Proportion Word Problems
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Examples, videos, worksheets, solutions, and activities to help Algebra students learn how to solve word problems that involve proportions.
Compare Direct & Inverse Proportion Word Problems
Direct proportion and inverse proportion are two types of proportional relationships that describe how two quantities change relative to each other. Understanding the distinction is key to setting up and solving them correctly. Here’s a comparison of direct and inverse proportion problems, along with examples and step-by-step solutions.
The following diagram gives a comparison of direct and inverse proportion.
Proportion Word Problems
Direct Proportion Problems
Inverse Proportion Problems
Proportion Word Problems
Ratio & Proportion Problems
Ratio & Proportion Worksheets
Practice your skills with the following worksheets:
Printable & Online Ratio & Proportion Worksheets
1. Direct Proportionality (Direct Variation)
Definition: Two quantities are directly proportional if they increase or decrease at the same rate.
Mathematically: \(y = kx\)
where:
\(y\) and \(x\) are the two variables,
\(k\) is the constant of proportionality.
Key Characteristics:
If \(x\) increases, \(y\) increases proportionally.
If \(x\) decreases, \(y\) decreases proportionally.
The ratio \(\frac{y}{x}=k\) remains constant.
For two pairs of values: \(\frac{y_{1}}{x_{1}}=\frac{y_{2}}{x_{2}}\)
2. Inverse Proportionality (Inverse Variation)
Definition: Two quantities are inversely proportional if one quantity increases while the other decreases at a proportional rate.
Mathematically:
\(y=\frac{k}{x}\)
or
\(xy=k\)
where:
\(y\) and \(x\) are the two variables,
\(k\) is the constant of proportionality.
Key Characteristics:
If x increases, y decreases proportionally.
If x decreases, y increases proportionally.
The product \(xy=k\) remains constant.
For two pairs of values: \(x_1y_1=x_2y_2)
Videos
Compare direct and inverse proportion
Direct proportion and inverse proportion (also sometimes called indirect proportion).
Word Problems Involving Proportions
Two problems showing how to use proportions to solve certain word problems.
Examples:
(1) Jacob ran 10 miles in 80 minutes. At that rate how far would he run in 2.5 hours?
(2) Mark bought 12 cookies at $2.70. At that rate how much would it cost him to buy 20 cookies?
Algebra Help: Solving Proportion Word Problems
This video demonstrates how to setup and solve a proportion word problem. We must make sure to have the same units in the numerators and the denominators, then we can cross multiply and solve for our unknown.
Examples:
(1) Biologists tagged 900 rabbits in Bryer Lake national park. At a later date, they found 6 tagged rabbits in a sample of 2000. Estimate the total number of rabbits in Bryer Lake national park.
(2) Mel fills his gas tank with 6 gallons of premium unleaded gas for a cost of $26.58. How much would it cost to fill an 18 gallon tank?
(3) If twelve pairs of jeans cost $513.72, how much would four pairs cost?
(4) If 4 U.S. dollars can be exchanged for 1.75 Euros, how many Euros can be obtained for 144 U.S. dollars?
Inverse proportion word problem
Proportion Word Problem
How to create a proportion and solve it.
Example: Crayola can make 2400 crayons in 4 minutes. How many can be made in 15 min? How long will it take to make 18,000?
Proportion Word Problems - Math Help
Students learn that a proportion is an equation that states that two ratios are equal. Students then learn the properties of proportion, and are asked to solve for x in given proportions, and to solve word problems involving proportions.
Example: If a car gets 20 miles to the gallon, how many gallons of gas will it use to travel 180 miles?
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