cm ⓑ 379.94 sq.cm

Solve Equations with Decimals

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.

x−0.8=2.3x - 0.8=2.3

ⓐ x=2x=2 ⓑ x=−1.5x=-1.5 ⓒ x=3.1x=3.1

ⓐ no ⓑ no ⓒ yes

y+0.6=−3.4y+0.6=-3.4

ⓐ y=−4y=-4 ⓑ y=−2.8y=-2.8 ⓒ y=2.6y=2.6

h1.5=−4.3\frac{h}{1.5}=-4.3

ⓐ h=6.45h=6.45 ⓑ h=−6.45h=-6.45 ⓒ h=−2.1h=-2.1

ⓐ no ⓑ yes ⓒ no

0.75k=−3.60.75k=-3.6

ⓐ k=−0.48k=-0.48 ⓑ k=−4.8k=-4.8 ⓒ k=−2.7k=-2.7

Solve Equations with Decimals In the following exercises, solve the equation.

y+2.9=5.7y+2.9=5.7

y = 2.8

m+4.6=6.5m+4.6=6.5

f+3.45=2.6f+3.45=2.6

f = −0.85

h+4.37=3.5h+4.37=3.5

a+6.2=−1.7a+6.2=-1.7

a = −7.9

b+5.8=−2.3b+5.8=-2.3

c+1.15=−3.5c+1.15=-3.5

c = −4.65

d+2.35=−4.8d+2.35=-4.8

n−2.6=1.8n - 2.6=1.8

n = 4.4

p−3.6=1.7p - 3.6=1.7

x−0.4=−3.9x - 0.4=-3.9

x = −3.5

y−0.6=−4.5y - 0.6=-4.5

j−1.82=−6.5j - 1.82=-6.5

j = −4.68

k−3.19=−4.6k - 3.19=-4.6

m−0.25=−1.67m - 0.25=-1.67

m = −1.42

q−0.47=−1.53q - 0.47=-1.53

0.5x=3.50.5x=3.5

x = 7

0.4p=9.20.4p=9.2

−1.7c=8.5-1.7c=8.5

c = −5

−2.9x=5.8-2.9x=5.8

−1.4p=−4.2-1.4p=-4.2

p = 3

−2.8m=−8.4-2.8m=-8.4

−120=1.5q-120=1.5q

q = −80

−75=1.5y-75=1.5y

0.24x=4.80.24x=4.8

x = 20

0.18n=5.40.18n=5.4

−3.4z=−9.18-3.4z=-9.18

z = 2.7

−2.7u=−9.72-2.7u=-9.72

a0.4=−20\frac{a}{0.4}=-20

a = −8

b0.3=−9\frac{b}{0.3}=-9

x0.7=−0.4\frac{x}{0.7}=-0.4

x = −0.28

y0.8=−0.7\frac{y}{0.8}=-0.7

p−5=−1.65\frac{p}{-5}=-1.65

p = 8.25

q−4=−5.92\frac{q}{-4}=-5.92

r−1.2=−6\frac{r}{-1.2}=-6

r = 7.2

s−1.5=−3\frac{s}{-1.5}=-3

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

x−5=−11x - 5=-11

x = −6

−25=x+34-\frac{2}{5}=x+\frac{3}{4}

p+8=−2p+8=-2

p = −10

p+23=112p+\frac{2}{3}=\frac{1}{12}

−4.2m=−33.6-4.2m=-33.6

m = 8

q+9.5=−14q+9.5=-14

q+56=112q+\frac{5}{6}=\frac{1}{12}

q=−34q=-\frac{3}{4}

8.615=−d\frac{8.6}{15}=-d

78m=110\frac{7}{8}m=\frac{1}{10}

m=435m=\frac{4}{35}

j−6.2=−3\frac{j}{-6.2}=-3

−23=y+38-\frac{2}{3}=y+\frac{3}{8}

y=−2524y=-\frac{25}{24}

s−1.75=−3.2s - 1.75=-3.2

1120=−f\frac{11}{20}=-f

f=−1120f=-\frac{11}{20}

−3.6b=2.52-3.6b=2.52

−4.2a=3.36-4.2a=3.36

a = −0.8

−9.1n=−63.7-9.1n=-63.7

r−1.25=−2.7r - 1.25=-2.7

r = −1.45

14n=710\frac{1}{4}n=\frac{7}{10}

h−3=−8\frac{h}{-3}=-8

h = 24

y−7.82=−16y - 7.82=-16

Translate to an Equation and Solve In the following exercises, translate and solve.

The difference of nn and 1.91.9 is 3.43.4.

n−1.9=3.4;5.3n - 1.9=3.4;5.3

The difference nn and 1.51.5 is 0.80.8.

The product of −6.2-6.2 and xx is −4.96-4.96.

−6.2x = −4.96; 0.8

The product of −4.6-4.6 and xx is −3.22-3.22.

The quotient of yy and −1.7-1.7 is −5-5.

y−1.7=−5;8.5\frac{y}{-1.7}=-5;8.5

The quotient of zz and −3.6-3.6 is 33.

The sum of nn and −7.3-7.3 is 2.42.4.

n + (−7.3) = 2.4; 9.7

The sum of nn and −5.1-5.1 is 3.83.8.

Everyday Math

Shawn bought a pair of shoes on sale for $78 . Solve the equation 0.75p=780.75p=78 to find the original price of the shoes, pp.

$104

Mary bought a new refrigerator. The total price including sales tax was \text{$1,350}. Find the retail price, rr, of the refrigerator before tax by solving the equation 1.08r=1,3501.08r=1,350.

Writing Exercises

Think about solving the equation 1.2y=601.2y=60, but do not actually solve it. Do you think the solution should be greater than 6060 or less than 60?60? Explain your reasoning. Then solve the equation to see if your thinking was correct.

Answers will vary.

Think about solving the equation 0.8x=2000.8x=200, but do not actually solve it. Do you think the solution should be greater than 200200 or less than 200?200? Explain your reasoning. Then solve the equation to see if your thinking was correct.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

  Averages and Probability Find the Mean of a Set of Numbers In the following exercises, find the mean of the numbers. 2,4,1,0,1,and12,4,1,0,1,\text{and}1 \text{$270}[/latex] , [latex]\text{$310.50}[/latex] , [latex]\text{$243.75}[/latex] , and [latex]\text{$252.15} $269.10 Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited 3,0,8,1,and83,0,8,1,\text{and}8 minutes. Find the mean In the last three months, Raul’s water bills were \text{$31.45},\text{$48.76},\text{and}\text{$42.60}. Find the mean. $40.94 Find the Median of a Set of Numbers In the following exercises, find the median. 41[/latex],[latex]45[/latex],[latex]32[/latex],[latex]60[/latex],[latex]5841[/latex] , [latex]45[/latex] , [latex]32[/latex] , [latex]60[/latex] , [latex]58 25[/latex],[latex]23[/latex],[latex]24[/latex],[latex]26[/latex],[latex]29[/latex],[latex]19[/latex],[latex]18[/latex],[latex]3225[/latex] , [latex]23[/latex] , [latex]24[/latex] , [latex]26[/latex] , [latex]29[/latex] , [latex]19[/latex] , [latex]18[/latex] , [latex]32 24.5 The ages of the eight men in Jerry’s model train club are 52,63,45,51,55,75,60,and5952,63,45,51,55,75,60,\text{and}59. Find the median age. The number of clients at Miranda’s beauty salon each weekday last week were 18,7,12,16,and2018,7,12,16,\text{and}20. Find the median number of clients. 16 clients Find the Mode of a Set of Numbers In the following exercises, identify the mode of the numbers. 6[/latex],[latex]4[/latex],[latex]4,5[/latex],[latex]6,6[/latex],[latex]4[/latex],[latex]4[/latex],[latex]4[/latex],[latex]3[/latex],[latex]56[/latex] , [latex]4[/latex] , [latex]4,5[/latex] , [latex]6,6[/latex] , [latex]4[/latex] , [latex]4[/latex] , [latex]4[/latex] , [latex]3[/latex] , [latex]5 The number of siblings of a group of students: 22 , 00 , 33 , 22 , 44 , 11 , 66 , 55 , 44 , 11 , 22 , 33 2 Use the Basic Definition of Probability In the following exercises, solve. (Round decimals to three places.) The Sustainability Club sells 200200 tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal. Luc has to read 33 novels and 1212 short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal. 15;0.2\frac{1}{5};0.2

Ratios and Rate

Write a Ratio as a Fraction In the following exercises, write each ratio as a fraction. Simplify the answer if possible. 28[/latex]to[latex]4028[/latex] to [latex]40 56[/latex]to[latex]3256[/latex] to [latex]32 74\frac{7}{4} 3.5[/latex]to[latex]0.53.5[/latex] to [latex]0.5 1.2[/latex]to[latex]1.81.2[/latex] to [latex]1.8 23\frac{2}{3} 134to1581\frac{3}{4}\text{to}1\frac{5}{8} 213to5142\frac{1}{3}\text{to}5\frac{1}{4} 49\frac{4}{9} 6464 ounces to 3030 ounces 2828 inches to 33 feet 79\frac{7}{9} Write a Rate as a Fraction In the following exercises, write each rate as a fraction. Simplify the answer if possible. 180180 calories per 88 ounces 9090 pounds per 7.57.5 square inches 90pounds7.5square inches\frac{90\text{pounds}}{7.5\text{square inches}} 126126 miles in 44 hours \text{$612.50} for 3535 hours \frac{\text{$612.50}}{35\text{hours}} Find Unit Rates In the following exercises, find the unit rate. 180180 calories per 88 ounces 9090 pounds per 7.57.5 square inches 12 pounds/sq.in. 126126 miles in 44 hours \text{$612.50} for 3535 hours $17.50/hour Find Unit Price In the following exercises, find the unit price. t-shirts: 33 for \text{$8.97} Highlighters: 66 for \text{$2.52} $0.42 An office supply store sells a box of pens for \text{$11}. The box contains 1212 pens. How much does each pen cost? Anna bought a pack of 88 kitchen towels for \text{$13.20}. How much did each towel cost? Round to the nearest cent if necessary. $1.65 In the following exercises, find each unit price and then determine the better buy. Shampoo: 1212 ounces for \text{$4.29} or 2222 ounces for \text{$7.29}? Vitamins: 6060 tablets for \text{$6.49} or 100100 for \text{$11.99}? $0.11, $0.12; 60 tablets for $6.49 Translate Phrases to Expressions with Fractions In the following exercises, translate the English phrase into an algebraic expression. 535[/latex]milesper[latex]hhours535[/latex] miles per [latex]h\text{hours} aa adults to 4545 children aadults45children\frac{a\text{adults}}{45\text{children}} the ratio of 4y4y and the difference of xx and 1010 the ratio of 1919 and the sum of 33 and nn 193+n\frac{19}{3+n}

Simplify and Use Square Roots

Simplify Expressions with Square Roots In the following exercises, simplify. 64\sqrt{64} 144\sqrt{144} 12 −25-\sqrt{25} −81-\sqrt{81} −9 −9\sqrt{-9} −36\sqrt{-36} not a real number 64+225\sqrt{64}+\sqrt{225} 64+225\sqrt{64+225} 17 Estimate Square Roots In the following exercises, estimate each square root between two consecutive whole numbers. 28\sqrt{28} 155\sqrt{155} 12<155<1312<\sqrt{155}<13 Approximate Square Roots In the following exercises, approximate each square root and round to two decimal places. 15\sqrt{15} 57\sqrt{57} 7.55 Simplify Variable Expressions with Square Roots In the following exercises, simplify. (Assume all variables are greater than or equal to zero.) q2\sqrt{{q}^{2}} 64b2\sqrt{64{b}^{2}} 8b −121a2-\sqrt{121{a}^{2}} 225m2n2\sqrt{225{m}^{2}{n}^{2}} 15mn −100q2-\sqrt{100{q}^{2}} 49y2\sqrt{49{y}^{2}} 7y 4a2b2\sqrt{4{a}^{2}{b}^{2}} 121c2d2\sqrt{121{c}^{2}{d}^{2}} 11cd Use Square Roots in Applications In the following exercises, solve. Round to one decimal place. Art Diego has 225225 square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be? Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of 3030 square feet. How long can a side of the flower garden be? 5.5 feet Gravity A hiker dropped a granola bar from a lookout spot 576576 feet above a valley. How long did it take the granola bar to reach the valley floor? Accident investigation The skid marks of a car involved in an accident were 216216 feet. How fast had the car been going before applying the brakes? 72 mph    

Chapter Practice Test

Write six and thirty-four thousandths as a decimal. Write 1.731.73 as a fraction. 1731001\frac{73}{100} Write 58\frac{5}{8} as a decimal. Round 16.74916.749 to the nearest ⓐ tenth ⓑ hundredth ⓒ whole number ⓐ 16.7 ⓑ 16.75 ⓒ 17 Write the numbers 45,−0.1,0.804,29,−7.4,0.21\frac{4}{5},-0.1,0.804,\frac{2}{9},-7.4,0.21 in order from smallest to largest. In the following exercises, simplify each expression. 15.4+3.0215.4+3.02 18.42 20−5.7120 - 5.71 (0.64)(0.3)\left(0.64\right)\left(0.3\right) 0.192 (−4.2)(100)\left(-4.2\right)\left(100\right) 0.96÷(−12)0.96\div \left(-12\right) −0.08 −5÷0.025-5\div 0.025 −0.6÷(−0.3)-0.6\div \left(-0.3\right) 2 (0.7)2{\left(0.7\right)}^{2} 24÷(0.1+0.02)24\div \left(0.1+0.02\right) 200 4(10.3−5.8)4\left(10.3 - 5.8\right) 1.6+381.6+\frac{3}{8} 1.975 23(14.65−4.6)\frac{2}{3}\left(14.65 - 4.6\right) In the following exercises, solve. m+3.7=2.5m+3.7=2.5 −1.2 h0.5=4.38\frac{h}{0.5}=4.38 −6.5y=−57.2-6.5y=-57.2 8.8 1.94=a−2.61.94=a - 2.6 Three friends went out to dinner and agreed to split the bill evenly. The bill was \text{$79.35}. How much should each person pay? $26.45 A circle has radius 1212. Find the ⓐ circumference and ⓑ area. [Use3.14forπ.]\text{[}\text{Use}3.14\text{for}\pi \text{.]} The ages, in months, of 1010 children in a preschool class are: 55[/latex],[latex]55[/latex],[latex]50[/latex],[latex]51[/latex],[latex]52[/latex],[latex]50[/latex],[latex]53[/latex],[latex]51[/latex],[latex]55[/latex],[latex]4955[/latex] , [latex]55[/latex] , [latex]50[/latex] , [latex]51[/latex] , [latex]52[/latex] , [latex]50[/latex] , [latex]53[/latex] , [latex]51[/latex] , [latex]55[/latex] , [latex]49 Find the ⓐ mean ⓑ median ⓒ mode ⓐ 59 ⓑ 51.5 ⓒ 55 Of the 1616 nurses in Doreen’s department, 1212 are women and 44 are men. One of the nurses will be assigned at random to work an extra shift next week. ⓐ Find the probability a woman nurse will be assigned the extra shift. ⓑ Convert the fraction to a decimal. Find each unit price and then the better buy. Laundry detergent: 6464 ounces for \text{$10.99} or 4848 ounces for \text{$8.49} 64 ounces for $10.99 is the better buy In the following exercises, simplify. 36+64\sqrt{36+64} 144n2\sqrt{144{n}^{2}} 12n Estimate 54\sqrt{54} to between two whole numbers. Yanet wants a square patio in her backyard. She has 225225 square feet of tile. How long can a side of the patio be? 15 feet

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