Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

1. [latex]3[/latex] , [latex]8[/latex] , [latex]2[/latex] , [latex]2[/latex] , [latex]5[/latex]
   Show Solution

   4
2. [latex]6[/latex] , [latex]1[/latex] , [latex]9[/latex] , [latex]3[/latex] , [latex]4[/latex] , [latex]7[/latex]
3. [latex]65[/latex] , [latex]13[/latex] , [latex]48[/latex] , [latex]32[/latex] , [latex]19[/latex] , [latex]33[/latex]
   Show Solution

   35
4. [latex]34[/latex] , [latex]45[/latex] , [latex]29[/latex] , [latex]61[/latex] , and [latex]41[/latex]
5. [latex]202[/latex] , [latex]241[/latex] , [latex]265[/latex] , [latex]274[/latex]
   Show Solution

   245.5
6. [latex]525[/latex] , [latex]532[/latex] , [latex]558[/latex] , [latex]574[/latex]
7. [latex]12.45[/latex] , [latex]12.99[/latex] , [latex]10.50[/latex] , [latex]11.25[/latex] , [latex]9.99[/latex] , [latex]12.72[/latex]
   Show Solution

   11.65
8. [latex]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]32.7[/latex]
9. [latex]2,4,1,0,1,\text{and}1[/latex]
10. [latex]{$270}[/latex] , [latex]{$310.50}[/latex] , [latex]{$243.75}[/latex] , and [latex]{$252.15}[/latex]
    Show Solution

    $269.10
11. Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited [latex]3,0,8,1, and 8[/latex] minutes. Find the mean
12. In the last three months, Raul’s water bills were [latex]{$31.45}, {$48.76},\text{and} {$42.60}[/latex]. Find the mean.
    Show Solution

    $40.94

Calculate the Mean of a Set of Numbers in Applications

In the following exercises, find the mean.

1. Four girls leaving a mall were asked how much money they had just spent. The amounts were [latex]{$0}[/latex] , [latex]{$14.95}[/latex] , [latex]{$35.25}[/latex] , and [latex]{$25.16}[/latex] . Find the mean amount of money spent.
   Show Solution

   $18.84
2. Juan bought [latex]5[/latex] shirts to wear to his new job. The costs of the shirts were [latex]{$32.95}[/latex] , [latex]{$38.50}[/latex] , [latex]{$30.00}[/latex] , [latex]{$17.45}[/latex] , and [latex]{$24.25}[/latex] . Find the mean cost.
3. The number of minutes it took Jim to ride his bike to school for each of the past six days was [latex]21[/latex] , [latex]18[/latex] , [latex]16[/latex] , [latex]19[/latex] , [latex]24[/latex] , and [latex]19[/latex] . Find the mean number of minutes.
   Show Solution

   19.5 minutes
4. Norris bought six books for his classes this semester. The costs of the books were [latex]{$74.28}[/latex] , [latex]{$120.95}[/latex] , [latex]{$52.40}[/latex] , [latex]{$10.59}[/latex] , [latex]{$35.89}[/latex] , and [latex]{$59.24}[/latex] . Find the mean cost.
5. The top eight hitters in a softball league have batting averages of [latex].373[/latex] , [latex].360[/latex] , [latex].321[/latex] , [latex].321[/latex] , [latex].320[/latex] , [latex].312[/latex] , [latex].311[/latex] , and [latex].311[/latex] . Find the mean of the batting averages. Round your answer to the nearest thousandth.
   Show Solution

   0.329
6. The monthly snowfall at a ski resort over a six-month period was [latex]60.3[/latex], [latex]79.7[/latex], [latex]50.9[/latex], [latex]28.0[/latex], [latex]47.4[/latex], and [latex]46.1[/latex] inches. Find the mean snowfall.

Find the Median of a Set of Numbers

In the following exercises, find the median.

1. [latex]24[/latex] , [latex]19[/latex] , [latex]18[/latex] , [latex]29[/latex] , [latex]21[/latex]
   Show Solution

   21
2. [latex]48[/latex] , [latex]51[/latex] , [latex]46[/latex] , [latex]42[/latex] , [latex]50[/latex]
3. [latex]65[/latex] , [latex]56[/latex] , [latex]35[/latex] , [latex]34[/latex] , [latex]44[/latex] , [latex]39[/latex] , [latex]55[/latex] , [latex]52[/latex] , [latex]45[/latex]
   Show Solution

   45
4. [latex]121[/latex] , [latex]115[/latex] , [latex]135[/latex] , [latex]109[/latex] , [latex]136[/latex] , [latex]147[/latex] , [latex]127[/latex] , [latex]119[/latex] , [latex]110[/latex]
5. [latex]4[/latex] , [latex]8[/latex] , [latex]1[/latex] , [latex]5[/latex] , [latex]14[/latex] , [latex]3[/latex] , [latex]1[/latex] , [latex]12[/latex]
   Show Solution

   4.5
6. [latex]3[/latex] , [latex]9[/latex] , [latex]2[/latex] , [latex]6[/latex] , [latex]20[/latex] , [latex]3[/latex] , [latex]3[/latex] , [latex]10[/latex]
7. [latex]99.2[/latex] , [latex]101.9[/latex] , [latex]98.6[/latex] , [latex]99.5[/latex] , [latex]100.8[/latex] , [latex]99.8[/latex]
   Show Solution

   99.65
8. [latex]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]32.7[/latex]
9. [latex]41[/latex] , [latex]45[/latex] , [latex]32[/latex] , [latex]60[/latex] , [latex]58[/latex]
10. [latex]25[/latex] , [latex]23[/latex] , [latex]24[/latex] , [latex]26[/latex] , [latex]29[/latex] , [latex]19[/latex] , [latex]18[/latex] , [latex]32[/latex]
    Show Solution

    24.5

Find the Median of a Set of Numbers in Applications

In the following exercises, find the median.

1. Last week Ray recorded how much he spent for lunch each workday. He spent [latex]{$6.50}[/latex] , [latex]{$7.25}[/latex] , [latex]{$4.90}[/latex] , [latex]{$5.30}[/latex] , and [latex]{$12.00}[/latex] . Find the median.
   Show Solution

   $6.50
2. Michaela is in charge of 6 two-year olds at a daycare center. Their ages, in months, are [latex]25[/latex] , [latex]24[/latex] , [latex]28[/latex] , [latex]32[/latex] , [latex]29[/latex] , and [latex]31[/latex] . Find the median age.
3. Brian is teaching a swim class for [latex]6[/latex] three-year olds. Their ages, in months, are [latex]38,41,45,36,40,\text{and}42[/latex]. Find the median age.
   Show Solution

   40.5 months
4. Sal recorded the amount he spent for gas each week for the past [latex]8[/latex] weeks. The amounts were [latex]{$38.65}[/latex], [latex]{$32.18}[/latex], [latex]{$40.23}[/latex], [latex]{$51.50}[/latex], [latex]{$43.68}[/latex], [latex]{$30.96}[/latex], [latex]{$41.37}[/latex], and [latex]{$44.72}[/latex]. Find the median amount.
5. The ages of the eight men in Jerry’s model train club are [latex]52,63,45,51,55,75,60,\text{and}59[/latex]. Find the median age.
6. The number of clients at Miranda’s beauty salon each weekday last week were [latex]18,7,12,16,\text{and}20[/latex]. Find the median number of clients.
   Show Solution

   16 clients

Identify the Mode of a Set of Numbers

In the following exercises, identify the mode.

1. [latex]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]1[/latex]
   Show Solution

   2
2. [latex]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]7[/latex]
3. [latex]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]20[/latex]
   Show Solution

   22
4. [latex]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]30[/latex]
5. The number of children per house on one block: [latex]1[/latex] , [latex]4[/latex] , [latex]2[/latex] , [latex]3[/latex] , [latex]3[/latex] , [latex]2[/latex] , [latex]6[/latex] , [latex]2[/latex] , [latex]4[/latex] , [latex]2[/latex] , [latex]0[/latex] , [latex]3[/latex] , [latex]0[/latex].
   Show Solution

   2 children
6. The number of movies watched each month last year: [latex]2[/latex] , [latex]0[/latex] , [latex]3[/latex] , [latex]0[/latex] , [latex]0[/latex] , [latex]8[/latex] , [latex]6[/latex] , [latex]5[/latex] , [latex]0[/latex] , [latex]1[/latex] , [latex]2[/latex] , [latex]3[/latex].
7. The number of units being taken by students in one class: [latex]12[/latex] , [latex]5[/latex] , [latex]11[/latex] , [latex]10[/latex] , [latex]10[/latex] , [latex]11[/latex] , [latex]5[/latex] , [latex]11[/latex] , [latex]11[/latex] , [latex]11[/latex] , [latex]10[/latex] , [latex]12[/latex] .
   Show Solution

   11 units
8. The number of hours of sleep per night for the past two weeks: [latex]8[/latex] , [latex]5[/latex] , [latex]7[/latex] , [latex]8[/latex] , [latex]8[/latex] ,
9. [latex]6[/latex] , [latex]6[/latex] , [latex]6[/latex] , [latex]6[/latex] , [latex]9[/latex] , [latex]7[/latex] , [latex]8[/latex] , [latex]8[/latex] , [latex]8[/latex] .
10. [latex]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]5[/latex]
11. The number of siblings of a group of students: [latex]2[/latex] , [latex]0[/latex] , [latex]3[/latex] , [latex]2[/latex] , [latex]4[/latex] , [latex]1[/latex] , [latex]6[/latex] , [latex]5[/latex] , [latex]4[/latex] , [latex]1[/latex] , [latex]2[/latex] , [latex]3[/latex]
    Show Solution

    2

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.)

1. Josue is in a book club with [latex]20[/latex] 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.
   Show Solution

   [latex]\Large\frac{1}{20}\normalsize,0.05[/latex]
2. 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.
3. There are [latex]24[/latex] 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.
   Show Solution

   [latex]\Large\frac{1}{24}\normalsize,0.041\stackrel{-}{6}\approx 0.042[/latex]
4. 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.
5. 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.
   Show Solution

   [latex]\Large\frac{4}{10}\normalsize,0.4[/latex]
6. 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.
7. Donovan is considering transferring to a [latex]\text{4-year college}[/latex]. He is considering [latex]10[/latex] out-of state colleges and [latex]4[/latex] 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.
   Show Solution

   [latex]\Large\frac{10}{14}\normalsize,0.\stackrel{\text{—}}{714285}\approx 0.714[/latex]
8. There are [latex]258,890,850[/latex] 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.
9. The Sustainability Club sells [latex]200[/latex] 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.
10. Luc has to read [latex]3[/latex] novels and [latex]12[/latex] 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.

Write a Ratio as a Fraction

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

1. [latex]20[/latex] to [latex]36[/latex]
   Show Solution

   [latex]\Large\frac{5}{9}[/latex]
2. [latex]20[/latex] to [latex]32[/latex]
3. [latex]42[/latex] to [latex]48[/latex]
   Show Solution

   [latex]\Large\frac{7}{8}[/latex]
4. [latex]45[/latex] to [latex]54[/latex]
5. [latex]49[/latex] to [latex]21[/latex]
   Show Solution

   [latex]\Large\frac{7}{3}[/latex]
6. [latex]56[/latex] to [latex]16[/latex]
7. [latex]84[/latex] to [latex]36[/latex]
   Show Solution

   [latex]\Large\frac{7}{3}[/latex]
8. [latex]6.4[/latex] to [latex]0.8[/latex]
9. [latex]0.56[/latex] to [latex]2.8[/latex]
   Show Solution

   [latex]\Large\frac{1}{5}[/latex]
10. [latex]1.26[/latex] to [latex]4.2[/latex]
11. [latex]1\Large\frac{2}{3}[/latex] to [latex]2\Large\frac{5}{6}[/latex]
    Show Solution

    [latex]\Large\frac{10}{17}[/latex]
12. [latex]1\Large\frac{3}{4}[/latex] to [latex]2\Large\frac{5}{8}[/latex]
13. [latex]4\Large\frac{1}{6}[/latex] to [latex]3\Large\frac{1}{3}[/latex]
    Show Solution

    [latex]\Large\frac{5}{4}[/latex]
14. [latex]5\Large\frac{3}{5}[/latex] to [latex]3\Large\frac{3}{5}[/latex]
15. [latex]{$18}[/latex] to [latex]{$63}[/latex]
    Show Solution

    [latex]\Large\frac{2}{7}[/latex]
16. [latex]{$16}[/latex] to [latex]{$72}[/latex]
17. [latex]{$1.21}[/latex] to [latex]{$0.44}[/latex]
    Show Solution

    [latex]\Large\frac{11}{4}[/latex]
18. [latex]{$1.38}[/latex] to [latex]{$0.69}[/latex]
19. [latex]28[/latex] ounces to [latex]84[/latex] ounces
    Show Solution

    [latex]\Large\frac{1}{3}[/latex]
20. [latex]32[/latex] ounces to [latex]128[/latex] ounces
21. [latex]12[/latex] feet to [latex]46[/latex] feet
    Show Solution

    [latex]\Large\frac{6}{23}[/latex]
22. [latex]15[/latex] feet to [latex]57[/latex] feet
23. [latex]246[/latex] milligrams to [latex]45[/latex] milligrams
    Show Solution

    [latex]\Large\frac{82}{15}[/latex]
24. [latex]304[/latex] milligrams to [latex]48[/latex] milligrams
25. total cholesterol of [latex]175[/latex] to HDL cholesterol of [latex]45[/latex]
    Show Solution

    [latex]\Large\frac{35}{9}[/latex]
26. total cholesterol of [latex]215[/latex] to HDL cholesterol of [latex]55[/latex]
27. [latex]27[/latex] inches to [latex]1[/latex] foot
    Show Solution

    [latex]\Large\frac{9}{4}[/latex]
28. [latex]28[/latex] inches to [latex]1[/latex] foot
29. [latex]28[/latex] to [latex]40[/latex][latex]56[/latex] to [latex]32[/latex]
    Show Solution

    [latex]\Large\frac{7}{4}[/latex]
30. [latex]3.5[/latex] to [latex]0.5[/latex]
31. [latex]1.2[/latex] to [latex]1.8[/latex]
    Show Solution

    [latex]\Large\frac{2}{3}[/latex]
32. [latex]1\Large\frac{3}{4}\normalsize\text{to}1\Large\frac{5}{8}[/latex]
33. [latex]2\Large\frac{1}{3}\normalsize\text{to}5\Large\frac{1}{4}[/latex]
    Show Solution

    [latex]\Large\frac{4}{9}[/latex]
34. [latex]64[/latex] ounces to [latex]30[/latex] ounces
35. [latex]28[/latex] inches to [latex]3[/latex] feet
    Show Solution

    [latex]\Large\frac{7}{9}[/latex]

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

1. [latex]140[/latex] calories per [latex]12[/latex] ounces
   Show Solution

   [latex]\Large\frac{\text{35 calories}}{\text{3 ounces}}[/latex]
2. [latex]180[/latex] calories per [latex]16[/latex] ounces
3. [latex]8.2[/latex] pounds per [latex]3[/latex] square inches
   Show Solution

   [latex]\Large\frac{\text{41 lbs}}{\text{15 sq. in}.}[/latex]
4. [latex]9.5[/latex] pounds per [latex]4[/latex] square inches
5. [latex]488[/latex] miles in [latex]7[/latex] hours
   Show Solution

   [latex]\Large\frac{\text{488 miles}}{\text{7 hours}}[/latex]
6. [latex]527[/latex] miles in [latex]9[/latex] hours
7. [latex]{$595}[/latex] for [latex]40[/latex] hours
   Show Solution

   [latex]\Large\frac{{$119}}{{8 hours}}[/latex]
8. [latex]{$798}[/latex] for [latex]40[/latex] hours
9. [latex]180[/latex] calories per [latex]8[/latex] ounces
10. [latex]90[/latex] pounds per [latex]7.5[/latex] square inches
    Show Solution

    [latex]\Large\frac{90\text{pounds}}{7.5\text{square inches}}[/latex]
11. [latex]126[/latex] miles in [latex]4[/latex] hours
12. [latex]{$612.50}[/latex] for [latex]35[/latex] hours
    Show Solution

    [latex]\Large\frac{$612.50}{35\text{hours}}[/latex]

Find Unit Rates

Exercise 1

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

1. 1. [latex]140[/latex] calories per [latex]12[/latex] ounces
      Show Solution

      11.67 calories/ounce
   2. [latex]180[/latex] calories per [latex]16[/latex] ounces
   3. [latex]8.2[/latex] pounds per [latex]3[/latex] square inches
      Show Solution

      2.73 lbs./sq. in.
   4. [latex]9.5[/latex] pounds per [latex]4[/latex] square inches
   5. [latex]488[/latex] miles in [latex]7[/latex] hours
      Show Solution

      69.71 mph
   6. [latex]527[/latex] miles in [latex]9[/latex] hours
   7. [latex]{$595}[/latex] for [latex]40[/latex] hours
      Show Solution

      $14.88/hour
   8. [latex]{$798}[/latex] for [latex]40[/latex] hours
   9. [latex]576[/latex] miles on [latex]18[/latex] gallons of gas
      Show Solution

      32 mpg
   10. [latex]435[/latex] miles on [latex]15[/latex] gallons of gas
   11. [latex]43[/latex] pounds in [latex]16[/latex] weeks
       Show Solution

       2.69 lbs./week
   12. [latex]57[/latex] pounds in [latex]24[/latex] weeks
   13. [latex]46[/latex] beats in [latex]0.5[/latex] minute
       Show Solution

       92 beats/minute
   14. [latex]54[/latex] beats in [latex]0.5[/latex] minute
   15. [latex]180[/latex] calories per [latex]8[/latex] ounces
   16. [latex]90[/latex] pounds per [latex]7.5[/latex] square inches
       Show Solution

       12 pounds/sq.in.
   17. [latex]126[/latex] miles in [latex]4[/latex] hours
   18. [latex]{$612.50}[/latex] for [latex]35[/latex] hours
       Show Solution

       $17.50/hour

Exercise 2

1. 1. The bindery at a printing plant assembles [latex]96,000[/latex] magazines in [latex]12[/latex] hours. How many magazines are assembled in one hour?
      Show Solution

      8,000
   2. The pressroom at a printing plant prints [latex]540,000[/latex] sections in [latex]12[/latex] hours. How many sections are printed per hour?

Find Unit Price

Exercise 1

In the following exercises, find the unit price. Round to the nearest cent.

1. 1. Soap bars at [latex]8[/latex] for [latex]{$8.69}[/latex]
      Show Solution

      $1.09/bar
   2. Soap bars at [latex]4[/latex] for [latex]{$3.39}[/latex]
   3. Women’s sports socks at [latex]6[/latex] pairs for [latex]{$7.99}[/latex]
      Show Solution

      $1.33/pair
   4. Men’s dress socks at [latex]3[/latex] pairs for [latex]{$8.49}[/latex]
   5. Snack packs of cookies at [latex]12[/latex] for [latex]{$5.79}[/latex]
      Show Solution

      $0.48/pack
   6. Granola bars at [latex]5[/latex] for [latex]{$3.69}[/latex]
   7. CD-RW discs at [latex]25[/latex] for [latex]{$14.99}[/latex]
      Show Solution

      $0.60/disc
   8. CDs at [latex]50[/latex] for [latex]{$4.49}[/latex]
   9. t-shirts: [latex]3[/latex] for [latex]{$8.97}[/latex]
   10. Highlighters: [latex]6[/latex] for [latex]{$2.52}[/latex]
       Show Solution

       $0.42
   11. An office supply store sells a box of pens for [latex]{$11}[/latex]. The box contains [latex]12[/latex] pens. How much does each pen cost?
   12. Anna bought a pack of [latex]8[/latex] kitchen towels for [latex]{$13.20}[/latex]. How much did each towel cost? Round to the nearest cent if necessary.
       Show Solution

       $1.65

Exercise 2

1. 1. The grocery store has a special on macaroni and cheese. The price is [latex]{$3.87}[/latex] for [latex]3[/latex] boxes. How much does each box cost?
      Show Solution

      $1.29/box
   2. The pet store has a special on cat food. The price is [latex]{$4.32}[/latex] for [latex]12[/latex] cans. How much does each can cost?

Exercise 3

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

1. 1. Mouthwash, [latex]{50.7-ounce}[/latex] size for [latex]{$6.99}[/latex] or [latex]{33.8-ounce}[/latex] size for [latex]{$4.79}[/latex]
      Show Solution

      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.
   2. Toothpaste, [latex]6[/latex] ounce size for [latex]{$3.19}[/latex] or [latex]7.8-ounce[/latex] size for [latex]{$5.19}[/latex]
   3. Breakfast cereal, [latex]18[/latex] ounces for [latex]{$3.99}[/latex] or [latex]14[/latex] ounces for [latex]{$3.29}[/latex]
      Show Solution

      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.
   4. Breakfast Cereal, [latex]10.7[/latex] ounces for [latex]{$2.69}[/latex] or [latex]14.8[/latex] ounces for [latex]{$3.69}[/latex]
   5. Ketchup, [latex]{40-ounce}[/latex] regular bottle for [latex]{$2.99}[/latex] or [latex]{64-ounce}[/latex] squeeze bottle for [latex]{$4.39}[/latex]
      Show Solution

      The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.
   6. Mayonnaise [latex]{15-ounce}[/latex] regular bottle for [latex]{$3.49}[/latex] or [latex]{22-ounce}[/latex] squeeze bottle for [latex]{$4.99}[/latex]
   7. Cheese [latex]{$6.49}[/latex] for [latex]1[/latex] lb. block or [latex]{$3.39}[/latex] for [latex]\Large\frac{1}{2}[/latex] lb. block
      Show Solution

      The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.
   8. Candy [latex]{$10.99}[/latex] for a [latex]1[/latex] lb. bag or [latex]{$2.89}[/latex] for [latex]\Large\frac{1}{4}[/latex] lb. of loose candy
   9. Shampoo: [latex]12[/latex] ounces for [latex]{$4.29}[/latex] or [latex]22[/latex] ounces for [latex]{$7.29}?[/latex]
   10. Vitamins: [latex]60[/latex] tablets for [latex]{$6.49}[/latex] or [latex]100[/latex] for [latex]{$11.99}?[/latex]
       Show Solution

       $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.

1. 1. [latex]793[/latex] miles per [latex]p[/latex] hours
      Show Solution

      [latex]\Large\frac{\text{793 miles}}{p \text{hours}}[/latex]
   2. [latex]78[/latex] feet per [latex]r[/latex] seconds
   3. [latex]{$3}[/latex] for [latex]0.5[/latex] lbs.
      Show Solution

      [latex]\Large\frac{{$3}}{{0.5 lbs}.}[/latex]
   4. [latex]j[/latex] beats in [latex]0.5[/latex] minutes
   5. [latex]105[/latex] calories in [latex]x[/latex] ounces
      Show Solution

      [latex]\Large\frac{\text{105 calories}} {x \text {ounces}}[/latex]
   6. [latex]400[/latex] minutes for [latex]m[/latex] dollars
   7. the ratio of [latex]y[/latex] and [latex]5x[/latex]
      Show Solution

      [latex]\Large\frac{y}{5x}[/latex]
   8. the ratio of [latex]12x[/latex] and [latex]y[/latex]
   9. [latex]535[/latex] miles per [latex]h\text{hours}[/latex]
   10. [latex]a[/latex] adults to [latex]45[/latex] children
       Show Solution

       [latex]\Large\frac{a\text{adults}}{45\text{children}}[/latex]
   11. the ratio of [latex]4y[/latex] and the difference of [latex]x[/latex] and [latex]10[/latex]
   12. the ratio of [latex]19[/latex] and the sum of [latex]3[/latex] and [latex]n[/latex]
       Show Solution

       [latex]\Large\frac{19}{3+n}[/latex]

Everyday Math

Simplify Expressions with Square Roots

In the following exercises, simplify.

1. 1. [latex]\sqrt{36}[/latex]
      Show Solution

      6
   2. [latex]\sqrt{4}[/latex]
   3. [latex]\sqrt{64}[/latex]
      Show Solution

      8
   4. [latex]\sqrt{144}[/latex]
   5. [latex]-\sqrt{4}[/latex]
      Show Solution

      −2
   6. [latex]-\sqrt{100}[/latex]
   7. [latex]-\sqrt{1}[/latex]
      Show Solution

      −1
   8. [latex]-\sqrt{121}[/latex]
   9. [latex]\sqrt{-121}[/latex]
      Show Solution

      not a real number
   10. [latex]\sqrt{-36}[/latex]
   11. [latex]\sqrt{-9}[/latex]
       Show Solution

       not a real number
   12. [latex]\sqrt{-49}[/latex]
   13. [latex]\sqrt{9+16}[/latex]
       Show Solution

       5
   14. [latex]\sqrt{25+144}[/latex]
   15. [latex]\sqrt{9}+\sqrt{16}[/latex]
       Show Solution

       7
   16. [latex]\sqrt{25}+\sqrt{144}[/latex]
   17. [latex]\sqrt{64}[/latex]
   18. [latex]\sqrt{144}[/latex]
       Show Solution

       12
   19. [latex]-\sqrt{25}[/latex]
   20. [latex]-\sqrt{81}[/latex]
       Show Solution

       −9
   21. [latex]\sqrt{-9}[/latex]
   22. [latex]\sqrt{-36}[/latex]
       Show Solution

       not a real number
   23. [latex]\sqrt{64}+\sqrt{225}[/latex]
   24. [latex]\sqrt{64+225}[/latex]
       Show Solution

       17

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

1. 1. [latex]\sqrt{70}[/latex]
      Show Solution

      [latex]8<\sqrt{70}<9[/latex]
   2. [latex]\sqrt{55}[/latex]
   3. [latex]\sqrt{200}[/latex]
      Show Solution

      [latex]14<\sqrt{200}<15[/latex]
   4. [latex]\sqrt{172}[/latex]
   5. [latex]\sqrt{28}[/latex]
   6. [latex]\sqrt{155}[/latex]
      Show Solution

      [latex]12<\sqrt{155}<13[/latex]

Approximate Square Roots with a Calculator

In the following exercises, use a calculator to approximate each square root and round to two decimal places.

1. 1. [latex]\sqrt{19}[/latex]
      Show Solution

      4.36
   2. [latex]\sqrt{21}[/latex]
   3. [latex]\sqrt{53}[/latex]
      Show Solution

      7.28
   4. [latex]\sqrt{47}[/latex]
   5. [latex]\sqrt{15}[/latex]
   6. [latex]\sqrt{57}[/latex]
      Show Solution

      7.55

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

1. 1. [latex]\sqrt{{y}^{2}}[/latex]
      Show Solution

      y
   2. [latex]\sqrt{{b}^{2}}[/latex]
   3. [latex]\sqrt{49{x}^{2}}[/latex]
      Show Solution

      7x
   4. [latex]\sqrt{100{y}^{2}}[/latex]
   5. [latex]-\sqrt{64{a}^{2}}[/latex]
      Show Solution

      −8a
   6. [latex]-\sqrt{25{x}^{2}}[/latex]
   7. [latex]\sqrt{144{x}^{2}{y}^{2}}[/latex]
      Show Solution

      12xy
   8. [latex]\sqrt{196{a}^{2}{b}^{2}}[/latex]
   9. [latex]\sqrt{{q}^{2}}[/latex]
   10. [latex]\sqrt{64{b}^{2}}[/latex]
       Show Solution

       8b
   11. [latex]-\sqrt{121{a}^{2}}[/latex]
   12. [latex]\sqrt{225{m}^{2}{n}^{2}}[/latex]
       Show Solution

       15mn
   13. [latex]-\sqrt{100{q}^{2}}[/latex]
   14. [latex]\sqrt{49{y}^{2}}[/latex]
       Show Solution

       7y
   15. [latex]\sqrt{4{a}^{2}{b}^{2}}[/latex]
   16. [latex]\sqrt{121{c}^{2}{d}^{2}}[/latex]
       Show Solution

       11cd

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 [latex]75[/latex] square feet. How long can a side of his garden be?

1. Show Solution

1. 8.7 feet