These are the Web sites that
Algebra Connections
directs readers to for further study, practice, and information. 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 Mathematics.
The Primes Pages.
You can learn EVERYTHING you could ever imagine about prime numbers
here!
Prime 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 problems.
Fractions, Decimals, Percentages: Explanations. Great
presentation of these concepts and how they relate -- highly
recommended!
Simplifying Fractions. 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.
Fraction Links. 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 well done.
Properties of Real Numbers
Properties 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.
Properties 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.
Real Numbers: Properties. Here is a short, concise,
and clear explaination of the properties of real numbers.
Properties 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.
Positive and Negative Numbers. This set of links from Math
League covers almost anything you need to know of the topic.
Combining Like Terms &
Simplifying Expressions
Combining 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.
Combining 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 "5x^2".
Graphical 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!
Expressions 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.
Equation
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.
Problem Solving With Story Problems
Translating 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.
Solving Math
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.
Solving 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.
MORE! 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.
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.
Inequalities: 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 see why.
Exponents: First Glance. In algebra, you'll often be working
with exponents. Here are some rules.
Exponents: 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.
Exponents. Here is a set of lessons about what exponents
are, how they work, and rules to use them in expressions and equations.
Scientific Notation. While not hard, working with scientific
notation is a fundamental skill in most college science classes. This
"refresher" is from ChemTutor.
Scientific 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.
Understanding 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.
More On Scientific Notation. Astronomy deals with big
numbers. Really big numbers. It’s 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.
Why Use Scientific Notation? Or "Why your wrist (or keyboard)
will thank you for not writing all those zeros."
What Is Scientific Notation And How Is It Used? The
title of this page says it all.
Interactive 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.
Polynomial Basics. Here is a good primer to review and get
us started.
Polynomials. 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.
Ask 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.
Like Terms. Adding or subtracting polynomials is really all
about collecting like terms. Let's start with a quick review.
Polynomials:
Adding & 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.
Adding & Subtracting Polynomials. Adding and
subtracting polynomials is all about collecting like terms and looking
at the order of operations.
Adding 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 understanding.
More Links
for Polynomial Expressions. Links to review all kinds of
important concepts about polynomials, including adding and subtracting
them.
Solve 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.
How 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.
Multiplying Polynomials. This online tutorial looks at at
multiplying polynomials together with and emphasis on the distributive
property of multiplication.
Polynomials: Multiplying. This tutorial looks at the process
of multiplying polynomials, from simplest to more complex.
Dividing 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.
Polynomials: 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.
Polynomial Long Division (also called synthetic division). Here
is another review of division. Everything here is also a review for
working with numbers.
Division of Polynomials and Synthetic Division (Word
Document). There is a summary of the steps used to divide polynomials
and long (synthetic) division of polynomials.
Polynomials Worksheets. Huge collection of links for
free worksheets to review virtually EVERYTHING about operations with
polynomials including multiplication and division.
Solve
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.
Graphical 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 step-by-step
instructions.
Greatest 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.
Factoring
Out GCF. The basics of factoring polynomials is presented
here.
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.
Factoring 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).
Factoring 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.
Factoring 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.
Undoing FOIL: Factoring Trinomials. Because factoring is the
reverse of multiplication, factoring skills depend on multiplication
skills. Let's look at how this works.
Factoring Polynomials. Animated PowerPoint presentation
about factoring polynomials & trinomials.
Factoring Trinomials in the form ax2+bx+c.
Another animated PowerPoint presentation about factoring
polynomials.
Factoring & Dividing Polynomials: Undoing FOIL. This is a
clever presentation of factoring polynomials that looks at the process
as the reverse of FOIL.
Factoring 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.
Algebrator: Factoring. Enter an expression and click the
FACTOR button. This Web will return the solution.
Introduction to Quadratic Equations. This tutorial is
designed to give a brief introduction to the concepts of Quadratic
Equations.
Ask Dr. Math: Quadratic Equations. As usual, Drexel's
Dr. Math has a great presentation to understanding algebraic concepts.
Quadratic Equations. Here's a simple review that addresses
basic questions students often have about quadratic equations.
The 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
College 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.
101 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.
101 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.
Solving
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.
Quadratic 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 .
Solving 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.
Quadratic 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.
Quadratic 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.
Preliminaries: Rational Expressions A rational expression
is nothing more than a fraction in which the numerator and/or the
denominator are polynomials.
Algebraic 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:
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 rational
expression.
Rational Expressions Lesson. This 2 part lesson Explains
what rational expressions are, and describes how to find their domain.
Rational Algebraic Expressions. This interactive lesson
reviews rational rexpressions.
SparkNotes: Rational Expressions. This site contains a set
of links to review almost anything you would want to know about rational
expressions.
Simplifying Rational Expressions (pdf). Here is a direct,
brief explanation of simplifying rational expression.
Rational 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.
Multiplying & Dividing
Rational Expressions
Multiplying Rational Expressions. This tutorial presents the
process of multiplying rational expressions as a series of simple
steps.
Multiplying
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.
Dividing
Rational Expressions Lesson. Just like dividing fractions,
remember to "flip-n-multiply."
Multiplying & Dividing Rational Expressions. This tutorial
reviews factor, simplify rational expressions and multiply polynomials
to be able to complete the multiplication or division problems.
Multiplying & 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."
Math 101: Multiplying and Dividing Rational Expressions.
Here is a simple, short, direct review of simplifying, multiplying, and
dividing rational expressions.
Rational 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 Rational
Expressions
Fraction 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.
Adding 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 to
start.
Adding 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 same.
Rational Expressions: Adding or Subtracting. This tutorial
starts with the simplest case, common denominators, and then moves to
more complex cases.
Addition and Subtraction of Rational Expressions. Whenever
fractions are added or subtracted, we must find a common denominator.
The same is true for rational expressions.
Adding 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.
ThinkQuest: 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.
