Math Forum - Problems Library - Pre-Algebra, Ratio and Proportion

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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 6-8

Access to these problems requires a Membership.

Apple Picking - Richard Tchen, Suzanne Alejandre, Annie Fetter
Pre-Algebra, difficulty level 1. Calculate the approximate cost of each apple at the pick-your-own orchard. ... more>>

Balancing Mobiles - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile. ... more>>

Bartering for Bananas - Suzanne Alejandre
Pre-Algebra, difficulty level 4. How many bananas can Byron get with five fish? ... more>>

Bella's Bagel Bakery - Suzanne Alejandre
Pre-Algebra, difficulty level 1. How much more area is covered with cream cheese on the large bagel than on the small bagel? ... more>>

The Big Picture! - Judy Ann Brown
Pre-Algebra, difficulty level 3. A picture is enlarged to four times its area. ... more>>

Boxes of Stationery - Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery? ... more>>

Building on Water - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building. ... more>>

Buying Cola - Leon Roland & class
Pre-Algebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy? ... more>>

Citius, Altius, Fortius - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Would record-holding speed skaters and runners break the speed limit in a residential zone? ... more>>

The Cost of Chocolate - Suzanne Alejandre
Pre-Algebra, difficulty level 2. How can I get the most chocolate for my $30.00? ... more>>

Days on Other Planets - Cynthia Lanius, Suzanne Alejandre
Pre-Algebra, difficulty level 2. How old in Earth years would you be after spending time on another planet? ... more>>

Designing Doorways for Rich and Riz - Suzanne Alejandre
Pre-Algebra, 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. ... more>>

Downhill All the Way - Judy Ann Brown
Pre-Algebra, 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? ... more>>

Downloading Duel - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Whose downloading task should take longer? ... more>>

Drama Dollars - Andrea Stitt and Suzanne Alejandre
Pre-Algebra, difficulty level 2. Find the percentage of the earnings that came from the adult tickets sold by the school drama club. ... more>>

Election Day in Prealgpoweria - Steve Risberg, Suzanne Alejandre
Pre-Algebra, difficulty level 3. How many votes does each candidate in Prealgpoweria receive and how many eligible voters are there? ... more>>

Garden Grove - Steve Risberg & Stephen Weimar
Pre-Algebra, 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. ... more>>

The Gates - Suzanne and Richard Alejandre
Pre-Algebra, difficulty level 3. How much time did Suzanne spend walking on "The Gates" pathway? ... more>>

Gearing Up - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears. ... more>>

Golfing Luck? - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Work with probability on the practice hole of the golf course. ... more>>

He Ate It All! - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. The professor ate an entire pizza in 28 minutes. Figure out the size of the pizza. ... more>>

Heavy Hoisting - Math Forum Staff
Pre-Algebra, difficulty level 2. Using the information given in the problem, find the weight of an average human adult. ... more>>

How Wide Is My Garden? - Judy Ann Brown
Pre-Algebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden. ... more>>

I'm a Groundhog? - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Using Suzanne's height, Phil's height, and Suzanne's shadow length, find Phil's shadow length. ... more>>

Join Us for a Quarter-pound Burger - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Work with fractions and percents to help plan this cookout. ... more>>

Kaytee's Contest - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use clues to figure out how much Kaytee's cows weigh. ... more>>

Lee's Lawn Chair - Lee & Suzanne Alejandre
Pre-Algebra, difficulty level 3. Using the measurements given in the problem, determine the scale factor used to create the larger chair. ... more>>

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 thirty-two seconds pass between the flash of the lightning bolt and the sound of the thunder? ... more>>

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? ... more>>

Membership Boom! - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the number of students involved in the Math Club, and the number of students in the school. ... more>>

Mikey and Lily Eat Cereal - Stephen Weimar, Annie Fetter, Suzanne Alejandre
Pre-Algebra, difficulty level 3. How much of a box of cereal do Mikey and Lily each have left? ... more>>

Milk Madness - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes. ... more>>

The Most Appealing Nose Contest - Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the given information to determine the amount of money raised for the Humane Society by the Student Council. ... more>>

My Almond Cookie Bake - Lisa Lavelle
Pre-Algebra, difficulty level 3. Convert this cookie recipe to feed the March Madness celebrators. ... more>>

New Home for Fibonacci and Fractal - Judy Ann Brown
Pre-Algebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15-gallon aquarium. ... more>>

The Nutty Squirrel - Alice Miller
Pre-Algebra, difficulty level 3. How high could a human jump if she could jump with the power of a squirrel? ... more>>

Oceans of Fun - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help the Math Club approximate the portion of the Earth's surface that is covered by the oceans. ... more>>

The Oracle's Oration - Annie Fetter
Pre-Algebra, difficulty level 3. Explain how payment should be distributed based on the number of rolls two people shared with the group of three. ... more>>

Ostrich Llama Count - Suzanne Alejandre
Pre-Algebra, 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. ... more>>

Peeling Potatoes - Terry Trotter
Pre-Algebra, difficulty level 2. How many potatoes did Annie and Steve have to peel? ... more>>

Photo Wall - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Find the dimensions of the large poster. ... more>>

Pi Day Treats - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration. ... more>>

A Pound of Valentine's Chocolates - Suzanne Alejandre, Claire Mead
Pre-Algebra, difficulty level 2. How long should a one pound box of chocolates last if Isolde eats it alone? ... more>>

Saturday Bike Ride - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Seesaw - Suzanne Alejandre
Pre-Algebra, difficulty level 3. How did the four friends balance on the seesaw? ... more>>

Sing a Song of Sunscreen - Mai Sidawi and Lillian Ray
Pre-Algebra, 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 my-neck-is-sunburnt blues. ... more>>

Sizing Up Sequoias - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Compared to a given seed weight, find out how much an average mature sequoia weighs. ... more>>

A Snowy Driveway - Claire Mead
Pre-Algebra, difficulty level 3. Usually Bertha and Gertrude shovel snow together. How long would it take Bertha to shovel the same amount alone? ... more>>

Tasty Tomato Salsa - Suzanne Alejandre
Pre-Algebra, 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? ... more>>

The World's Largest Popcorn Ball* - Annie Fetter
Pre-Algebra, difficulty level 1. How many boxes of microwave popcorn would it take to make a giant popcorn ball? ... more>>

Tiling Triangles - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it. ... more>>

Timber! - Steve Risberg
Pre-Algebra, difficulty level 3. A tree breaks three-eighths 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? ... more>>

Two Heads Are Better Than One - Lillian Ray
Pre-Algebra, difficulty level 3. Given the combined number of heads and legs of ostriches and pushmi-pullyus, will Raquel and Esperanza be able to know for sure how many ostriches and pushmi-pullyus are on the farm? ... more>>

Valley Springs Snow Cream - Kelly Crisp
Pre-Algebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream. ... more>>

Watch Where You Step! - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Using statistics about slugs, about how many might be in a certain sized yard? ... more>>

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