Math Forum - Problems Library - Pre-Algebra, Fractions, Decimals, and Percentages

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Pre-Algebra
operations with numbers
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Fractions, Decimals, and Percentages
Problems in this category require knowledge of fractions, decimals, and percentages including understanding the effects of arithmetic operations on these numbers and skill in converting between them. They may also require understanding of percents greater than 100 and less than 1.

Related Resources
Interactive resources from our Math Tools project:
   Math 7: Fractions
   Math 7: Percentages
The closest match in our Ask Dr. Math archives:
   Middle School: Fractions & Percentages
From our Teacher2Teacher service:
   FAQ: Fraction Help
NCTM Standards:
   Number and Operations Standard for Grades 6-8

Access to these problems requires a Membership.

Back-to-School Shopping - Judy Ann Brown
Math Fundamentals, difficulty level 2. Mrs. Bender noticed that the total of the items her children purchased was $155. Can you determine the cost of one pair of jeans? ... more>>

Batter Up! - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use statistics to help Lee convince his manager to give him a raise. ... more>>

Building a Snow Statue - Judy Ann Brown
Pre-Algebra, difficulty level 3. Determine the height of a snow statue using the given information. ... 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>>

Cara's Cookies - Cynthia Lanius
Pre-Algebra, difficulty level 2. How many cookies did Cara make for the Math Club Bake Sale? ... more>>

Car Rental Quandary - Judy Ann Brown
Pre-Algebra, difficulty level 3. Compare the car rental deals using the given information. ... 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>>

Coast to Coast Driving Costs - Suzanne and Richard Alejandre
Pre-Algebra, difficulty level 2. If the price of gas has increased 61% in the five years since we took our first coast to coast trip in October 2000, what would it cost per mile to make the same trip in October of 2005? ... more>>

Coin Count - Roya Salehi and Judy Ann Brown
Pre-Algebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank. ... more>>

Cyndy's Curtains - Cynthia Paul, Suzanne Alejandre, Annie Fetter
Pre-Algebra, difficulty level 2. How many sets of shorter curtains can Cyndy make from the one set of extra-long curtains that she already has? ... more>>

Cynthia's Solitaire Challenge - Cynthia Lanius, Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help Cynthia think about how to keep her winning percentage at 90% or above. ... more>>

Dishwasher Discounts - Pat Hagan
Pre-Algebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal. ... 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>>

Do you listen to WMTH or WALG? - Judy Ann Brown
Pre-Algebra, difficulty level 4. Each week listeners switch radio stations. Predict the long-term distribution of listeners for each station. ... 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>>

Duke is Missing - Judy Ann Brown
Pre-Algebra, difficulty level 3. Duke's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and tail combined. How long is Duke? ... 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>>

Gas Guzzlers - Mai Sidawi and Lillian Ray
Pre-Algebra, difficulty level 2. Students are asked to decide which car model to replace to get the most savings in gas costs. ... more>>

The Good Samaritan - Piedmont High School 2nd- and 7th-period Geometry Classes
Pre-Algebra, difficulty level 4. Can the butler afford the paint needed to repair the sign? Did the butler do it? ... 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>>

A Holiday Gift for Grandmother Brown - Judy Ann Brown
Pre-Algebra, difficulty level 3. Determine the cost of the dishwasher and the contribution from each of five children. ... more>>

Homerun Percentages - Judy Ann Brown
Pre-Algebra, difficulty level 3. Baseball box scores give us a chance to practice percent skills. ... more>>

January Sales - Judy Ann Brown
Pre-Algebra, difficulty level 2. Mathematicians, put away your calculators and help Lynne estimate the cost of a set of golf clubs. ... 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>>

Lemonade Fun - Maria Fung and her students
Pre-Algebra, difficulty level 2. How many cups of each size lemonade did Jose and Nick sell? ... more>>

Math Club Lollipop Profits - Judy Ann Brown
Math Fundamentals, difficulty level 3. The Math Club plans to sell lollipops. Help them to calculate their profit. ... 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>>

Office Tile Choice - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the total cost of purchasing tiles for my office. ... more>>

Olympic Temperature - Judy Ann Brown
Pre-Algebra, difficulty level 3. Compare the difference in temperatures between Sydney, Australia at 14 degrees Celsius and Swarthmore, Pennsylvania, U.S.A. at 63 degrees Fahrenheit. ... more>>

Postal Rates - Richard Tchen, Suzanne Alejandre
Pre-Algebra, difficulty level 3. Find the largest percentage increase in stamp price. ... 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>>

Price Fluidity - Judy Ann Brown
Pre-Algebra, difficulty level 2. Compare the per-gallon cost of eleven different liquids, and put them in order from least to most expensive. ... more>>

Scientific Sums - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the sum of a set of numbers written in scientific notation. ... more>>

Sharing Birthday Cake - Ian Underwood
Pre-Algebra, difficulty level 2. Ian and his father have the same birthday, and share a cake based on the ratio of their ages. Determine when Ian will get certain amounts of cake. ... more>>

Shine On Harvest Moon - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the area of the largest circle that can be cut from a nine-inch by twelve-inch sheet of paper. ... more>>

The Silver Mile - Judy Ann Brown
Pre-Algebra, difficulty level 3. Determine the total value of the coins in a silver mile. ... 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>>

Spring Garden Planning - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area as well as the length and width of my fractional garden. ... more>>

Super Bowl XXXIII - Judy Ann Brown
Pre-Algebra, difficulty level 2. Based on the winners and points scored during the past 15 Super Bowl games, which team should win Super Bowl XXXIII? ... more>>

A Surfer's Tessellation - Mr. Marthinsen's First Period Class
Pre-Algebra, difficulty level 2. Shane is re-tiling his surf shack. How many of each kind of tile will he need, and what does a big tile cost? ... more>>

Temperature Change - Judy Ann Brown
Pre-Algebra, difficulty level 2. Use the given information to find the temperature. ... more>>

Thanksgiving Travel - Suzanne Alejandre & Maria Fung and her students
Pre-Algebra, difficulty level 3. Help Zach decide whether to take the PA Turnpike or the scenic route to see his parents for Thanksgiving. ... more>>

Top Notch Nose Contest* - Judy Ann Brown, Suzanne Alejandre
Pre-Algebra, difficulty level 2. Use the given information to determine how many photos of pets were entered in the contest. ... 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>>

Waste Not, Want Not - Suzanne and Richard Alejandre
Pre-Algebra, difficulty level 2. Explain what you know about the number of bananas the store had at the beginning of the week. ... more>>

Which Coupon Is Better? - Cynthia Paul
Pre-Algebra, difficulty level 1. Help Cynthia decide which coupon will save her more money when she goes to the store to buy sheets. ... more>>

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