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Math Fundamentals
Ratio and Proportion

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 \(\displaystyle\frac{2}{3}\) to \(\displaystyle\frac{4}{9}\) as a fraction in lowest terms.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc spanish language icon
Matt
David cc
David
Problem 3
example image
Choose instructor to watch:
Molly S. cc
Molly S.
Gordon
Gordon
Problem 4

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 5

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 6

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 7

Use the information given in the table to find the ratio of CO2 produced by a Chevrolet Suburban to that of a Honda Civic.

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Katherine cc
Katherine
Octabio cc
Octabio
Octabio spanish language icon
Octabio
Problem 8
example image
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Gordon
Gordon
Problem 9

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

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
Solving Equations by Division

Problem 1

Divide the expression \(5n\) by \(5\)

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Betsy cc
Betsy
Aaron cc
Aaron
David cc spanish language icon
David
Problem 2

Divide \(7y\) by \(7\)

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Betsy cc
Betsy
Winston cc
Winston
David spanish language icon
David
Problem 3

Solve \(7y=42\) for \(y\) by dividing both sides by \(7\)

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Betsy cc
Betsy
Aaron cc
Aaron
David spanish language icon
David
Problem 4

Solve for \(a\): \(\;30=5a\)

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Betsy cc
Betsy
Winston cc
Winston
David cc spanish language icon
David

4
Proportions

Problem 1

In the proportion \(\frac{3}{4}=\frac{6}{8}\), 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 \(x\): \(\displaystyle\frac{2/3}{5}=\displaystyle\frac{x}{6}\)

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Matt cc
Matt
David cc spanish language icon
David
Problem 7

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

5
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

6
Similar Figures

Problem 1

Two triangles are similar, one has sides \(x, 24,\) and \(28\). The second has sides \(5, 6,\) and \(7\) respectfully. Find side \(x\).

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

The width and height of the two video clips are proportional. Find the height, \(h\), in pixels of the larger video window.

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

Draw a triangle similar to triangle \(ABC\), if \(AC\) is proportional to \(DF\). Make \(E\) the third vertex of the new triangle.

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

A building casts a shadow of \(105\) feet while a \(21\)-foot flagpole casts a shadow that is \(15\) feet. Find the height of the building.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 5

The entire length of a violin is \(24\) inches, while the body length is \(15\) inches. Find the body length of a cello if the entire length is \(48\) inches.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Aaron cc
Aaron
Problem 6
example image
Choose instructor to watch:
Katherine cc
Katherine
Octabio cc
Octabio
Octabio spanish language icon
Octabio

7
Test Yourself!

Problem 1

Write a fraction in lowest terms: 24 to 8.

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Richard cc
Richard
Sirena cc
Sirena
Problem 2

Write as a fraction in lowest terms: \(\displaystyle\frac{3}{4}\) to \(\displaystyle\frac{5}{6}\).

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Richard cc
Richard
Sirena cc
Sirena
Problem 3

Write as a fraction in lowest terms: 5 to 3\(\displaystyle\frac{1}{3}\).

Choose instructor to watch:
Richard cc
Richard
Sirena cc
Sirena
Problem 4

Write fraction in lowest terms: 0.18 to 0.6.

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Richard cc
Richard
Sirena cc
Sirena
Problem 5

Write as a fraction in lowest terms: \(\displaystyle\frac{3}{11}\) to \(\displaystyle\frac{5}{11}\).

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Richard cc
Richard
Sirena cc
Sirena
Problem 6

A car travels 414 miles on 18 gallons of gas. What is the rate of gas mileage in miles per gallon?

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Richard cc
Richard
Sirena cc
Sirena
Problem 7

Find the unknown term in the proportion: \(\displaystyle\frac{5}{6}\)=\(\displaystyle\frac{30}{x}\)

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Richard cc
Richard
Sirena cc
Sirena
Problem 8

Find the unknown term in the proportion: \(\displaystyle\frac{1.8}{6}\)=\(\displaystyle\frac{2.4}{x}\)

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Richard cc
Richard
Sirena cc
Sirena
Problem 9

A baseball player gets 9 hits in his first 21 games of the season. If he continues at the same rate, how many hits will he get in 56 games?

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Richard cc
Richard
Sirena cc
Sirena
Problem 10

The scale on a map indicates that 1 inch of the map corresponds to an actual distance of 60 miles. Two cities are 2\(\displaystyle\frac{1}{4}\) inches apart on the map. What is the actual distance between the two cities?

Choose instructor to watch:
Richard cc
Richard
Sirena cc
Sirena
Problem 11
example image
Choose instructor to watch:
Richard cc
Richard
Sirena cc
Sirena