Ask Dr. Math
Middle School Archive
Dr. Math Home ||
Middle School ||
High School ||
Dr. Math FAQ
See also the
Dr. Math FAQ:
order of operations
3D and higher
Browse Middle School Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Direct and indirect variation.
Inequalities and negative numbers.
Positive/negative integer rules.
Solving simple linear equations.
- Calendar Puzzle [12/02/1999]
A student cuts a 3x3 square from a calendar page. If the sum of the nine
dates is divisible by 19, what is the date in the lower left-hand corner
of the square?
- Can Police Clock Speeding Car? [06/30/2003]
Car A travels 3 miles at an average speed of 87 mph. Car B begins the
same distance from an initial speed of 0, but accelerates from 0-100
mph in 14 seconds. What must the maximum speed of Car B be in order to
catch up to Car A at the end of the 3 miles?
- Can Variables Be Capital Letters? [09/19/2006]
Can you use capital letters for variables, like X, or does it always
have to be x?
- Car Laps [01/26/2001]
On a race track, one car travels 5 laps a minute and another car travels
8 laps a minute. How long will it be before the second car laps the
- Cars Leaving at Different Times [09/28/2003]
Two cars leave a garage traveling in opposite directions. One car
leaves at 8 am and averages 60 mph. The other car leaves at 9 am and
averages 50 mph. At what time will they be 225 miles apart?
- Challenging Algebra Age Problem [02/29/2004]
A man has nine children whose ages are at an exact interval. The sum
of the squares of the ages of each is the square of his own age. What
is the age of each child and the man?
- Checking Equations [01/30/2001]
I know how to solve an equation, but I can't figure out how to check it.
- Combining Positive and Negative Exponents [06/30/1999]
When you simplify exponential expressions using the power rule, how do
you combine positive and negative exponents in the numerator and
- Common PEMDAS Errors [12/28/2001]
What does PEMDAS mean?
- Comparing Numbers: Two Equations, Two Unknowns [01/14/1998]
One number is 25 percent of another. The larger number is 12 more than
the smaller. What are the numbers?
- Comparison of On-line Rates [5/20/1996]
Jack is interested in two on-line companies, Easy Comp and Destruct
- Completing the Square: How Does it Work? [01/20/1999]
Can you explain why completing the square works? How exactly do you do
- Completing the Square to Solve Quadratic Equations [12/21/1998]
Steps for solving quadratic equations.
- Completing the Square Using a Diagram [11/09/1999]
How can I draw a diagram that represents the "completing the square"
operation of x^2 - 6x + ...?
- Complicated Age Problem [02/04/2002]
Eight years ago Mary was half as old as Jane will be when Jane is one
year older than Tim will be at that time when Mary will be five times as
old as Tim will be two years from now...
- Complicated Computation [2/23/1995]
Could you please answer this math question? 34(67+789(47*79(243-
157)76-31)-85)48(34*423)-879) = ?
- Concept of Factoring [03/22/1997]
Could you explain the concept of factoring and give examples of its
- Confusion over Interpretation of PEMDAS [03/24/2005]
Students take PEMDAS letter by letter, tending to do all
multiplication before any division, rather than working from left to
right. Here's a suggestion on how to help avoid that confusion.
- Consecutive Integers [04/16/1997]
If the sum of two consecutive integers is less than one hundred, find the
- Consecutive Integers Problem [2/16/1996]
Find three consecutive integers whose sum equals 66.
- Consecutive Odd Integers [08/28/1997]
I need to know three consecutive odd integers that equal 150.
- A Container Holds 5/8 Gallon... [11/05/1997]
If the container is 4/5 full and then 25 percent of the liquid is lost
due to evaporation, how much liquid is left in the container?
- Converting between Celsius and Fahrenheit [06/23/2009]
How can I use algebra to derive the unusual temperature conversion
formulas °F = 9/5(°C + 40) - 40 and °C = 5/9(°F + 40) - 40 ?
- Converting Seconds to MPH [07/11/2000]
I'm looking for a chart that converts the number of seconds needed to
travel one mile to miles per hour.
- Converting to an Equation [06/13/1999]
How can I convert "the square of a number is 96 more than 10 times the
number" into an equation?
- Correct Usage of Equal and Equivalent in Math Statements [02/20/2008]
Is there a mathematical difference between "equal" and "equivalent"?
- Cost of a Ruler [08/01/1997]
Alice and Betty want to buy the same kind of ruler but Alice is 22 cents
short and Betty is 3 cents short...
- Cost of Pencils [6/26/1996]
Drawing pencils cost ... and coloured pencils cost... Two dozen assorted
pencils cost $2.16. How many coloured pencils are there?
- Cycling Digits [01/07/1998]
I have in mind a number which when you remove the units digit and place
it at the front, gives the same result as multiplying the original number
- Cycling Motion Problem [6/26/1996]
A cyclist travels from A to B over a high pass...
- Cycling Uphill [7/8/1996]
I don't know how to handle the unknown speed at which the cyclist travels
- Dealing with Duplicate Elements [05/17/2002]
I need to develop a general formula to calculate the number of
different 'words' that can be formed from an N letter word where
some of the letters may be duplicated.
- Definition of 'Solve' [11/29/2005]
In algebra class I was told that a problem such as 2 + 2 cannot be
solved. In order to 'solve' a problem there has to be a variable
involved. Is this correct?
- Dependent and Independent Variables [12/26/2001]
Identify the dependent and independent variable: time it takes to travel
50 miles and the speed of the vehicle.
- Deriving the Quadratic Formula [10/15/1998]
How do you derive the quadratic formula from ax^2 + bx + c = 0?
- Difference in Radius, Difference in Speed [06/25/2002]
What is the difference in speed between a point on the tread of a tire
and another point closer to the center, if the tire is rotating at
- Difference of Squares of Two Integers [7/2/1996]
Which positive integers can be written as the difference of the squares
of two integers?
- Difference of Two Squares [08/17/1997]
Prove that every cube can be expressed as the difference of two squares.
- The Difference of x and y... [06/05/2003]
The difference of a number and its square is 42. Is the equation x^2 -
x = 42 or x - x^2 = 42?
- Different Approach to a Set of Equations [11/13/2002]
The sum of four numbers is 22. The first number is twice the
difference of the second and the fourth. The second number is five
times the difference of the third and the fourth. The third number
is twice the difference of the first and the fourth. What are the
Search the Dr. Math Library:
© 1994- The Math Forum at NCTM. All rights reserved.
Home || The Math Library || Quick Reference || Search || Help