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



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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:

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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.

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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.

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