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.
- Visualizing 1 + 1/x [10/10/2003]
Show that the sum of a positive number and its reciprocal is at least 2.
- Walking the Shortest Distance [10/07/2002]
A single boy lives in each of n equally spaced houses on a straight
line. At what point should the boys meet so that the sum of the
distances that they walk from their houses is as small as possible?
- Water Level in a Well [10/09/2001]
A man wishes to determine the water level in a deep well. He drops a
stone into the well and hears it hit the water 3 seconds later...
- Water Main Section Lengths [01/09/2003]
A water main is being laid using pipe that comes in either 18-foot or
20-foot sections. The water main will require 14 fewer sections of 20-
foot pipe than if 18-foot sections are used. Find the total length of
the water main.
- Weighted Average of the Velocities [01/30/2003]
Finding the average velocity for each of the three phases of the
- What are Piecewise Functions? [05/13/2001]
I know piecewise functions are based on expressions between specific
intervals, but I do not know how to describe this function family.
- What are the solutions to x^4+9 = 0 ? [03/31/2003]
How to work with complex numbers when the root is higher than two?
- What Does It Mean to Distribute [08/25/2007]
I understand the basics of the distributive property, but I'm confused
about what the 'over' means, like in the distributive property of
multiplication over addition or over subtraction.
- What is a Partial Fraction? [01/08/1999]
What do partial fractions have to do with polynomials?
- What is the Purpose of a Matrix? [11/04/2003]
What is the purpose of a matrix?
- What's the Second Part? [3/21/1995]
If x = root3 + root2, show that x^4 - 10x^2 +1 = 0. Hence prove that
root3 + root2 is irrational.
- What Time Did Ajay Start? [08/06/2003]
Three persons, Ajay, Bhanu, and Chandu, plan to travel from P and reach
Q at 4.00 PM...
- What We're Doing When We Do Algebra [03/25/2002]
How do you graph x + y = 5 on a graph sheet?
- When FOIL Fails [03/22/2001]
Find the product - (2c-3)3rd power. I can do FOIL on a question to the
second power, but I cannot figure out how to do a question to the third
- When Hands of a Clock Meet [8/29/1996]
To the nearest second, what is the first time after 12:00 that the hour
hand and the minute hand of a clock are together?
- Who Picked the Most? [09/12/1998]
Arrange the names of the people in the order of the number of peaches
that each picked, starting with the person who picked the most.
- Who Will Win the Race? [01/14/1998]
Harry runs 3/4 mile every 6 minutes and Tortisha runs 1/2 mile every 5
minutes. Harry says, "I'll give you a 2 mile head start and still beat
you in the race."
- Why Algebraic Expressions with Parentheses? [03/18/2003]
How would you write these algebraic expressions without parentheses?
-(2x-3y-6) and -(5x-13y-1).
- Why Does Long Division Work? [12/22/2006]
I'm curious why the standard long division algorithm works. How do all
the "bringing down" and other steps lead to the right answer?
- Why Does the Algorithm for Polynomial Long Division Ignore Smaller Terms? [03/24/2011]
A student wonders how polynomial long division works if, at each stage, it disregards terms of smaller degrees. Starting from integer division, Doctor Peterson builds up an example to explain.
- Why Does the Order of Square/Square Root Matter? [8/28/1996]
Why does the square root of x^2 equal absolute value of x, but the square
of the square root of x equals just plain old x?
- Why Do I Have to Learn This? [05/03/2004]
When, in the real world, would I have to find the roots of a quadratic
- Why Do We Have the Order of Operations? [03/05/2006]
Why do we have the order of operations? Why can't we just calculate
from left to right? That seems much easier and more logical to me.
- Why Do We Use Variables in Algebra? [01/31/2004]
Why do we use letters to represent numbers in algebra?
- Why Factor? [08/18/2001]
I've been explained the how's, the where's, the what's, but not the WHY.
What is the practical use of factoring?
- Why Flip the Inequality Sign? [10/26/2001]
Please tell me why you flip the inequality sign when dividing by a
- Why FOIL? [11/21/2002]
How can I explain to the class the importance of learning FOIL?
- Why Some Solutions to Absolute Value Equations are False [10/24/2004]
When solving equations involving absolute value, you sometimes get an
answer that doesn't check in the original equation. What is it about
absolute value that makes this happen?
- Why Use n for Any Number? [09/28/2002]
Why do people use n when any number can fit in or when they want to
- Width and Area of a Field [8/22/1996]
Find a quadratic equation that relates the area of a field to its width.
- Wind Chill Formula [2/1/1996]
Could you tell us the formula used for finding the wind chill?
- Word Problem Regarding Time and Distance [05/30/2002]
A train is going through a tunnel that is 650 feet long. The train
is traveling 100 feet per second. The train enters the tunnel on
one end. Twenty-six seconds later the last car exits the other end
of the tunnel. How long is the train?
- Working with Quadratic Roots [08/15/2002]
Given that a and b are the roots of the quadratic equation x^-5x+3=0,
form, without solving the equation, the quadratic equation whose
roots are a/b and b/a.
- x^3 + y^3 [10/17/2002]
Given: x + y = 1, x^2 + y^2 = 4; x^3 + y^3 = ?
- Young's Formula [08/21/1999]
Calculating a child's dose of medicine based on the adult dose.
- Zero Product Property [02/14/1998]
How do you find the answer to a zero product property question?