The GED Mathematics Test

Introduction to Algebra

Margaret A. Rogers, M.A.

ABE/GED Teacher

Adult School Administrator

Education Consultant

California Distance Learning Project

www.cdlponline.org

GED

Video Partner

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.

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 a. statement that two expressions are

equal

_____2. algebra b. letters used to substitute for

numbers

_____3. variable c. the set of positive and negative

numbers

_____4. equation d. the opposite operation as addition

is to subtraction and multiplication is

to division

_____5. inverse operation e. branch of mathematics

Points to Remember:

• 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!

#38

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

3 x 8 = 4 x 6

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.

3 x 8 = A x 6

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.

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.

3 x 8 = A x 6

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 ÷ _____ _____ - 12 = 6 x 6

1,000 = B 4A = 24 25 = a

2 + 3 x 5 = X - 3 (2 + 3)5 = 50/y _____ = 4

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 = 1/2 BH P = 2L + 2W V = LWH

A = 12 A = 24 P = 36 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 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. circle zero f. draw a triangle around 10

b. draw a box around -8 g. add 7 3/4 in the correct place

c. add 4.5 in the correct place h. add the next whole number to the left and right

d. put a star above -2 i. add - 2 1/2 in the correct place

e. add -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.

Operations with Signed Numbers

Operation

The Rules

Addition

Checks and Bills

Subtraction

Change the sign of the number being subtracted.

Checks and Bills

Multiplication

Multiply ignoring the signs.

Give a sign to the answer: Like signs + Unlike signs -

Division

Divide ignoring the signs.

Give a sign to the answer: Like signs + Unlike signs -

Addition - Checks and Bills

One way to think of the rules for adding signed (positive and negative) numbers is to just think

of checks and bills. An illustration for checks and bills is found in postman stories.

Although my father, who was born in 1908, clearly remembers when the mail was delivered

twice a day, that has not been the case since the 1950s. There is now only one delivery each day;

and yet we still use the phrase, “I’ll put it in the morning mail.” Every day is a new day when

analyzing postman stories.

Answers are on page 21.

Monday

On Monday the postman brought two checks, one for $56.00 and one for $10.00. Assuming you

have no other money in the world, what is your financial situation after this delivery?

_______________

Tuesday

On Tuesday, the postman brought a check for $25.00 and a bill for $13.00. Assuming you have

no other money in the world, what is your financial situation after this delivery?

_______________

Wednesday

On Wednesday, the postman brought two bills. One was for $68.50, and the other was for

$16.00. Assuming you have no other money in the world, what is your financial situation after

this delivery? _______________

Thursday

On Thursday, the postman brought two checks and one bill. The checks were for $24.75 and

$34.00. The bill was for $100.00. Assuming you have no other money in the world, what is your

financial situation after this delivery? _______________

Friday

On Friday, the postman brought three checks and one bill. The checks were for $14.00, $39.50,

and $45.00. The bill was for $64.00. Assuming you have no other money in the world, what is

your financial situation after this delivery? _______________

Saturday

On Saturday, the postman brought only bills. Alas, there were three of them. There was an

electric bill for $44.50, a magazine subscription for $24.95, and a parking ticket for $6.00.

Assuming you have no other money in the world, what is your financial situation after this

delivery? _______________

There are no mail deliveries on Sunday.

Challenge problem: If every day were not a new day, how much money would you have or owe

at the end of the week? _______________

As adults experienced with money, we may have used different ways to arrive at the total each

day. No matter what we did, including subtraction, we were still adding signed numbers as we

completed this exercise. Continue to practice with some numerical problems:

Add (Checks and Bills):

Note: Any number without a sign is positive (a check).

+36 - 8 +100 -100 +32 60

- 5 -17 - 25 + 25 -17 40

-40 +81 +3 (+17) + (+5) + (-6) + (-2) + 15 = _____

-60 -36 - 7

- 2 12 + (-17) + (+8) + (-75) + (-8) = _____

During the holiday mail season, bills were mounting up for Carrie. She had placed many catalog

orders that were arriving C.O.D. She kept her checkbook right by the front door so she would be

ready to settle the bills and accept the items. On December 10

, she received C.O.D. orders for

$12.64, $39.57, and $19.11. She wrote checks for all of them. The same day, she received a gift

check for $50.00 from her Aunt Tilda. Did she spend more or come out ahead that day? How

much? _________________________________

Subtraction

The rules for subtracting signed numbers are completed in two steps:

1. Change the sign of the number being subtracted.

2. Add (Checks and Bills)

When you are subtracting (-4) from (+16), you would first change the sign of the number being

subtracted (-4). Then add (checks and bills). In this case, you now have two checks.

Subtract: +16 +16

- 4 + 4

+20

Subtract: Answers are on page 22.

-12 +16 +38 +19 -37 -85

+3 -5 +2 -6 +5 -50

+8 +3 +50 75 -75 -75

-3 -8 -2 -60 60 -60

(+6) - (-9) - (+3) - (+7) = _____ (-6) - (+9) - (30) - (-7) = _____

Multiplication

The rules for multiplying signed numbers are completed in two steps:

1. Multiply ignoring the signs.

2. Give a sign to the answer: Like signs + Unlike signs -

Multiply: Answers are on page 22.

(8) (-3) (-3) (-5) (+5) (-11) (+5) (-3)

_______ _______ _______ _______

(-2) (-12) (+3) (-5) (+6) (+8) (-10) (-10)

_______ _______ _______ _______

(-7) (+9) (-20) (+5) (-5) (20) (-9) (+6)

_______ _______ _______ _______

Division

The rules for dividing signed numbers are the same as multiplication and are completed in two

steps:

1. Divide ignoring the signs.

2. Give a sign to the answer: Like signs + Unlike signs -

Divide: Answers are on page 22.

(+48) ÷ (-12) (-25) ÷ (-5) (+36) ÷ (-6) (-24) ÷ (+6)

__________ __________ __________ __________

-10 -76 +64 +50 +366

-2 +4 +8 -25 -6

Mixed Practice

Add Subtract Multiply Subtract Add Add Subtract

-16 +12 +50 +38 -17 -12 12

+4 -7 +8 -6 +5 -50 -12

(-35) ÷ (-7) (-2) (+15) (-5) (10) (-18) (+6) 35/-7

____________ _____________ ____________ ____________ ______

(-100) ÷ (-20) (+50) ÷ (-10) (+9) (-7) 50 + (-3) -100/4

__________ ___________ __________ __________ _____

Measure Up

Calculator Permitted

An acre-foot is a measurement used for irrigation water. It is the amount of water that would

cover an acre of land one foot deep. An acre is equal to 160 square rods. A square rod is equal to

30.25 square yards. Practice your unit conversion skills by answering the following questions.

Answers are on page 22.

How many square yards of water one foot deep are in two acre-feet? _____________________

How many square feet of water one foot deep are in an acre-foot? _____________________

Properties of Operations

Commutative Property of Addition and Multiplication

The commutative property is a law in mathematics that states that the order in which you add

or multiply numbers does not affect the result; for example, 3 + 4 = 4 + 3. In algebra you will use

the commutative property.

a + b = b + a

ab = ba

Associative Property of Addition and Multiplication

The associative property is a law in mathematics that states that when you add or multiply more

than two numbers, you can group the numbers in any order without affecting the result; for

example 3 + (4 + 5) = (3 + 4) + 5. You will use the associative property in algebra.

a + (b + c) = (a + b) + c

a(bc) = (ab)c

Distributive Property of Multiplication

The distributive property is a law in mathematics that states when a number is multiplied by a

sum written in parentheses, you can find the result by multiplying the number outside the

parentheses by each number in the parentheses and then adding. In other words, you are

distributing the multiplier across all of the terms; for example, 4 x (5+6) = 4 x 5 + 4 x 6 = 20 +

24 = 44. You will use the distributive property in algebra.

a(b + c) = ab + ac

Practice identifying the law of mathematics that is used in each of the following expressions.

Write commutative, associative, or distributive after each expression to show which law is

modeled by the expression. Answers are on page 22.

12 + 13 = 13 + 12 ______________________________ 5(c + d) = 5c + 5d ____________________________

10 x 6 = 6 x 10 _______________________________ x(yz) = (xy)z ________________________________

10 + (8 +9) = (10 + 8) + 9 _______________________ (2 x 3) + (2 x 4) = 2 (3 + 4) ____________________

xy = yx _____________________________________ 4 + 10 = 10 + 4 ______________________________

About Math and Life

Marina was excited about her new home business to wrap gifts and make gift

baskets. She knew starting a new business would require patience. She had to do

marketing and recruit a group of returning customers. She was prepared to have only a small

profit or even take a loss the first year. She set up a spreadsheet to track her expenses and

income. Working with this type of spreadsheet is like adding positive and negative numbers. You

can think of the income as checks and the expenses as bills. Marina’s spreadsheet appears below.

Excel Worksheet

Gifts by Marina 2005

Month

Income

Expenses

Paper

Tape

Ribbon

Office

Cards

Baskets

Total

January

150

100

300

670

February

225

March

April

May

160

June

July

August

September

October

November

250

December

300

Total

994

335

100

325

896

How much of a profit or loss did Marina show during the first year of her business?

______________________________________________________________________________

Explain whether or not she met her goals and why.

______________________________________________________________________________

Do you think that Marina will continue her business during the following year. Why or why not

______________________________________________________________________________

Answers are on page 22.

Isolating Variables and Solving for Unknowns

An equation is a mathematical statement that two expressions are equal. Look at the

equation below:

3x + 5 = 35

This equations states that 3x + 5 is equal to 35. In order to solve the equation, you must find the

value for the variable, x, that will make the equation true. Since an equation is like a balance

scale, you can add or subtract the same quantity on both sides of the equation without upsetting

the balance. You can also multiply or divide by the same quantity on both sides of the equation

without upsetting the balance. Remember that whatever you do on one side of the equation, you

must do on the other side to maintain the balance.

Isolating Variables

To solve an equation, you must first isolate the variable. In the equation above, the variable, x, is

part of the term 3x. So you want to isolate that term on the left side of the equals sign. In order to

isolate that term, you must eliminate the other term, + 5. To eliminate terms, use the inverse

operation. An inverse operation is the opposite operation. Addition and subtraction are opposites

Multiplication and division are opposites. Subtract 5 from the left side to eliminate the + 5.

Remember, you also must subtract 5 from the other side.

3x + 5 = 35

- 5 = 35 - 5

3x = 30

Now the term with the variable, x, is isolated on the left side of the equals sign. In order to

solve for the value of x, now eliminate the 3 from the term 3x by using the inverse operation of

multiplication. Divide by 3. Then you must divide the right side by 3 as well.

3x = 30

3 3

x = 10

Substitute 10 into the original equation to check you answer.

3x + 5 = 35

3(10) + 5 = 35

30 + 5 = 35

35 = 35

Solving for Unknowns

Practice these steps to solve for the unknown in the following equations:

a. Use inverse operations to eliminate terms without variables (remember to keep the

equation in balance by performing the same operation on both sides of the equals

sign).

b. Isolate the term with the variable on one side of the equals sign.

c. Use inverse operations to eliminate numbers from the term with the variable leaving

just the letter by itself (remember to keep the equation in balance by performing the

same operation on both sides of the equals sign).

d. After finding the value of the variable, plug it into the equation to check your work.

2x + 8 = 30

a. 2x + 8 = 30 b. 2x = 22 c. 2x = 22

2x - 8 = 30 - 8 2 2

x = 11

d. 2x + 8 = 30

2(11) + 8 = 30

22 + 8 = 30

30 = 30

Exercise: Answers are on page 22.

x + 5 = 20 a - 12 = 48 5 = 100 60/y = 12

2x - 8 = 32 2y - 6 = 22 5 = 3y - 28 4q = 48

20 + 5 = 10 16 - z = 12 x + 25 = 100 48 + 2 = 72

Measure Up - It’s Just a Matter of Time

120 seconds = _____ minutes _____ minutes = 3 hours 1 day = _____ hours

1 century = _____ years 3 decades = _____ years 2 years = _____ days

_____ weeks = 2 years 3 weeks = _____ days 3 days = _____ hours

36 months = _____ years 40 minutes = _____ hour 3 months = _____year

Combining Like Terms

Sometimes an equation will contain terms that should be combined before solving the equation.

Any like terms can be combined to simplify the process of solving the equation. In the equation

below, there are examples of like terms that can be combined.

3x + 6 -12 + 4 -x = 16

Before solving this equation, you can combine the terms that contain the variable, x. These are

like terms because they contain the same variable. Remembering the rules for signed numbers,

we know that 3x + (-x) = 2x.

2x + 6 -12 + 4 = 16

Now you can combine the numerical terms that are on the same side of the equals sign. In this

equation, the two positive numbers can be combined to make + 10. Add +10 to -12, and you are

left with -2.

2x - 2 = 16

Now solve the equation using the steps on page 13. Answer is on page 23.

Practice by combining like terms in the following expressions. Answers are on page 23.

5t - 6 + 2t + 3 2xy - xy + 13 + 3 x + x + 5 + 7 + 4x

_______________ _______________ _______________

26 - 35 + c + 5c + 100 3(2x - 4) + 6 - 2x 15" + 16 + " - 12

_______________ _______________ _______________

Now practice solving more complex equations by combining like terms and then following the

other rules:

" Combine like terms on each side of the equals sign.

" Isolate the term with the variable on one side of the equals sign.

" Use inverse operations to solve for the variable.

" Check your answer.

12x + 13 = 74 6x + 7 = 37 x + x + 5 + 2x = 25

8y - 4y + 12 = 33 8(k - 3) = 5k + 3 5z + 4z - 10 = 35

Out into Space

3 3

Circle Up

Write four 1’s and three 2’s in the circles so that no three numbers that are next to each other

have a sum that is divisible by three. Answers are on page 23.

Circle Up courtesy of Alva Carlson, adapted from Ted Lewis

Evaluating Algebraic Expressions

In some algebra problems, the value of the variable(s) is given, and students are asked to

evaluate or find the value of the expression. For example, if a = 2, the value of a + 5 = 7. To

evaluate an algebraic expression, substitute the value of the variable(s) into the expression and

perform the necessary operations.

If a = 2, then a + 5 = _____

2 + 5 = 7

If x = 3 and y = 10, evaluate the following expressions. Answers are on page 23.

x + y = _____ y - x = _____ xy = _____ y/x = _____

2x + 3y = _____ 3(x + y) = _____ x

= _____ y

= _____

- x

= _____ (y

) (x

) = _____ xy +15 = x(y - x) = _____

If a = 6, b = 4, and c = 8, evaluate the following expression: ab + ac + b/c = _____

Algebra Word Problems

Some word problems can be solved by setting up an algebraic equation and then solving for all

or part of the answer. Sometimes word problems seem very confusing, and algebra will help you

set them up for solution. Here is an example of such a problem:

This year Andrew is two years less than twice his brother’s age. Their combined ages are equal

to 22. How old are the boys?

Let x = the brother’s age

Let 2x - 2 = Andrew’s age

Now set up the equation to solve for x, the brother’s age.

x + 2x - 2 = 22

3x - 2 = 22

+2 = 22 + 2

3x = 24

3 3

x = 8

Andrew’s brother is 8, so Andrew is 14.

It is important to practice setting up the proper equation to solve algebra word problems. You

will definitely see algebra word problems on all forms of the GED Math Test. Practice setting up

equations for the following questions. Answers are on page 23.

1. Stan and Oliver have a lawn-mowing business. If Stan earns $3.00 for every $1.00 that

Oliver earns, how much is Oliver’s share for the day that they earned $75.00?

______________________________________________________________________

2. The length of a rectangle is twice the width. If the perimeter of the rectangle is 24 inches,

what is the length of the rectangle?

______________________________________________________________________

3. The swim team sold tickets to their skit night to earn money to go to the finals in another

city that was 200 miles away. They sold four adult tickets for each child’s ticket. If they

sold 155 tickets, how many adults bought tickets?

______________________________________________________________________

4. Stella’s sock drawer contains 30 pairs of socks. There are 3 times less 2 the number of

pink socks than blue socks. How many pairs of pink socks and blue socks does Stella

have?

______________________________________________________________________

Algebra Review

Answers are on page 24.

Add:

+3 + (-12) = (-3) + (-4) = (-6) + (4) + (-2) + (+8) + (-4) =

Subtract:

+3 - (-5) = (-16) - (-35) = (-4) - (+27) = 67 - (-60) =

Multiply:

(-3)(+6) = (-6)(-3) = (8)(+10) = (9)(-7) =

Divide:

36/-12 = 100 -225 ÷ -5 = (-16)/(+4) =

-25

If a = 2, b = 6, and c = 7, evaluate the following expressions:

ab - c = _____ a + b + c = _____ bc/a = _____ a + b - c = _____

a(b + c) = _____ c

- ab = _____ c + ab = _____ abc = _____

(-a)(c) = _____ b + a

= _____ bc ÷ -a = _____ abc = _____

-a

Simplify by Combining Like Terms:

6x - 5x + 5 - 2 7xy + 4xy + x + y - 2y 3a

+ a

- 2 + 8 - 4 s + 6 + 6s + 6 - 2s

____________ __________________ _______________ _______________

Solve:

6k + 7 = 37 6x - 16 = 56 7(y - 2) = 21 11q + 12 = 9q - 32

Suki and Mei Li worked out at the gym together and jumped rope for aerobic exercise. Suki

jumped for several minutes, but Mei Li was able to jump 12 minutes longer. Together

they jumped for one hour and six minutes. How many minutes did Suki jump? Write

an equation and solve it. Show your work.

Mei Li

Strategy Session

Analyze Method for Solution

For some of the questions on the GED Math Test, the answer choices will not be the solution, but

rather the method to find the solution. About 10 of the 50 questions will require the test taker to

choose the method for solving the problem.

Before taking the GED Math Test, it is important to practice writing how to solve problems. For

example, look at the following sample question.

Bradley and Marcia walked to school each day in the morning. The walk was 12 blocks long.

After school, Marcia took the same route home. Bradley walked four blocks to the dime

store, back to the school, and home the same route as in the morning. How many blocks did

the children walk altogether? What is the correct solution?

1) (2 x 12) + 12 + (4 + 4)

2) (12 + 12) - 8 + 12

3) (3)(12) - 8

4) (3)(12) + 8 ÷ 2

5) (4)12 + 8

Use some of the other strategies that you know to select the best method to solve the problem.

" Look for key words.

" Remember order of operations.

" Keep in mind the properties of operations.

" Eliminate incorrect choices.

To answer the questions above, look at the key word altogether. It is italicized to show its

importance. That word lets you know you are going to be adding. Therefore, choices 2), 3), and

4) are not correct because they use the operations of subtraction and division. Now analyze

choices 1) and 5) to see which one best describes the situation in the problem. Choice 1) leaves

out one of the 12-block legs of one of the children. Therefore 5) is the correct answer.

Often the problems that require algebra will just require that you choose the correct set-up for

the equation, and you will not have to solve the equation to find the correct answer. Here is an

example of an algebra problem.

Which of the following expressions could be used to find 212 plus the sum of d - 4c?

1) (d - 4c) - 212

2) 212 + (d - 4c)

3) -212 + (4c + d)

4) 212 + 4cd

5) 212(d - 4c)

The key word is plus, so you know you must add. This time it is not pointed out as a key word.

Only choices 2), 3), and 4) have addition. Of those, only choice 2) contains d-4c. It is correct.

Practice choosing the correct method to solve each problem below. Underline the key word(s) in

each problem before you make a choice. Answers are on page 24.

1. Belinda works for a factory that manufactures cameras. She can inspect 12 cameras in her

6 hour shift. Which expression shows how to find how many cameras (C) she could

inspect if she increased her shift to 8 hours?

1) C = (12)(6)

2) 12/6 = C/8

3) C = (12)(8)

4) 12(6 + 8) = C

5) C = 6(12)/8

2. The Green Guys Landscapers were hired to make a circular garden for Mrs. Peters. She

wanted the circle to be 12 feet across the center. Which expression shows how to find the

measurement for the circumference of the new garden?

1) (3.14)6

2) (3.14)6

3) (3.14)12

4) (3.14)12

5) (3.14)

3. LuAnn and Billy had a backyard business making birdhouses. They bought the

birdhouses and then painted and decorated them for sale. They bought each birdhouse for

$5.00 and sold each one for $11.00. If they sold 40 houses last year, which expression

shows how much money they made?

1) (11 - 5)40

2) 40(11 + 5)

3) (11 - 5) ÷ 40

4) (11 + 5) ÷ 40

5) 11 x 40

4. Two angles of a scalene triangle measure 95 degrees and 50 degrees. Which expression

could be used to find the measurement of the third angle?

1) 360 - (95 + 50)

2) 360 - (95 - 50)

3) 180 - (95 - 50)

4) 180 - (95 + 50)

5) 90 + 95 + 50

Analyze Method for Solution

GED Exercise

1. If x = 7, and y = 10, what is the value

of the expression xy - (y + 2)?

1) 71

2) 66

3) 58

4) 50

5) 5

2. Max has a brother who is four years

more than twice his age. If their

combined ages equal 37, how old is

Max?

1) 29

2) 22

3) 15

4) 11

5) 10 Max

3. Which of the following expressions

is the simplified form of

3t - 5t + 16 - 9?

1) 8t + 25

2) 2t + 25

3) 8t + 7

4) 15t -7

5) -2t + 7

4. Carl and Jim participated in a

walkathon to raise money for a

medical charity. Carl raised $15 for

every mile he walked. How many

miles did he walk if he raised

$180.00?

1) 10 miles Jim

2) 11.5 miles

3) 12 miles

4) 15 miles

5) 17 miles

Carl

5. The geometry teacher drew a right

triangle on the board and labeled one

of the angles 50 degrees. What is the

measure of the other two angles?

1) 90 degrees and 60 degrees

2) 40 degrees and 80 degrees

3) 40 degrees and 90 degrees

4) 90 degrees and 45 degrees

5) not enough information is given

6. Levi took three tests in his

geography class and scored 85, 72,

and 78. He needed to have an

average of 80 to get a B in the class.

What minimun score did he need on

the fourth and last test?

1) 95

2) 91

3) 90

4) 89

5) 85

7. A grocer stocks cans of vegetables

on a shelf. The peas are in cans that

have a circular bottom with an area

of 9.42 square inches and hold 56.52

cubic inches. How tall are the cans?

1) 3 inches

2) 6 inches

3) 9 inches

4) 10 inches

5) 11 inches

Answers and Explanations

Words You Need to Know page 2

1. c.

2. e.

3. b.

4. a.

5. d.

Balancing Equations page 4

18 2 48

B = 10,000 A = 6 a = 5

X = 20 y = 2 16

k = 6 40 b = 4

Variables

L = 12, W = 1 B = 6, H = 8 L = 10, W = 8 L = 15, W = 10, H = 2

L = 4, W = 3 B = 4, H = 12 L = 14, W = 4 L = 10, W = 7.5, H = 4

L = 6, W = 2 B = 3, H = 16 L = 11, W = 7 L = 10, W = 6, H = 5