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Ratio and Proportion

These problems require students to understand and use ratios and proportions to represent quantitative relationships. They may require developing,
analyzing, and explaining methods such as scaling, finding equivalent ratios to solve problems involving proportions, and unit pricing.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Ratio and Proportion
The closest match in our Ask Dr. Math archives:
Middle School: Ratio and Proportion
NCTM Standards:
Number and Operations Standard for Grades 68
Access to these problems requires a Membership.

Apple Picking
 Richard Tchen, Suzanne Alejandre, Annie Fetter

PreAlgebra, difficulty level 1. Calculate the approximate cost of each apple at the pickyourown orchard.
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Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
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Bartering for Bananas
 Suzanne Alejandre

PreAlgebra, difficulty level 4. How many bananas can Byron get with five fish?
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Bella's Bagel Bakery
 Suzanne Alejandre

PreAlgebra, difficulty level 1. How much more area is covered with cream cheese on the large bagel
than on the small bagel?
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The Big Picture!
 Judy Ann Brown

PreAlgebra, difficulty level 3. A picture is enlarged to four times its area.
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Boxes of Stationery
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
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Building on Water
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building.
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Buying Cola
 Leon Roland & class

PreAlgebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy?
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Citius, Altius, Fortius
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Would recordholding speed skaters and runners break the speed limit in a residential zone?
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The Cost of Chocolate
 Suzanne Alejandre

PreAlgebra, difficulty level 2. How can I get the most chocolate for my $30.00?
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Days on Other Planets
 Cynthia Lanius, Suzanne Alejandre

PreAlgebra, difficulty level 2. How old in Earth years would you be after spending time on another planet?
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Designing Doorways for Rich and Riz
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Find the height for a doorway for Riz that gives him a proportional
amount of room as Rich has in the pictured doorway.
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Downhill All the Way
 Judy Ann Brown

PreAlgebra, difficulty level 2. Starting at 10,000 feet above sea level, descending a 6% grade followed by a 4% grade will put a car how many feet above sea level?
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Downloading Duel
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Whose downloading task should take longer?
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Drama Dollars
 Andrea Stitt and Suzanne Alejandre

PreAlgebra, difficulty level 2. Find the percentage of the earnings that came from the adult tickets sold by the school drama club.
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Election Day in Prealgpoweria
 Steve Risberg, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many votes does each candidate in Prealgpoweria receive and how
many eligible voters are there?
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Garden Grove
 Steve Risberg & Stephen Weimar

PreAlgebra, difficulty level 3. Determine the amount of dirt and the amount of peat moss needed to have the correct ratio of dirt to peat moss for the garden.
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The Gates
 Suzanne and Richard Alejandre

PreAlgebra, difficulty level 3. How much time did Suzanne spend walking on "The Gates" pathway?
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Gearing Up
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Think about and explain the relationship between three differentsized gears.
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Golfing Luck?
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Work with probability on the practice hole of the golf course.
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He Ate It All!
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. The professor ate an entire pizza in 28 minutes. Figure out the size of the pizza.
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Heavy Hoisting
 Math Forum Staff

PreAlgebra, difficulty level 2. Using the information given in the problem, find the weight of an
average human adult.
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How Wide Is My Garden?
 Judy Ann Brown

PreAlgebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden.
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I'm a Groundhog?
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Using Suzanne's height, Phil's height, and Suzanne's shadow length, find Phil's shadow length.
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Join Us for a Quarterpound Burger
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Work with fractions and percents to help plan this cookout.
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Kaytee's Contest
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Use clues to figure out how much Kaytee's cows weigh.
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Lee's Lawn Chair
 Lee & Suzanne Alejandre

PreAlgebra, difficulty level 3. Using the measurements given in the problem, determine the scale
factor used to create the larger chair.
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Lightning Strikes
 Judy Ann Brown

midpow, difficulty level 1. It takes five seconds for the sound of thunder to travel one mile.
How far away is the lightning if thirtytwo seconds pass between the
flash of the lightning bolt and the sound of the thunder?
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Luscious Lemonade
 Judy Ann Brown

Math Fundamentals, difficulty level 3. The label on the lemon concentrate says that I need to mix 2 cups of concentrate with 3 cups of water. How much lemon concentrate should I buy to make 25 gallons of lemonade?
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Membership Boom!
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the number of students involved in the Math Club, and the number of students in the school.
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Mikey and Lily Eat Cereal
 Stephen Weimar, Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How much of a box of cereal do Mikey and Lily each have left?
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Milk Madness
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes.
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The Most Appealing Nose Contest
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to determine the amount of money raised for the Humane Society by the Student Council.
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My Almond Cookie Bake
 Lisa Lavelle

PreAlgebra, difficulty level 3. Convert this cookie recipe to feed the March Madness celebrators.
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New Home for Fibonacci and Fractal
 Judy Ann Brown

PreAlgebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15gallon aquarium.
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The Nutty Squirrel
 Alice Miller

PreAlgebra, difficulty level 3. How high could a human jump if she could jump with the power of a squirrel?
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Oceans of Fun
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help the Math Club approximate the portion of the Earth's surface that is covered by the oceans.
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The Oracle's Oration
 Annie Fetter

PreAlgebra, difficulty level 3. Explain how payment should be distributed based on the number of rolls two people shared with the group of three.
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Ostrich Llama Count
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Given the combined number of heads and legs of ostriches and llamas, help Raul and Esteban figure out how many ostriches and how many llamas there are.
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Peeling Potatoes
 Terry Trotter

PreAlgebra, difficulty level 2. How many potatoes did Annie and Steve have to peel?
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Photo Wall
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Find the dimensions of the large poster.
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Pi Day Treats
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration.
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A Pound of Valentine's Chocolates
 Suzanne Alejandre, Claire Mead

PreAlgebra, difficulty level 2. How long should a one pound box of chocolates last if Isolde eats it
alone?
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Saturday Bike Ride
 Judy Ann Brown

PreAlgebra, difficulty level 2. Now that spring has arrived, Ali and Maya decide to dust off their bikes and go for a Saturday ride. Help find what time they will meet.
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Seesaw
 Suzanne Alejandre

PreAlgebra, difficulty level 3. How did the four friends balance on the seesaw?
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Sing a Song of Sunscreen
 Mai Sidawi and Lillian Ray

PreAlgebra, difficulty level 2. A poem will provide the clues / For you to help me to choose / The lowest SPF to buy / So I don't have to fry / And get the myneckissunburnt blues.
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Sizing Up Sequoias
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Compared to a given seed weight, find out how much an average mature sequoia weighs.
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A Snowy Driveway
 Claire Mead

PreAlgebra, difficulty level 3. Usually Bertha and Gertrude shovel snow together. How long would it
take Bertha to shovel the same amount alone?
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Tasty Tomato Salsa
 Suzanne Alejandre

PreAlgebra, difficulty level 2. If I use all of the olives, how many grams of tomatoes should I use to
keep the same proportions in my salsa recipe?
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The World's Largest Popcorn Ball*
 Annie Fetter

PreAlgebra, difficulty level 1. How many boxes of microwave popcorn would it take to make a giant
popcorn ball?
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Tiling Triangles
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it.
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Timber!
 Steve Risberg

PreAlgebra, difficulty level 3. A tree breaks threeeighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree?
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Two Heads Are Better Than One
 Lillian Ray

PreAlgebra, difficulty level 3. Given the combined number of heads and legs of ostriches and
pushmipullyus, will
Raquel and Esperanza be able to know for sure how many ostriches and
pushmipullyus
are on the farm?
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Valley Springs Snow Cream
 Kelly Crisp

PreAlgebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
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Watch Where You Step!
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Using statistics about slugs, about how many might be in a certain sized yard?
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