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Operations with Numbers

Problems in this category can be solved using basic operations (addition, subtraction, multiplication, division, exponentiation), applying estimation skills, applying the order of operations, or using the properties of numbers (identity, associative, multiplicative, distributive). They should be suitable for the beginning prealgebra student.
Some of these problems are also in the following subcategories:
 Related Resources

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

Accuracy Please
 Judy Ann Brown

PreAlgebra, difficulty level 3. Considering precision, accuracy, and appropriateness in finding the volume of a cone.
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Anh's Code
 Annie Fetter

PreAlgebra, difficulty level 2. Decode the five mathematical operations symbolized in three equations, then evaluate an expression.
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BacktoSchool 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?
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Baseball Attendance Figures
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the difference between the greatest possible number of people at the stadium and the least possible number of paid admissions to the game.
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Building a Snow Statue
 Judy Ann Brown

PreAlgebra, difficulty level 3. Determine the height of a snow statue using the given information.
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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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Calculator KeyIn
 Terry Trotter

PreAlgebra, difficulty level 1. Why do the two calculators give different answers to the problem?
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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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Coding Conundrums
 Mary DeYoung & class

PreAlgebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
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Commuting Conundrum
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar.
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The Complex Apartment Complex
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above.
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Dishwasher Discounts
 Pat Hagan

PreAlgebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal.
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Divisible by a Dozen
 Terry Trotter & Annie Fetter

PreAlgebra, difficulty level 3. If you take any three consecutive integers, multiply the first times the square of the second, then multiply by the third, is 12 a factor of the product?
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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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Do you listen to WMTH or WALG?
 Judy Ann Brown

PreAlgebra, difficulty level 4. Each week listeners switch radio stations. Predict the longterm distribution of listeners for each station.
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Fall Festival Frolic
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different types of candy are needed to make at least 50 different treat bags?
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Falling into Sequences
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the 20th term in a sequence using both a recursive method and an explicit formula.
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Frequent Flier Figuring
 Judy Ann Brown

Math Fundamentals, difficulty level 2. Use Web resources to help plan the shortest route from Allentown, Pennsylvania, to New Orleans, Louisiana.
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The Good Samaritan
 Piedmont High School 2nd and 7thperiod Geometry Classes

PreAlgebra, difficulty level 4. Can the butler afford the paint needed to repair the sign? Did the butler do it?
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Guess My Number If You Can!
 Judy Ann Brown

PreAlgebra, difficulty level 4. Use division clues to reveal the secret number.
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Happy New Year!
 Judy Ann Brown

PreAlgebra, difficulty level 4. A puzzle for the new year: how is the grid designed?
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Homerun Percentages
 Judy Ann Brown

PreAlgebra, difficulty level 3. Baseball box scores give us a chance to practice percent skills.
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I Get A Kick Out Of Soccer!
 Judy Ann Brown

Math Fundamentals, difficulty level 3. How many laps of the soccer field would a team member need to complete to run more than a mile?
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Inching Along Down the Football Field
 Terrel Trotter

Math Fundamentals, difficulty level 3. Fred put his football down on a goal line of the 100yard field. He then moved it forward half the field distance, over and over again. When did the distance first become less than one inch?
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An Interesting Integer
 Judy Ann Brown

PreAlgebra, difficulty level 2. I'm thinking of a particular integer. It is a multiple of three, five, and seven. No digit occurs more than once. Can you find my number?
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January Sales
 Judy Ann Brown

PreAlgebra, difficulty level 2. Mathematicians, put away your calculators and help Lynne estimate the cost of a set of golf clubs.
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Kate's Combination
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Find Kate's locker combination using mathematical clues. Is there more than one possibility?
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Lost in Des Moines
 Judy Ann Brown

PreAlgebra, difficulty level 2. Calculate the speed of a car using given information.
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The Magic of Number 6174
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Have fun exploring this number magic.
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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.
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The Name Game
 Judy Ann Brown

PreAlgebra, difficulty level 3. The first student says his/her own name; the second student repeats the first student's name and adds his/her own name... How many names are said if the numbers of students in my math classes on the first day are 27, 28, 32, 31, and 30?
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Office Tile Choice
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
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Olympic Temperature
 Judy Ann Brown

PreAlgebra, 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.
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Open and Shut Case
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the locker combination using mathematical clues.
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Operating Diagonally
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Think about the effect of multiplication and addition on the numbers in the hundreds chart.
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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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Organization of Data
 Judy Ann Brown

PreAlgebra, difficulty level 2. Use the information on the graph to find the range, mean, median, and mode of the data.
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Partial Area
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square.
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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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Ready for Football?
 Terry Trotter & Suzanne Alejandre

PreAlgebra, difficulty level 2. Find the final score of the game between the Eagles and the Dragons.
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Rounding Mountains
 Judy Ann Brown

Math Fundamentals, difficulty level 2. Use estimated figures to determine the maximum and minimum differences between the heights of two mountains.
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Runsums, Part 1
 Ron Knott

PreAlgebra, difficulty level 3. By spotting the pattern, tell me the smallest number that is a sum of a run of one hundred consecutive numbers.
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Runsums, Part 2
 Ron Knott

PreAlgebra, difficulty level 3. Explore number patterns and report on what you have learned.
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Sailing Around the World
 Leon Roland & class

PreAlgebra, difficulty level 2. Determine the amounts of the supplies that Giuseppi Linguini will need to sail around the world.
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Scientific Sums
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the sum of a set of numbers written in scientific notation.
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The Silver Mile
 Judy Ann Brown

PreAlgebra, difficulty level 3. Determine the total value of the coins in a silver mile.
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A Simple Reversal
 Judy Ann Brown

Math Fundamentals, difficulty level 1. The product of 3 and 24 is 72. The sum of 3 and 24 is 27, which is the reverse of 72. Can you find other pairs of numbers such that their product is the reverse of their sum?
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Snow Day Phone Chain
 Judy Ann Brown

PreAlgebra, difficulty level 4. Use the given information to find out how many phone calls were made.
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A Surfer's Tessellation
 Mr. Marthinsen's First Period Class

PreAlgebra, difficulty level 2. Shane is retiling his surf shack. How many of each kind of tile will he need, and what does a big tile cost?
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Threedimensional Television
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook.
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Time Is Power
 Terry Trotter

PreAlgebra, difficulty level 2. During which hour of the day am I most likely to see a square number
on my computer
time display? How many times total during the day does this happen?
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Treasure Hunt Math
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use clues to find the mystery palindrome.
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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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