The GED Mathematics Test - Online Math Tutorials
The GED Mathematics Test
Introduction to Algebra
Margaret A. Rogers, M.A.
ABE/GED Teacher
Adult School Administrator
Education Consultant
California Distance Learning Project
1
GED
Video Partner
#38 Passing the GED Math Test
Algebra and money are essentially levelers: the first
intellectually, the second effectively.
Simone Weil (1909 - 1943)
Video 38 Focus: how you use algebra to simplify equations and solve for variables.
You Will Learn From Video 38:
!
!
!
!
!
How to use algebra to solve equations.
How to simplify algebraic expressions.
How to isolate variables as a rule for solving equations.
The rules for operations with signed numbers.
That algebra has a language of its own.
Points to Remember:
?
Words You Need to Know:
While viewing the video, put the letter of the meaning by the
correct vocabulary word.
Answers are on page 21.
_____1. signed numbers
_____2. algebra
_____3. variable
_____4. equation
_____5. inverse operation
a. statement that two expressions are
equal
b. letters used to substitute for
numbers
c. the set of positive and negative
numbers
d. the opposite operation as addition
is to subtraction and multiplication is
to division
e. branch of mathematics
2
?
?
?
?
Algebra is a branch of
mathematics that uses
rules to strategically
solve for variables.
You need to know
some basic rules of
algebra for the GED
Math Test.
Less than one-fourth
of the GED Math Test
must be solved with
algebra.
Some of the simple
problems in algebra
can be solved using
basic arithmetic and
logical thinking.
Algebra can be fun!
Introduction to Algebra
Algebra is the branch of mathematics where the object is to use rules strategically to solve for
variables. Algebra has a symbolic language that is used to express relationships. Many of the
same rules and algorithms that we use in arithmetic we also use in algebra. However, in algebra,
these rules are often used to solve equations. Equations are statements that two expressions are
equal. An example of such an equation is:
3 x 8 = _____ x 6
In algebra, we are trying to find out which solution will make both sides of the equation equal.
We are trying to balance the equation. There are many solutions to this equation. A solution will
be any number or expression that can fill the blank to make the right side of the equation equal to
the left. The simplest solution is the number 4. However, we could also fill the blank with
expressions such as (2 + 2) or (9 - 5). After we fill the blank we want to test to make sure that
both sides of the equation are equal.
3 x 8 = _____ x 6
3x8=4x6
24 = 24
In algebra, letters are used to stand for unknown numbers. These letters are called variables. A
variable can stand for a single number or a complete expression. In the example above, we can
replace the blank line with a letter to stand for the variable answers.
3x8=Ax6
On the GED Math Test you will have to simplify equations, solve for variables, and use
operations with signed numbers. There are many other skills that are associated with the
branch of mathematics. However, if you are comfortable with these skills, you will be well on
your way to answering most of the algebra questions correctly.
It is also important to understand the properties that allow you to manipulate an equation as you
simplify or solve for variables. In this Video Partners workbook, you will learn about and
practice with the following properties:
"
"
"
Commutative properties of addition and multiplication
Associative properties of addition and multiplication
Distributive property of multiplication
Although algebra is more abstract than arithmetic, it is important not to be afraid of it. Algebra is
full of step-by-step procedures. If you learn the steps one by one and then systematically apply
them when you are simplifying or solving equations, you will be successful on the algebra
questions on the GED Math Test. And remember, there are only about 10 algebra questions out
of the 50 questions on the GED Math Test.
3
Balancing Equations
Equations are statements that two expressions are equal. In algebra, often some part of the
equation is missing. The object of solving the equation is to discover what part(s) will balance
the equation and make the two sides equal to one another.
Even though there are certain steps that are recommended to balance equations using the rules of
algebra, it is often possible to balance equations just by using arithmetic skills. In this equation, it
is easy to see that 4 is the only number that will make a true statement.
3x8=Ax6
Using your arithmetic skills, find one number which will balance each of the following
equations. Answers are on page 21.
3 x 8 = _____ + 6
8 x 3 = 48 ¡Â _____
_____ - 12 = 6 x 6
1,000 = B
10
4A = 24
25 = a2
2+3x5=X-3
(2 + 3)5 = 50/y
_____ = 42
1/2 x 1/3 = k/36
.2 + .2 = ____ %
1 dozen = b x 3
Variables
A variable is a letter or symbol used to represent an unknown quantity in an equation or
formula. The value of a variable can change. Sometimes the value is dependent on other
quantities and which quantities are known or unknown in the equation or formula. For example,
the formula for finding the area of a rectangle is A = LW. If the area is known to be 24, there are
several solutions for L and W. If L = 6, W = 4. If L = 8, W = 3. The solution for one variable is
dependent on the value of the other.
Write at least three solutions for the variables in the following formulas:
Answers are on page 21.
A = LW
A = 12
A = 1/2 BH
A = 24
P = 2L + 2W
P = 36
V = LWH
V = 300
____________
____________
____________
____________
____________
____________
_____________
_____________
_____________
_____________
_____________
_____________
Often there is a single solution for a variable. Find the solution for the missing value in the
formulas below:
A = LW
L = 10, W = 5
A = _____
C = !D
4
D=3
C = _____
Operations with Signed Numbers
Before using the basic rules of algebra to solve for variables, it is essential to know how to
perform the four operations, addition, subtraction, multiplication, and division, with positive and
negative numbers. Positive numbers are those to the right of zero on the number line. Negative
numbers have values less than zero and are found to the left of zero on the number line.
negative
positive
¡ -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 ¡
Remember, the number line is a representation of all numbers even though there is not enough
space to write all of the whole numbers, fractions, decimals, etc. They are all theoretically sitting
in their proper place on the number line. Also, the number line is infinite. It extends in both
directions with no end.
Practice this exercise to review your understanding of the number line. Answers are on page 21.
negative
positive
¡ -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 ¡
On the number line above:
a.
b.
c.
d.
e.
circle zero
draw a box around -8
add 4.5 in the correct place
put a star above -2
add -1/2 in the correct place
f. draw a triangle around 10
g. add 7 3/4 in the correct place
h. add the next whole number to the left and right
i. add - 2 1/2 in the correct place
j. shade +9
There are special rules to add, subtract, multiply, and divide signed numbers. These rules are not
difficult, but you must be able to perform these operations with confidence in order to succeed in
algebra.
When solving algebraic equations, you must be able to move terms from one side of the equals
sign to the other in order to isolate variables. In order to move terms, you will make use of the
rules for operations with signed numbers. You will also be using inverse operations as well.
Inverse operations are the opposite operations. Addition and subtraction are opposites, and
multiplication and division are opposites. Later you will learn to eliminate terms using inverse
operations.
However, before we follow the basic rules of algebra to solve equations, we must practice using
the rules for operations with positive and negative numbers. Different math books explain the
rules in slightly different ways, but the result is always the same. Read and practice the rules for
each of the four operations, addition, subtraction, multiplication and division. When you find you
are comfortable with these methods, then you will be ready for the basic rules of algebra.
5
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