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Quantitative Literacy
Rates, Ratios, Proportions, and Percents

1
Ratios

Problem 1

Write the ratio \(16\) to \(48\) as a fraction in lowest terms.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David cc spanish language icon
David
Problem 2

Give the ratio \(\dfrac{2}{3}\) to \(\dfrac{4}{9}\) as a fraction in lowest terms.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David cc spanish language icon
David
Problem 3

Write \(0.08\) to \(0.12\) as a fraction in lowest terms.

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Mr. McKeague cc
Mr. McKeague
Lauren cc
Lauren
Matt cc
Matt
Octabio cc spanish language icon
Octabio
Problem 4

During a game, a basketball player makes \(12\) out of the \(18\) free throws he attempts. Write the ratio of the number of free throws he makes to the number of free throws he attempts as a fraction in lowest terms.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
Cynthia cc spanish language icon
Cynthia
Problem 5

A solution of alcohol and water contains \(15\) milliliters of water and \(5\) milliliters of alcohol. Find the ratio of alcohol to water, water to alcohol, water to total solution, and alcohol to total solution. Write each ratio as a fraction and reduce to lowest terms.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
Cynthia cc spanish language icon
Cynthia
Problem 6

Suppose a pizza restaurant advertised the prices shown in the book for their deep dish pizza. Use the information to find the ratio of the cost of the large cheese pizza to the medium cheese pizza.Then change the ratio to a decimal rounded to the nearest tenth.

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Joshua cc
Joshua
Lauren cc
Lauren
Cynthia spanish language icon
Cynthia
Problem 7

Write the ratio \(1\displaystyle\frac{2}{3}\) to \(3\displaystyle\frac{1}{3}\) as a fraction in lowest terms.

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Problem 8

Mini Lecture
Write each ratio as a fraction in lowest terms:

  1. \(64\) to \(12\)

  2. \(\dfrac{3}{4}\) to \(\dfrac{1}{4}\)

  3. \(2\dfrac{2}{3}\) to \(\dfrac{5}{3}\)

  4. \(2.5\) to \(\dfrac{3}{2}\)

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Mr. McKeague cc
Mr. McKeague

2
Rates and Unit Pricing

Problem 1

A train travels \(125\) miles in \(2\) hours. What is the train’s rate in miles per hour?

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Aaron cc
Aaron
David cc spanish language icon
David
Problem 2

A car travels \(90\) miles on \(5\) gallons of gas. Give the ratio of miles to gallon as a rate in miles per gallon.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David cc spanish language icon
David
Problem 3

A supermarket sells low-fat milk in three different containers at the following prices: \(1\) gallon for \(\$3.58\), \(1/2\) gallon for \(\$1.99\), and \(1\) quart for \(\$1.29\). Give the unit price in dollars per gallon for each one.

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Matt cc
Matt
Katrina cc
Katrina
Cynthia cc spanish language icon
Cynthia
Problem 4

Mini Lecture

  1. Write \(220\) miles in \(4\) hours as a rate in miles per hour.

  2. Six ounces of orange juice costs \(48\) cents. What is the unit price in cents per ounce?

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Betsy cc
Betsy

3
Proportions

Problem 1

In the proportion \(\dfrac{3}{4}=\dfrac{6}{8}\), name the four terms, the means, and the extremes.

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Matt cc
Matt
David cc spanish language icon
David
Problem 2

Verify the fundamental property of proportions for the following proportions.

  1. \(\displaystyle\frac{3}{4}=\displaystyle\frac{6}{8}\)

  2. \(\displaystyle\frac{17}{34}=\displaystyle\frac{1}{2}\)

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Matt cc
Matt
David cc spanish language icon
David
Problem 3

Solve for \(x\): \(\displaystyle\frac{2}{3}=\displaystyle\frac{4}{x}\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Aaron cc
Aaron
David cc spanish language icon
David
Problem 4

Solve for \(y\): \(\displaystyle\frac{5}{y}=\displaystyle\frac{10}{13}\)

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David cc
David
Betsy cc
Betsy
Matt cc
Matt
David cc spanish language icon
David
Problem 5

Solve for \(n\): \(\displaystyle\frac{n}{3}=\displaystyle\frac{0.4}{8}\)

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David cc
David
Betsy cc
Betsy
Aaron cc
Aaron
David cc spanish language icon
David
Problem 6

Solve for \(b\): \(\displaystyle\frac{b}{15}=2\)

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Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Aaron cc
Aaron
David cc spanish language icon
David

4
Applications of Proportions

Problem 1

A woman drives \(270\) miles in \(6\) hours. If she continues at the same rate, how far will she travel in \(10\) hours?

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Aaron cc
Aaron
David cc spanish language icon
David
Problem 2

A baseball player gets \(8\) hits in the first \(18\) games of the season. If he continues at the same rate, how many hits will he get in \(45\) games?

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Logan cc
Logan
David cc spanish language icon
David
Problem 3

A solution contains \(4\) milliliters of alcohol and \(20\) milliliters of water. If another solution is to have the same ratio of alcohol to water and must contain \(25\) milliliters of water, how much alcohol should it contain?

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Aaron cc
Aaron
David cc spanish language icon
David
Problem 4

The scale on the map indicates that \(1\) inch on the map corresponds to an actual distance of \(85\) miles. Two cities are \(3.5\) inches apart on the map. What is the actual distance between the two cities?

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Nathan cc
Nathan
Katherine cc
Katherine

5
Percents, Decimals, and Fractions

Problem 1

Write each percent as a fraction with a denominator of \(100\).

  1. \(33\%\)

  2. \(6\%\)

  3. \(160\%\)

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Mrs. Mooney cc
Mrs. Mooney
Preston cc
Preston
Stephanie cc
Stephanie
Edwin cc spanish language icon
Edwin
Problem 2

Change \(35.2\%\) to a decimal.

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Dr. Cavanah cc
Dr. Cavanah
Preston cc
Preston
Stephanie cc
Stephanie
Edwin cc spanish language icon
Edwin
Problem 3

Write each percent as a decimal.

  1. \(37\%\)

  2. \(68\%\)

  3. \(120\%\)

  4. \(0.8\%\)

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Preston cc
Preston
Stephanie cc
Stephanie
Edwin cc spanish language icon
Edwin
Problem 4

Change \(0.5\%\) to a decimal.

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Julieta cc
Julieta
Preston cc
Preston
Stephanie cc
Stephanie
Edwin cc spanish language icon
Edwin
Problem 5

Write each decimal as a percent.

  1. \(0.27\)

  2. \(4.89\)

  3. \(0.5\)

  4. \(0.09\)

  5. \(3\)

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Dr. Cavanah cc
Dr. Cavanah
Preston cc
Preston
Stephanie cc
Stephanie
Edwin cc spanish language icon
Edwin
Problem 6

A softball player has a batting average of \(0.650\). Write this number as a percent.

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Stephanie cc
Stephanie
Nathan cc
Nathan
Edwin cc spanish language icon
Edwin
Problem 7

Write each percent as a fraction in lowest terms.

  1. \(19\%\)

  2. \(45\%\)

  3. \(36\%\)

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Stephanie cc
Stephanie
Preston cc
Preston
Julieta cc
Julieta
Edwin cc spanish language icon
Edwin
Problem 8

Change \(4.5\%\) to a fraction.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 9

Change \(32\frac{1}{2}\%\) to a fraction.

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Katrina cc
Katrina
Nathan cc
Nathan
Julieta cc spanish language icon
Julieta
Problem 10

Change \(\dfrac{7}{10}\) to a percent.

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Mrs. Mooney cc
Mrs. Mooney
Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 11

Change \(\dfrac{3}{8}\) to a percent.

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Nathan cc
Nathan
Stephanie cc
Stephanie
Gordon cc
Gordon
Edwin cc spanish language icon
Edwin
Problem 12

Change \(\dfrac{5}{12}\) to a percent.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 13

Change \(2\frac{1}{2}\) to a percent.

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Gordon cc
Gordon
Stephanie cc
Stephanie
Mrs. Mooney cc
Mrs. Mooney
Edwin cc spanish language icon
Edwin
Problem 14
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6
Percent Problems

Problem 1

What number is \(15\%\) of \(63\)?

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Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Nathan cc
Nathan
David cc spanish language icon
David
Problem 2

What percent of \(42\) is \(21\)?

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Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Aaron cc
Aaron
David cc spanish language icon
David
Problem 3

\(25\) is \(40\%\) of what number?

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Mr. McKeague cc
Mr. McKeague
Nathan cc
Nathan
David cc spanish language icon
David
Problem 4

What number is \(43.5\%\) of \(25\)?

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Katrina cc
Katrina
Aaron cc
Aaron
David cc spanish language icon
David
Problem 5

What percent of \(78\) is \(31.9\)?

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Katherine cc
Katherine
Katrina cc
Katrina
Nathan cc
Nathan
David cc spanish language icon
David
Problem 6

The American Dietetic Association recommend eating foods in which the number of calories from fat is less than \(30\%\) of the total number of calories. According to the nutrition label, what percent of the total number of calories are fat calories?

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Katherine cc
Katherine
Katrina cc
Katrina
Gordon cc
Gordon
Julieta cc spanish language icon
Julieta
Problem 7

What number is \(15\%\) of \(63\)? (Use proportions.)

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 8

What percent of \(42\) is \(21\)? (Use proportions.)

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
Gordon cc
Gordon
Julieta cc spanish language icon
Julieta
Problem 9

\(25\) is \(40\%\) of what number? (Use proportions.)

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin

7
General Applications of Percent

Problem 1

On a \(120\)-question test, a student answered \(96\) correctly. What percent of the problems did the student work correctly?

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Anthony cc
Anthony
David cc spanish language icon
David
Problem 2

How much HCl is in a \(60\)-milliliter bottle that is marked \(80\%\) HCl?

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Mr. McKeague cc
Mr. McKeague
Mr. McKeague cc
Mr. McKeague
Aaron cc
Aaron
David cc spanish language icon
David
Problem 3

If \(48\%\) of the students in a certain college are female and there are \(2,400\) female students, what is the total number of students in the college?

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Mr. McKeague cc
Mr. McKeague
Anthony cc
Anthony
Arielle cc
Arielle
David cc spanish language icon
David
Problem 4

If \(25\%\) of the students in elementary algebra courses receive a grade of A, and there are \(300\) students enrolled in elementary algebra this year, how many students will receive A’s?

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Anthony cc
Anthony
David cc spanish language icon
David

8
Unit Analysis: Length

Problem 1

Convert \(5\) feet to inches.

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
David spanish language icon
David
Problem 2

Normal ceiling height is \(8\) feet, convert to yards.

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Molly M. cc
Molly M.
Betsy cc
Betsy
Aaron cc
Aaron
Cynthia spanish language icon
Cynthia
Problem 3

A football field is \(100\) yards long, convert to inches.

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Molly M. cc
Molly M.
Betsy cc
Betsy
Breylor cc
Breylor
David spanish language icon
David
Problem 4

Convert \(25\) millimeters to meters.

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Betsy cc
Betsy
Aaron cc
Aaron
Cynthia spanish language icon
Cynthia
Problem 5

Convert \(36.5\) centimeters to decimeters.

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Gordon cc
Gordon
Betsy cc
Betsy
Breylor cc
Breylor
David spanish language icon
David
Problem 6

A sheep rancher is making lambing pens. Each pen is a rectangle \(6\) feet wide and \(8\) feet long. The fencing material is \(\$1.36\) per foot. If he is planning to build five separate lambing pens, how much will it cost?

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Betsy cc
Betsy
Aaron cc
Aaron
Cynthia spanish language icon
Cynthia
Problem 7

A ski resort in Vermont advertised their new high-speed chair lift as the world’s fastest chair lift with a speed of 1,100 feet per second. Show why the speed cannot be correct.

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Betsy cc
Betsy
Breylor cc
Breylor
David spanish language icon
David
Problem 8

Mini Lecture
Make the conversions by multiplying by the appropriate conversion factor. Write the answer as a whole number or mixed numbers.

  1. \(27\) inches to feet

  2. \(2\) yds to feet

  3. \(4.8\) km to meters

  4. New pencils are \(19\) cm long. Convert to meters

  5. A furlong is \(220\) yds, how many feet are in \(12\) furlongs?

  6. Convert \(55\) miles/hour to feet/second

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Mr. McKeague cc
Mr. McKeague

9
Converting Between the Two Systems, and Temperature

Problem 1

Convert \(8\) inches to centimeters.

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Julieta cc
Julieta
Gordon cc
Gordon
David spanish language icon
David
Problem 2

Convert \(80.5\) kilometers to miles.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Cynthia spanish language icon
Cynthia
Problem 3

Convert \(3\) liters to pints.

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Julieta cc
Julieta
Gordon cc
Gordon
David spanish language icon
David
Problem 4

The engine in a car has a \(2\)-liter displacement. What is the displacement in cubic inches?

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Stephanie cc
Stephanie
Aaron cc
Aaron
Cynthia spanish language icon
Cynthia
Problem 5

If a person weighs \(125\) pounds, what is their weight in kilograms?

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Gordon cc
Gordon
Julieta cc
Julieta
David spanish language icon
David
Problem 6

Convert \(120^\circ\)C to degrees Fahrenheit.

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Stephanie cc
Stephanie
Aaron cc
Aaron
Cynthia spanish language icon
Cynthia
Problem 7

A man with the flu has a temperature of \(102^\circ\)F. What is his temperature on the Celsius scale?

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Stephanie cc
Stephanie
Graham cc
Graham
David spanish language icon
David
Problem 8

Mini Lecture
Convert:

  1. \(4\) meters to feet.

  2. \(2\) liters to quarts.

  3. \(1\) pound to grams.

  4. \(20^\circ\)C to \(^\circ\)F.

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Mr. McKeague cc
Mr. McKeague

10
Test & Summary

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