Math Forum - Problems Library - Middle School, Fractions/Decimals/Percents

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Middle School: Fractions, Decimals, Percents

In grades 6-8, students work flexibly with fractions, decimals, and percents, learning to compare and order them and to find their approximate locations on a number line. Students develop meaning for percents greater than 100 and less than 1, and explore the meaning and effects of arithmetic operations with fractions and decimals. They also learn to judge the reasonableness of estimates, and to convert among fractions, decimals, and percents.

Problems that allow middle-school students to practice these skills are listed below. They address the NCTM Number and Operations Standard for Grades 6-8 expectations that students should be able to work flexibly with fractions, decimals, and percents to solve problems; compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line; and understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

For background information elsewhere on our site, explore the Middle School Fractions & Percents area of the Ask Dr. Math archives, and see Fractions, Decimals, Percentages from the Dr. Math FAQ. For relevant sites on the Web, browse and search Fractions/Decimals/Percents in our Internet Mathematics Library; to find middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.


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>>

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>>

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>>

Mathematics Club Membership - Judy Ann Brown
Middle School, difficulty level 2. Find the number of students in the Mathematics Club using the given information. ... 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>>

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>>

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>>

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>>

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

Where Does Mrs. Darien Live? - Judy Ann Brown
Middle School, difficulty level 2. Use clues to help Mrs. Darien's students find her house number. ... more>>

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