See also the
Dr. Math FAQ:
order of operations
Browse High School Basic Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Solving simple linear equations.
Positive/negative integer rules.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- Math Virus Formula [10/23/2001]
The virus spreads to all the squares directly touching each other (not
including diagonally) and I have found the formula for the number of
newly infected cells (although this does not include the first minute)...
- Matrix Algebra [08/28/1997]
I am not sure which formula of matrices to use in this situation.
- Max and Min of Functions without Derivative [04/22/2003]
Is there a general way to find the maximum and minimum of cubic
functions without using derivatives?
- Maximizing Horizontal Distance [04/10/1998]
Using algebra, prove that an object needs to be thrown at 45 degrees to
travel the greatest possible horizontal distance.
- Maximizing Oranges [06/29/2002]
An orchard has 800 orange trees, each of which yields 120 oranges per
season. For each new tree that is added to the orchard, the output
per individual tree decreases by 2 oranges per season. Determine the
number of trees that would maximize the orchard's output.
- Maximizing Revenue by Analyzing a Parabola [03/13/2007]
When priced at $30 each, a toy has annual sales of 4000 units. The
manufacturer estimated that each $1 increase in cost will decrease
sales by 100 units. Find the unit price that will maximize total revenue.
- Maximum Number of Intersections of n Distinct Lines [10/07/1998]
Find a pattern for the maximum number of intersections of n lines, where
n is greater than or equal to 2.
- Meaning of Term in Algebra [09/16/2007]
Why is it that when you multiply or divide two numbers or variables
they become one term (such as 2*x becoming 2x), but when you add or
subtract two numbers or variables they are still two terms (such as 2
- The Method of False Position [02/06/2004]
There is a quantity such that 2/3 of it, 1/2 of it, and 1/7 of it
added together becomes 33. What is the quantity? Solve the problem
by the method of false position.
- Method of Finite Differences [10/12/2000]
How can I find the generating equation for the series -3, 2, 13, 30, 53?
- Minimum and Maximum Problems Using Algebra [04/05/2000]
Can you show me how to solve these minimum and maximum problems using
- 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
- Mixture Problem [11/11/1997]
How much pure antifreeze should be added to 3 gallons of a 30 percent
antifreeze solution to get 65 percent antifreeze?
- Modeling Multiplying Two Negatives with Number Lines [11/13/2006]
What is the logic behind the rule of a negative times a negative makes
a positive, and how do I demonstrate it on a number line?
- Monetary Conversions [01/27/2001]
Given these monetary exchanges: 2 coconuts = 1 banana; 3 bananas = 2
mangos; 4 papaya = 1 coconut, what is the exchange for banana to papaya
and for papaya to mango?
- Money Puzzle [01/05/1998]
A man goes to the bank and asks for x dollars and y cents.
- Monomials, Polynomials [03/02/2001]
Can you explain monomials and polynomials to me?
- More on Order of Operations [02/13/2000]
I have found contradictory information on the precedence of the
multiplication and division operations. Is there a universally accepted
rule for the order of these operations?
- More Variables Than Equations in a System [01/21/2002]
I have a problem that uses four variables but only two equations to
relate them. I don't seem to have enough information to figure out
the value of each variable or answer the question. Can you help?
- Mother's Age in Terms of Daughter's [06/27/2001]
The sum of the ages of a father, a mother, and a daughter is 73. When the
father is twice as old as the daughter, the sum of their two ages will be
- Motion Under Gravity [07/18/2003]
Use the equation s = -16t^2 + vt to determine when the height of an
object is 960 feet if the initial velocity is 272 feet per second.
- Mowing Half a Lawn [03/31/2002]
Chris and Lee are each responsible for mowing half of their 50-foot by
90-foot rectangular back yard...
- Multiple Absolute Value Inequalities/Equalities [08/09/2001]
I can solve inequalities containing absolute values, but not if there are
two in the same equation....
- Multiplicative Inverse [6/2/1996]
Find the multiplicative inverse of 2+5i.
- Multiplying/Adding Fractions Gives Same Answer [03/01/2002]
Find two fractions which, when multiplied and added, give the same
- Multiplying and Dividing Fractions [8/18/1996]
Three hard problems, illustrated.
- Multiplying Binomials and Other Polynomials [04/16/2004]
I have a hard time multiplying binomials properly, such as (2x + 5)(x
+ 7). I do not know what order the problem should be solved in.
- Multiplying or Dividing by a Negative Number [04/08/1999]
When x(x-4) is less than 0...
- Multi-Variable Equations [02/07/1997]
Solve for s in d = (log(f/e) + s * s * 0.5 * t)/(s * s * sqrt(t))
- Names of Polynomials [05/22/1999]
Why is an equation having only two roots, one of which is raised to the
second power, called a quadratic equation?
- Natural Domain of a Function [03/12/1999]
Some inputs don't make sense for some functions.
- Natural Numbers Coprime to 6 [02/16/1998]
Let N(x) denote the number of natural numbers less than x which are
coprime to 6. Show that lim as x goes to infinity of [N(x)/x] = 1/3.
- Negative Exponents [10/23/1996]
I have to simplify this expression with non-negative exponents: x^5.
- Negative Numbers Combined with Exponentials [03/09/2001]
Why in the order of operations is negation a multiplication done after
exponentiation, rather than as a part of the base? What about
- Negatives and Inequalities [09/10/1998]
Why when we multiply or divide an inequality by a negative number do we
reverse the inequality sign?
- Negative vs. Subtraction in Order of Operations [10/30/2002]
I am trying to find some definitive source for treatment of leading
negative numbers in simplifying with order of operations.
- Nested Negative Exponents [8/2/1996]
How do I deal with nested negative exponents?
- Net Result of Consecutive Percentage Increases [12/11/2003]
Suppose a quantity is increased by some percentage, and then is later
increased again by another percentage. How can I calculate the
overall percentage increase?
- Nonlinear Factors [10/12/1998]
I have been told that factoring the sum of two squared numbers is not
possible, but factoring x^4 + 4 is possible. Please explain.
- Non-Linear Simultaneous Equations [12/07/2003]
I have four simultaneous equations with four variables, but each one
has a non-linear term in it (e.g., ab + c + d = 3). So none of the
usual techniques will work! How can I solve the system?