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.
- Mixing Alcohol, Cable TV Pricing [8/2/1996]
What amounts of 9 percent and 12 percent alcohol do you mix to get
300,000 gallons of 10 percent alcohol? For each 5-cent increase in the
monthly subscription price, 4 people will decide not to subscribe to
- Mixing Milk and Butterfat [09/04/2001]
Milk that has 5% butterfat is mixed with milk that has 2% butterfat. How
much of each is needed to obtain 60 gallons of milk that has 3%
- Monomials and Polynomials [8/31/1995]
I really don't understand monomials and polynomials. Could you help
explain them simply?
- Monomials, Polynomials [01/21/1998]
I'm having trouble adding, subtracting, multiplying and dividing
monomials, adding and subtracting polynomials, and factoring.
- Multiples of 9 Number Puzzle [03/23/2003]
If you take a two-digit number, add the digits, and subtract the sum
from the original number, why is the answer always a multiple of 9?
- Negative Numbers in Equations [11/20/2001]
I don't know how to do some of the homework I am getting. Here are some
examples of confusing equations: -30 = -37+b/15; -c/4-8 = -48.
- No Solution, Infinite Solutions [01/03/2002]
Solve: 8(2x-3) = 4(4x-8); -3(x-3) is greater than or equal to 5-3x.
- Number of Quarters [9/11/1996]
Tony has eleven more nickels than quarters. How many quarters does he
have if the total value of his coins is $2.65?
- Number Puzzle Solved with and without Algebra [12/10/2001]
I am a number. Add 25 to me. Divide the sum by 2. You end with 75. What
number am I?
- Order of Operations [8/21/1995]
What is the reason for the order of operations in a math equation?
- Order of Operations: Math vs. English; Calculators [11/13/1996]
What is 144 divided by 3(8+4)? 4 or 576?
- Order of Operations Puzzle [09/22/2002]
What is _ + _ x _ - _ = 22? We're given the numbers 2, 3, 4, 8.
- Pre-Algebra: Equations and Other Tips [08/30/1997]
I'm in 8th Grade; can you give me tips on equations and other things that
will be useful for me to know?
- Pre-algebra variable expressions [09/01/99]
Please explain how to do variable expression problems.
- Properties of Algebra [5/8/1996]
What are the properties used for algebra?
- Properties of Exponents [01/22/2001]
Will you please help me understand exponents?
- Properties of Real Numbers [05/20/1997]
What are the associative, the commutative, and the zero product
- Purpose of Algebra [10/15/1996]
What is the purpose of algebra and who came up with the idea?
- Pythagorean Theorem Proof: Four Right Triangles [10/7/1996]
I don't understand the Pythagorean Theorem.
- Real and Complex Equations [09/21/1998]
I'm having trouble simplifying some real and complex equations for
Algebra II. Can you help?
- Renting Bike Safety Equipment [10/09/2001]
The Park Department rents a bike with safety equipment for $5 a day. If
you provide your own safety equipment, the bike rental is $3 a day. You
could buy equipment at a sports store for $28. How many times must you
use the trail to justify buying your own safety equipment?
- Representing Numbers in Different Bases [08/05/1998]
How did they get the 2 x 3 cubed? Plus some number less than 3 cubed?...
- Ruth Has $2300 More Than Ken [04/15/1999]
...If Ken gives Ruth $2000, Ruth will have eight times as much money as
Ken. How much money does each of them have?
- Silver Alloy [07/12/2001]
Sterling Silver is 92.5% pure silver. How many grams of pure silver and
sterling silver must be mixed to obtain 100g of a 94% Silver alloy?
- A Simple Formula? [02/21/1997]
If one person takes two hours to paint a wall and another only one hour,
how long will it take them to paint the wall together?
- Simplifying an Algebraic Expression [8/17/1996]
If 12y = 3, what do you do next?
- Sketch an Equation [10/07/1997]
How do I rearrange -3x+2y = -6 to sketch it?
- Solving Algebra Word Problems [10/16/1998]
I'm having trouble solving word problems. In particular, how do you
convert the words to variables and then make them into equations?
- Solving an Equation with Fractions [11/27/1995]
A student asks how to work the problem: (x + 5)/4 = (x-4)/(2/5).
- Solving Another Equation with Two Variables [1/30/1996]
6y = 3D = 54. I am supposed to solve the equation, but I don't even
- Solving ax + b is less than cx + d [12/11/2001]
Here is an inequality problem: 6-9x is less than or equal to 5x-1.
- Solving Equations [01/25/1997]
How do you solve equations like n/4 + 6 = -3?
- Solving Equations in Two Variables by Addition/Subtraction [09/08/2001]
The equations are: 2x + 3y = 7; 4x - 5y = 25.
- Solving for X [8/14/1996]
Solve: (x/7) - 4 = -2.
- Solving for x [10/22/1996]
How do you solve an equation like x/a = k for x?
- Solving Quadratic Equations [5/23/1996]
- Solving Simple One-Variable Equations [02/14/1998]
n+39 = 12, w+(-8) = -21, 24 = m-8.6 ... I need help on these problems.
- Solving Systems of Equations by Substitution [08/24/1998]
When they want you to substitute the x value in place of it in the y
problem I totally get lost.
- Substituting in Linear Equations [11/14/2001]
I am given two equations, 2y = 5x + 8x and 3y = 4x + 9x, and told to
substitute something. What should I do?
- Substitution and Elimination [01/13/2002]
Could you please explain substitution and elimination to me step by step?