These are the Web sites
that I direct students to in my "newsletter," Algebra
Connections. This online portal organizes the comprehensive
set of links that provide alternative presentations, explanations,
tutorials, and interactive lessons about the basic skills that prepare
students for higher-level math classes in the Math Department.
The Primes Pages.
You can learn EVERYTHING you could ever imagine about prime numbers
Factoring. To prime factor a number, begin dividing by the
smallest possible prime and continue until the quotient is a prime
number. Links on this site provide a "mini-lesson, "
worksheets, and an interactive factoring program that returns the prime
factorizations and solutions to any number that is entered.
Percents. These pages teach percent skills.
Each page has an explanation, interactive practice and challenge games
about percents and ratios.
The Three Percentage
Cases. To explain the cases that arise in problems
involving percents, it is necessary to define the terms that will be
used. Rate (r) is the number of hundredths parts taken. This is the
number followed by the percent sign. The base (b) is the whole on which
the rate operates. Percentage (p) is the part of the base determined by
the rate. These three cases are the key to all percentage story
Fractions, Decimals, Percentages: Explanations.
Great presentation of these concepts and how they relate -- highly
Simplifying fractions is really wimple, when you follow the rules.
Simplifying fractions is often required when your answer is not in the
form required by the assignment. As a matter of fact, most math
instructor will demand that you always simplify results.
Maintained by Math League, this set of links contains EVERYTHING you
would ever want to know about fractions.
Reducing Fractions &
the Least Common Denominator. This Sparks Notes study
guide covers reducing fractions and the LCD. There is also a
"pull-down" menu for more helpful topics and links to other
math and test taking resources.
Fractions Fast Facts.
As the name implies, another good site for an easy review of
fractions. This site includes a wide variety of fraction
resources, as well as a direct link to Mrs.
Glosser's Math Goodies.
Finding the Lowest Common Denominator.
Here is animated PowerPoint presentation that reviews important concepts
about working with fractions. I recommend that students look at this
presentation as a quick, easy, visual review of fractions -- its really
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Properties of Real Numbers
of Real Numbers: First Glance. In pre-algebra, you learned about the properties of integers. Real numbers have the same types of properties, and you need to be familiar with them in order to solve algebra problems.
Here is a wonderful interactive review.
of Real Numbers: In Depth. In this lesson we look at
some properties that apply to all real numbers. If you learn these
properties, they will help you solve problems in algebra. Let's look at
each property in detail, and apply it to an algebraic expression.
Numbers: Properties. Here is a short,
concise, and clear explaination of the properties of real
of Real Numbers. This site provides lessons, short
interactive practice activities, and even teacher resources to review properties
of real numbers.
Ask Dr. Math.
This award-winning math site at Drexel has answers to almost any math
related question. If not, you can always ask! Be sure to
check out what the Doctor has to say about adding
positive and negative numbers and negative
times a negative.
Adding and Subtracting
Positive and Negative Numbers. Remember! Adding a positive
and a negative number is like subtracting. If the greater number is
positive, the answer is positive. If the greater number is negative, the
answer is negative. Try this interactive exercise.
and Negative Numbers. This set of links from Math League
covers almost anything you need to know of the topic.
Combining Like Terms & Simplifying
Like Terms. This lesson explains the process of combining
like terms to simplify an expression or an equation using addition and
subtraction of the coefficients of terms.
Like Terms and Solving. Simplify each equation by
combining like terms, then solve. Enter exponents using the ^ symbol.
For example, "five x squared" should be entered as
Universal Expression Simplifier and Solver. Check this one
out -- you supply the expression and the site returns the answer, a
short animated solution, and detailed step-by-step instructions.
Pretty amazing stuff!
Calculator. When you enter an expression into the
calculator, the calculator will simplify the expression by expanding
multiplication and combining like terms. Additional capabilities
including factoring will be added with future updates. Use the following
rules to enter expressions into the calculator.
When you enter an equation into the calculator, the calculator will
begin by expanding (simplifying) the problem. Then it will attempt to
solve the equation by using one or more of the following: addition,
subtraction, division, taking the square root of each side, factoring,
and completing the square.
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Problem Solving With Story Problems
Word Problems. The hardest thing about doing word problems is taking the English problem and translating it into math. Usually, once you get the math equation, you're fine.
This site suggest tips and tricks to learn how to do word problems.
Word Problems. This study guide breaks the process of
working with story problems into two steps: (1). Translate the
wording into a numeric equation, (2). Solve the equation!
Solving Linear Equations in 1 Variable
Addition Property of Equality.
This is where we start getting into the heart of what algebra is about,
solving equations. In this tutorial we will be looking
specifically at linear equations and their solutions using the addition
and subtraction properties of equality.
Multiplication Property of Equality.
This Web picks up where the one above left off, we look at linear
equations and their solutions using the multiplication and division
properties of equality.
Linear Equations. In this this tutorial, we will be
solving linear equations by using a combination of simplifying
(combining like terms) and various properties of equality.
Knowing how to solve linear equations will open the door to being able
to work a lot of other types of problems that you will encounter in your
various algebra classes.
Solving Linear Equations.
This online practice session challenges students to solve some linear
equations in 1 variable and lets you see hints and step-by-step
solutions to the problems.
Solving Linear Equations. Here is another site that
presents examples of linear equations, asks you to solve them, and
presents step-by-step solutions.
Solving Linear Inequalities.
Wiki Books says, "Think free, learn free!" Here is an
excellent presentation on solving linear inequalities.
Solving'' an inequality means finding all of its solutions. A
"solution'' of an inequality is a number which when substituted for
the variable makes the inequality a true statement.
In Depth. Solving an inequality is very similar to solving
an equation. You follow the same steps, except for one very important
difference. When you multiply or divide each side of the inequality by a
negative number, you have to reverse the inequality symbol!
Solving Linear Inequalities.
This is a straight-forward, "no-frills" presentation on
solving linear inequalities.
ThinkQuest. Solving Linear Equations.
Inequalities are solved in ALMOST the same way as equations. Let's
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First Glance. In algebra, you'll often be working with
exponents. Here are some rules.
In Depth. Exponents are used in many algebra problems, so
it's important that you understand the rules for working with exponents.
Let's go over each rule in detail, and see some examples.
Here is a set of lessons about what exponents are, how they work, and
rules to use them in expressions and equations.
Notation. While not hard, working with scientific notation
is a fundamental skill in most college science classes. This
"refresher" is from ChemTutor.
Notation Lesson. Scientific notation is simply a method
for expressing, and working with, very large or very small numbers.
It is a short hand method for writing numbers, and an easy method for
calculations. Numbers in scientific notation are made up of three
parts: the coefficient, the base and the exponent.
Scientific Notation. Do you know this number, 300,000,000
m/sec.t's the Speed of light ! Do you recognize this number, 0.000
000 000 753 kg. ? This is the mass of a dust particle!
Scientists have developed a shorter method to express very large
numbers. This method is called "scientific notation" .
Scientific notation is based on powers of the base number 10.
On Scientific Notation. Astronomy deals with big numbers. Really
big numbers. Itís impossible to talk about the distance to the Sun or
the speed of light without thinking about the tremendously huge. But big
numbers intrude on all aspects of our lives and as responsible citizens,
we ought to have a way of dealing with them. WOW, this site makes
it all sound so important. They're right, it is.
Use Scientific Notation? Or "Why your wrist (or
keyboard) will thank you for not writing all those zeros."
Is Scientific Notation And How Is It Used? The
title of this page says it all.
Practice: Scientific Notation. This page is an
exercise in scientific notation. When you press "New Problem",
either the scientific notation or non-scientific notation representation
of a number will be shown. Put the corresponding value(s) in the empty
cell(s) and press "Check Answer". The results will appear in
the second table.
Basics. Here is a good primer to review and get us
We have covered variables and exponents and have looked
expressions. Polynomials are sums of these expressions. Each piece of the polynomial, each part that is being added, is called a
term;. Polynomial terms have variables to whole-number exponents; there are no square roots of exponents, no fractional powers, and no variables in the denominator.
Dr. Math: Polynomial Basics. Let's see what the
Doctor has to say.
Online Self-Check Quiz: Polynomial Basics.
Here is a short, interactive quiz to check understanding.
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Adding or subtracting polynomials is really all about collecting like
terms. Let's start with a quick review.
& Subtracting. This tutorial looks at looking
at the different components of polynomials. Then moves on to
evaluating polynomial functions as well as adding and subtracting them.
& Subtracting Polynomials. Adding and subtracting
polynomials is all about collecting like terms and looking at the order
and Subtracting Using Algebra Tiles. Here is an
alternative, visual presentation that let's you "see" how to
add and subtract polynomials.
Online Self-Check Quiz: Adding and Subtracting Polynomials.
Here is a short, interactive quiz to check for
More Links for Polynomial Expressions.
Links to review all kinds of important concepts about polynomials,
including adding and subtracting them.
Your Math Problem: Add
or Subtract Polynomials. This page will show you how to
add and/or subtract polynomials. You supply the probem and this
site generates your answer. Note: You need to use and
"MS Excel" style exponential notation. To square
"x," enter x^2.
to Add, Subtract, Multiply, and Divide Polynomials
. A one variable polynomial, the kind you will most often
see, is an algebraic expression made up from adding, subtracting, and
multiplying of the variable and numbers.
Polynomials. This online tutorial looks at at multiplying
polynomials together with and emphasis on the distributive property of
Multiplying. This tutorial looks at the process of
multiplying polynomials, from simplest to more complex.
Polynomials. In this tutorial we are dividing
polynomials, but it follows the same steps and thought process as when
you apply it numbers and is a good review of long division.
Dividing. There are only 2 methods to dividing
polynomials. The first is actually just simplification, reduction
of a fraction. The second method uses long division.
Long Division (also called synthetic division). Here is
another review of division. Everything here is also a review for
working with numbers.
of Polynomials and Synthetic Division (Word Document).
There is a summary of the steps used to divide polynomials and long
(synthetic) division of polynomials.
Worksheets. Huge collection of links for free
worksheets to review virtually EVERYTHING about operations with
polynomials including multiplication and division.
Your Math Problem: Multiplying Polynomials. This page will show you how to multiply polynomials together.
Here are some example you could try: (x+5)(x-3),
(x^2+5x+1)(3x^2-10x+15), or (x^2+5)(x^2-19x+9).
Solve Your Math Problem:
Dividing Polynomials. This page will show you how
to divide polynomials together. You supply the problem and the
Web site returns the solution.
Universal Expression Simplifier and Solver. This link is
also presented above under Simplifying Expressions, but
this site does so much more, including: reduction of constants,
removal of unneeded parentheses, reduction of similar factors and terms,
linear equations, quadratics, some polynomial reductions, associative
property, and some substitutions. You supply the expression and
the site returns the answer, a short animated solution, and detailed
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Common Factor. The first thing to do when factoring any
expression is to look for a greatest common factor. Let's look at
how this applies to polynomials.
Out GCF. The basics of factoring polynomials is presented
GCF & Factoring by Grouping.
Factoring is to write an expression as a product of factors. We can also do this with polynomial expressions. In this tutorial we
look at two ways to factor polynomial expressions, factoring out the greatest common factor and factoring by grouping.
GCF & Factoring by Grouping
Lesson. Here is another presentation of these two
important factoring strategies.
Factoring & Polynomials.
This is a short, concise presentation factoring polynomials.
Polynomials. Factoring a polynomial is the opposite
process of multiplying polynomials. Recall that when we factor a number,
we are looking for prime factors that multiply together to give the
number. When we factor a polynomial, we are looking for simpler
polynomials that can be multiplied together to give us the polynomial
that we started with.
Solve Your Math Problem:
GCF & Polynomials. This page will show you how
to factor a GCF out of a of a polynomial. You supply the problem and the
Web site returns the solution.
Simple Trinomials as Product of Binomials.
(MS Word document, many examples, printable. Factoring a trinomial
results in a product of 2 binomials. The simplest example is when
the "lead" coefficient is 1 (x2+bx+c).
Trinomials where a=1 (x2+bx+c). Whether we use
the FOIL method, or line up the factors vertically to multiply, the
answer is a trinomial. To factor a trinomial of this
form, we need to reverse the multiplication process.
Trinomials where a is not 1 (x2+bx+c). The
tutorial above showed us patterns when factorting trinomials with a lead
coefficient of 1. Now let's look at when the lead coefficient is
other than 1.
FOIL: Factoring Trinomials. Because factoring is the
reverse of multiplication, factoring skills depend on multiplication
skills. Let's look at how this works.
Polynomials. Animated PowerPoint presentation about
factoring polynomials & trinomials.
Trinomials in the form ax2+bx+c. Another
animated PowerPoint presentation about factoring polynomials.
& Dividing Polynomials: Undoing FOIL. This is a
clever presentation of factoring polynomials that looks at the process
as the reverse of FOIL.
Trinomials. This is another presentation that shows how factoring
trinomials is really just the revers of FOIL.
Solve Your Math Problem:
Factoring Polynomials. This page will show you how
to factor trinomials. You supply the problem and the
Web site returns the solution.
Factoring. Enter an expression and click the FACTOR
button. This Web will return the solution.
to Quadratic Equations. This tutorial is designed to give
a brief introduction to the concepts of Quadratic Equations.
Dr. Math: Quadratic Equations. As usual, Drexel's
Dr. Math has a great presentation to understanding algebraic concepts.
Equations. Here's a simple review that addresses basic
questions students often have about quadratic equations.
World of Quadratic Equations. An equation of the form ax2+bx+c=0
is called a quadratic equation, where a,b,c are known values (i.e.
constants), a is non-zero and x is the unknown value (i.e. a
variable). For ex: 5x2+7x+3=0, 4x2+2=0, 3x2+8x+4=8,
are all quadratic equations
Algebra Tutorial on Quadratic EquationsThis tutorial looks at
solving a specific type of equation called the quadratic equation.
The methods of solving these types of equations that we will take a look
at are solving by factoring, by using the square root method, by
completing the square, and by using the quadratic equation.
Uses of a Quadratic Equation. It isn't often that a
mathematical equation makes the national press, far less popular radio,
or most astonishingly of all, is the subject of a debate in the UK
parliament. However, in 2003 the good old quadratic equation, which we
all learned about in school, was all of those things.
Uses of a Quadratic Equation: Part II In 101 Uses of a
Quadratic Equation: Part I, we took a look at quadratic equations and
saw how they arose naturally in various simple problems. In this second
part we continue our journey. We shall soon see how the humble quadratic
makes its appearance in many different and important applications.
Quadratic Equations by Factoring. There are different ways
to solve quadratic equation. This online lesson starts with
factoring, but then covers other methods too if you continue to
"click" to the next level.
Equations: Solutions by Factoring. Sometimes it is easier
to find solutions or roots of a quadratic equation by factoring. Indeed,
the basic principle to be used is: if a and b are real or complex
numbers such that ab=0, then a=0 or b=0 .
Quadratic Equations. This program solves Quadratic
Equations. Enter the coefficients in appropriate boxes and click Solve.
It will show the results in boxes Root1 and Root2.
Equation Calculator. This site solves quadratic equations in standard
form (ax2+bx+c=0). Enter the values of the coefficients of a quadratic
equation and an answer is generated.
Equation Solver. Quadratic equations have
the form ax2 +bx+c=0. They will generally have two
solutions; that is, two different values of x that make the
equation true. It can happen that both solutions are the same
number, and it is possible that the solutions will be complex or
imaginary numbers. To use this utility, you type in values for a,
b, and c in the boxes below, and press the Solve button.
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Rational Expressions A rational expression is
nothing more than a fraction in which the numerator and/or the
denominator are polynomials.
Techniques: Rational Expressions. Rational
expressions are represented as the quotient of two algebraic
expressions. Thus, they can be manipulated like fractions. This tutorial
explains how properties of fractions can be used to deal with rational
Expressions. A rational expression is an algebraic
expression that can be written as the ratio of two polynomial
expressions. A rational function is a function whose value is given by a
Expressions Lesson. This 2 part lesson Explains what
rational expressions are, and describes how to find their domain.
Algebraic Expressions. This interactive lesson reviews
Rational Expressions. This site contains a set of links to
review almost anything you would want to know about rational
Rational Expressions (pdf). Here is a direct, brief
explanation of simplifying rational expression.
Expressions Self-Check. This interactive quiz will allow
you to see if you are comfortable with the concepts the rest of this
unit is based on.
Dividing Rational Expressions.
Rational Expressions. This tutorial presents the process
of multiplying rational expressions as a series of simple
Rational Expressions Lesson. Most students find
multiplying and dividing fractions easier than adding or subtracting
fractions with different denominators. The same is true with
rational expressions -- let's see why.
Dividing Rational Expressions. Dividing
fractions is done by leaving the first fraction as it is and then
multiplying by the reciprocal of the fraction following the division
sign. Multiply by the reciprocal is all you have to do.
Rational Expressions Lesson. Just like dividing fractions,
remember to "flip-n-multiply."
& Dividing Rational Expressions. This tutorial reviews
factor, simplify rational expressions and multiply polynomials to be
able to complete the multiplication or division problems.
& Dividing Rational Functions. For our purposes, a
rational expression is a rational function. When we call it a
function, we are simply referring to the set of numbers that result in a
fraction that does not have a denominator of "0." This
set of numbers is called the "domain."
101: Multiplying and Dividing Rational Expressions.
Here is a simple, short, direct review of simplifying, multiplying, and
dividing rational expressions.
Expressions: Multiplying, Dividing, Adding, and Subtracting.
This lesson is starting to get ahead of ourselves, but if you are ready
for the next section, then this is a good place to start.
Adding & Subtracting
Review & Lowest Common Denominator. Adding and subtracting
rational expressions is really like working with fractions.
Perhaps it will be appropriate to start with a review the basics.
and Subtracting Rational Expressions With Like Denominators.
Just like working with fractions, this is the simplest case when adding
or subtracting rational expressions. Perhaps this is a good place
or Subtracting Algebraic Fractions. Here is another tutorial
that looks at numeric fractions with fractions with variables to get us
ready for rational expressions -- these concepts are really all the
Expressions: Adding or Subtracting. This tutorial
starts with the simplest case, common denominators, and then moves to
more complex cases.
and Subtraction of Rational Expressions. Whenever
fractions are added or subtracted, we must find a common denominator.
The same is true for rational expressions.
and Subtracting Rational Expressions. If you have ever
felt dazed and confused when working with fractions, you are not alone.
This tutorial is devoted to rational expressions (fractions). In
this tutorial we will be looking at adding and subtracting them.
Graphing Linear Equations and Inequalities
The Coordinate Plane and Graphing Linear Equations. In this unit we'll be learning about equations in two variables. A coordinate plane is an important tool for working with these equations.
Tutorial: Graphing Linear Equations.
When you graph linear equations, you will end up with a straight line. Let's see what you can do with these linear equations.
Graph of a Line.
We can graph the linear equation defined by y = x + 1 by finding several ordered pairs. For example, if x = 2 then y = 2 + 1 = 3, giving the ordered pair (2, 3). Also, (0, 1), (4, 5), (-2, -1), (-5, -4), (-3, -2), among many others, are ordered pairs that satisfy the equation.
Graphs of Linear Equations: Lines and Slope. Lessons
and some practice sets.
Graphing Inequalities in 2 Variables. The solution set for an inequality in two variables contains ordered pairs whose graphs fill an area on the coordinate plane called a half-plane. An equation defines the boundary or edge of the half-plane.
Worksheets: Linear Equations and Inequalities. Need more practice? These worksheets will help.
Graphing Linear Equations and Inequities. Let's review basics of graphic equations and inequalities.
Automatic Graph Solutions: Equations. Enter the equation you want to plot, in terms of the variables x and y, set the limits and click the Plot button.
Automatic Graph Solutions: Inequalities. Enter the polynomial inequality you want to plot, in terms of the variables x and y, set the limits and click the Plot button.
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