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Rational Equations
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These problems involve fractional equations which contain variable expressions in the denominators. While many of them are of the proportion form,
students should be aware of any restrictions placed on the variables.
- Related Resources
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Interactive resources from our Math Tools project:
Algebra: Rational Equations
The closest match in our Ask Dr. Math archives:
High School: Basic Algebra
NCTM Standards:
Algebra Standard for Grades 9-12
Access to these problems requires a Membership.
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'Ace' Trotter
- Terry Trotter
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Algebra, difficulty level 1. A problem from the sports world regarding free-throw percentages.
... more>>
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Are You Positive?
- Steve Risberg
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Algebra, difficulty level 3. Find all values of x that make a rational expression have a positive value.
... more>>
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Blowin' in the Wind
- Steve Weimar Steve Risberg
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Algebra, difficulty level 3. A plane flies a round-trip on a calm day and then flies the same trip
on a windy day. How do the flying times compare?
... more>>
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Cherokee Creek Checkers Club
- Terry Trotter
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Algebra, difficulty level 1. Until one month ago, the Checkers Club had won 40 of 90 matches so far this year. But last
month they won 3 of every 5 games they played. How many games did
they play last month if their overall winning percentage is now 52%?
... more>>
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Examining an Equation
- Steve Risberg
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Algebra, difficulty level 2. Find integer solutions to an equation in two variables.
... more>>
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Family Fun
- Molly Stanley and Steve Risberg
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Algebra, difficulty level 3. The Gonzalez family is competing in a relay race where each family
member runs one lap. How long did it take Vicenta to run hers?
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Filling the Aquarium
- Terry Trotter
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Algebra, difficulty level 2. A workman at a zoo has to clean an aquarium, but forgets to do an important task, thus causing a problem (for us).
... more>>
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Fraction Action!
- Steve Risberg
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Algebra, difficulty level 2. What happens when you add the denominator to both the numerator and denominator of a fraction?
... more>>
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Fraction Debate
- Steve Risberg
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Algebra, difficulty level 3. Three students disagree about what happens when you perform a certain operation on a positive proper fraction. Which student do you agree with? Why?
... more>>
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Jack and Jill Go Jogging
- Terry Trotter
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Algebra, difficulty level 2. Two famous Mother Goose characters take up aerobics, running at some numerical speeds while exercising. How fast can each one jog?
... more>>
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The Length of Larry's Rectangle
- Larry Sue
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Algebra, difficulty level 2. Larry wants to know the length of his rectangle. Can you help him?
... more>>
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Make the Save!
- Steve Risberg
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Algebra, difficulty level 1. A hockey goalie has saved 112 out of 131 shots so far this season.
How many consecutive shots does she need to save to raise her save
percentage to .900?
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Marathon Mitch
- Terry Trotter
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Algebra, difficulty level 2. Mitch runs a road race and increases speed twice during the race.
Given his total finishing time, determine his standard running rate.
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My Bag of Marbles
- Terry Trotter
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Algebra, difficulty level 2. Find the probability of drawing a blue marble after additional marbles have been placed in a bag.
... more>>
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Painting Partners
- Terry Trotter
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Algebra, difficulty level 1. Two house painters combine their skills and talents to make short order of a painting job.
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Parakeets on Parade
- Terry Trotter
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Algebra, difficulty level 2. A flock of parakeets flies a round trip to the feeding ground and
back. Given the total time and distance of the round trip, and the
speed of the wind in each direction, find the flying speed of the
parakeets.
... more>>
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Pressed for Time
- Steve Risberg
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Algebra, difficulty level 2. Due to a late breaking story, a newspaper must use both presses to get
an edition printed in time. Find how long it takes to print a normal
edition using only the newer press.
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Ration Ratios
- Steve Risberg
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Algebra, difficulty level 3. Determine the ratio of vegetarian meals to vegetarians at the luncheon.
... more>>
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Romance by Rowboat
- Terry Trotter
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Algebra, difficulty level 1. Romance on the river motivates a nice upstream-downstream sort of problem.
... more>>
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Take Me Out to the Ballgame
- Annie Fetter
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Algebra, difficulty level 4. Determine how many innings a pitcher has thrown as his Earned Run Average changes during a game.
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The Great Northern Triathlon
- Steve Risberg
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Algebra, difficulty level 2. Sven skis, skates, and snowshoes in the winter triathlon. Use the
given information to determine how fast he snowshoes.
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Tiffany's Triumphs
- Terry Trotter
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Algebra, difficulty level 1. Given the number of games that Tiffany has played so far and the number that she has won, how many games would she have to win in a row to get her winning percentage up to 60%?
... more>>
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To B or Not To B
- Steve Risberg
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Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the
ratio of B's to total letters in the nth term.
... more>>
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To Grandmother's House We Go
- Ethel Breuche
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Algebra, difficulty level 4. Red Riding Hood goes to visit Grandmother for the holidays at the same time that Grandmother heads out to visit Red. What is the ratio of their speeds?
... more>>
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Vexing Variables
- Steve Risberg
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Algebra, difficulty level 3. Use two algebraic statements involving three variables to find the
numeric value of the ratio of two of those variables.
... more>>
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