Red Comet - MATH - Basic Math

Basic Math - 2nd Semester
Section 1: An Introduction to Algebra

Math Man! To the Student: Just like any topic that is new to us, or difficult for us, we need to get a strong start. To get a strong start in Algebra, we need to develop both the Language of Algebra and the basic skills of Algebra. Along this line I would like to recommend that you get a notebook designated just for Algebra. In your notebook, you should write:

1.  The vocabulary
2.  The rules
3.  The steps for solving problems

so you will have them to refer back to when difficulties arise. Good luck in your study of Algebra. I know that you will succeed.

Greg S Hurn

Topic 1.1 The Language of Algebra

Objectives: the student will be able to:

Utilize the language of Algebra

Real life mathematics requires us to be able to take a problem and write it in a form from which we can arrive at an answer. To do this effectively, we need to know what the problem is saying. Some initial vocabulary will start us along the correct path.

Variable - a letter that can represent any number. You may use any letter except o or i. An o looks too much like a zero. An I has a special meaning in higher mathematics.

Algebraic expression - an expression that contains at least one variable.

Examples:
3x - 5
ab + c
w
5

Numerical expression - an expression that contains only numbers.

Examples:
3(4) - 5
5(2) + 7
8
5

In reference to the examples for Algebraic expression and numerical expressions:

3x tells us to multiply 3 times the value of x

ab tells us to multiply the value of a times the value of b

So if there is not a sign between a number and a variable or between two variables, then you multiply.

3(4) tells us to multiply 3 times 4

So ( ) tells us to multiply

In writing either Algebraic or numerical expressions, we need to know the words that indicate the basic mathematical operations.

Addition the sum of
increase by
plus
more than
added to
the total of more than tells us to add that number
so five more than a number is written x + 5

If an expression contains the words "a number", it can be any number, so is represented by a variable.

Subtraction the difference of
decreased by
minus
less than
subtract from less than tells us to subtract that number
so seven less than a number is written x - 7

In the two examples x + 5 and x - 7, I chose to use x as my variable. You can use any letter except o or i.

Multiplication the product of
multiplied by
times 4(5) = 20

The numbers in a multiplication problem are called factors (4 and 5) and the answer is called the product (20).

Division the quotient of
divided by
the ratio of w
¾ means w ¸ 5
5
A ratio is a Fraction, so the ratio of 4 to 5 is written as
4
5
which is a division problem

A fraction bar tells us to divide.

Powers x^a where x is called the base
a is called the exponent
x^a is called a power

An exponent tells us how many equal factors there are. And since factors are the numbers in a multiplication problem, the exponent tells us how many times we multiply the base times itself.

Examples: 3⁴ = 3 · 3 · 3 · 3 a · a · a · a · a = a⁵

x³ = x · x · x m · m · n · n · n = m²n³

There are special names for x² and x³
x² can be read x to the second power or x squared
x³ can be read x to the third power or x cubed

In the example 3⁴ = 3 · 3 · 3 · 3:
3⁴ is called the exponential form
3 · 3 · 3 · 3 is called the factored form.

Students: In order for you to be successful on your tests, you need
to do and understand the following practice problems.

If you have difficulty with any of the problems, refer back to the
appropriate example which outlines for you the step by step
reasoning for the problem.

MATH
Basic Math - 2nd Semester

Section 1 Index

Topic 1.1 - The Language of Algebra

Topic 1.2 - Algebraic Expressions and Verbal Expressions

Topic 1.3 - Exponential Form and Factored Form

Topic 1.4 - Associative, Commutative and Distributive Properties

Topic 1.5 - Using Formulas