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.
- Savings on Gasoline [05/22/2001]
Your old car averaged 22 mpg and you new car should average 37 mpg.
Suppose you drive 12,500 miles per year and the cost of gas averages
$1.85 per gallon. How much will you save on gasoline each year?
- Scale Factor Acrobatics [07/15/2014]
A homeschooled teen struggles to make headway with a word problem in two
unknowns. After emphasizing the scale factor in their ratio, Doctor Ian models the
- Sets and Subsets [1/23/1995]
My teacher said that integers are a subset of reals, and whole numbers
are a subset of integers, and counting numbers are a subset of whole
numbers, and so on and so forth. What does that mean?
- Several Ways to Solve a Rate-Time-Distance Problem [02/14/2006]
A bus leaves point A travelling at a speed of 10 mph. 22 minutes
later a car leaves point A travelling in the same direction as the bus
at 40 mph. At what distance will the car catch the bus, and how much
time will have elapsed since the car left point A?
- Shadow Game [01/28/2001]
Tom is 6 feet tall and Carol is 5 feet tall. If Carol stands at the
"shadow top" of Tom's head, their two combined shadows total 15 feet.
How long is each shadow?
- Sharing the Cost of the Weekend Trip [07/24/2003]
A group of people planned to rent a large beach house for a weekend
trip. They were to share the $800 cost equally. However, two people
were unable to go and this increased the cost for each person by $20.
How many persons were in the original group?
- Shortcut for Comparing Fractions [01/14/2003]
My teacher showed us how to cross multiply to compare fractions.
- Sierpinski Gasket [8/29/1995]
What is the area of a Sierpinski gasket?
- Sign Switching [01/28/2002]
Can you explain sign switching in multiplying and dividing inequalities?
- Simple Algebraic Equations [5/26/1996]
How do you logically solve simple algebraic equations?
- Simple Equation: 3y + 2 over 4 equals 7 [10/17/2001]
I think you have to subtract 2 on both sides, but I'm lost.
- Simplification Problems [8/20/1996]
Simplify 2x(4-2x+y) - 5x(y^2+x-y)
- Simplify an Expression [6/15/1996]
- Simplifying a Fraction -- and Oversimplifying It [03/03/2012]
A student simplifies a fraction by selectively canceling terms. Doctor Peterson compares the algebraic expression before and after such unbalanced steps, revealing how this method does not maintain equality.
- Simplifying an Algebraic Fraction [05/09/2000]
How can I simplify 1 + 1/(x + 1/x)? I can't figure out the common
- Simplifying an Expression [04/29/1999]
Can you help me figure out (x+3)+(4x-7)+(x-20) ?
- Simplifying an Expression [05/04/1999]
How do you simplify 9x - 3x + 7 - 4x + y - 3 ?
- Simplifying Expressions [8/31/1996]
How do I simplify (y + 3) - 2(y + 7) ?
- Simplifying Expressions [01/27/1997]
How do you simplify 3x - 2y - x -3y?
- Simplifying Expressions [11/24/1997]
Solve: 2x - ( 3 - x ) = x - 7 .
- Simplifying Mixed Algebraic Expressions [05/08/1998]
Simplifying fractions such as 2x - (x+y)/y and 4 - 3/(y-1) - 1/(y+1).
- Simplifying Polynomials [4/26/1996]
How do you simplify polynomials?
- Simplifying Using the Distributive Property [09/07/99]
How do you simplify an expression like 12(c+3d+4e) + 2(2c+d+6e)?
- Simplifying with Cube Roots [01/22/1997]
Simplify: cube root(3) / [cube root(6) + cube root(3)]
- Simultaneous Equations [8/25/1996]
Ten percent of the reds were added to twenty percent of the blues, and
the total was 24...
- Simultaneous Equations [08/10/1997]
A, B, and C can finish a job in 6 days... In how many days can each man
working alone do the job?
- Simultaneous Equations [07/01/2002]
A man has a total of 20 dimes and quarters. If the dimes were quarters
and the quarters were dimes he would have 90 cents more than he has
now. How many of each coin does he have?
- Six Chickens, Five Minutes [01/09/2003]
If 1 and 1/2 chickens lay 1 and 1/2 eggs in 1 and 1/2 minutes, how
many eggs will 6 chickens lay in 5 minutes?
- Slope and (x, y) Intercept [02/19/1999]
Does slope depend on (x, y) intercept or does (x, y) intercept depend on
- Slope-Intercept Formula [06/05/2001]
Why does y = mx + b have to be that way?
- Solutions to Equations [01/16/1997]
How do you make a table of values of x and y that make the equation 3/4y
= -x true?
- Solution Using Verbal Argument and Model [02/06/2002]
Mr. Li has fewer than 200 sweets. He wants to give each pupil in his
class an equal number of sweets. If he gives each pupil 2 sweets, he will
have 70 sweets left over; if 4, he will need 10 more sweets. How many
pupils are there in the class? How many sweets does Mr. Li have?
- Solve 2x + 3 = 10 [09/17/2001]
I don't understand what to do to simplify the problem.
- Solve for g... [04/08/1997]
I understand -3x+5x+4 = -6 to solve for x, but I don't understand
g+.04g+60 = 8796.
- Solve Using Elimination [01/24/2001]
Solve by using elimination, and check solutions: x+6y=20, x+2y=12.
- Solving a Fraction Problem Using Common Sense [03/21/2004]
When the gun sounded, only two-fifths of the racers began to run. If
460 racers began to run, how many racers were there in all? Can you
show me how to figure out what a fraction is without knowing the total
- Solving a Linear Equation in One Variable [02/27/1998]
Solve for q: -13 - q - 9 = 5q - 9 - q.
- Solving a Math Poem [05/24/2000]
Take five times which plus half of what, and make the square of what
- Solving a Mixture Problem Intuitively and with Algebra [07/06/2007]
There are 7 litres of turpentine in a mixture of 21 litres of water
and turpentine. How many litres of turpentine must be added to make a
mixture of 75% turpentine?
- Solving an Algebraic Equation [12/21/1995]
If x = 2y = 3z = 1,then what is x(y-z)squared + y(z-x)squared + z(x-