TESTING CENTER HOURS:
(Testing times are subject to change)
Monday thru Wednesday 8:30am-3:30pm
Thursday 8:30am-6:00pm
Friday 8:30am-12:00pm
The tests are given in the Testing Center, A-Building Room 204. Be sure to bring
a Photo ID
and Social Security Card. Pencils and paper will be provided for Arithmetic and
Algebra
calculations. NO CALCULATORS ALLOWED!
For more information, please contact Laura Bracken, Testing Center
Coordinator, at
336-386-3443
The Arithmetic portion of ACCUPLACER is designed to test
your basic math skills and is
divided into three primary categories:
1. Ope rations with whole numbers and fractions, including:
• Addition, subtraction, multiplication, division
• Recognizing equivalent fractions and mixed numbers
2. Operations with decimals and percents, including:
• Addition, subtraction, multiplication, division
• Percent problems, decimal recognition, fractions
• Percent equivalences and estimation problems
3. Applications and problem solving include:
• Rate, percent, and measurement problems
• Geometry problems
• Distribution of a quantity into its fractional parts
A total of 16 questions will be asked.
Fol lowing are some helpful TIPS for taking the TEST:
1. MOST IMPORTANT: All tests are un-timed,
so please don’t rush.
2. Read each question very carefully to make sure that you
understand what it is
asking.
3. Read all choices for answers before picking one.
4. When having trouble, eliminate as many choices as possible.
5. On the Arithmetic and Elementary Algebra sections of the test,
try putting your
answer back into the original problem to check your work.
6. You cannot go back to previous questions . Make sure you are satisfied
with your
answer before continuing to the next question.
Fractions
Adding and Subtracting Fractions
...with common denominators :
A fraction is made up of three parts: the numerator, the fraction bar, and the
denominator.
So what exactly do we mean when we say that two fractions
have a common denominator?
Basically, it means that the numbers below the fraction bars in the fractions
you are adding or subtracting (the denominators) are the same. In this case, all
you
have to do is add or subtract the numbers above the fraction bars (the
numerators) in
the fractions; the denominator of the sum remains the same.
For example: 
All you’re doing is adding the
numerators on top .
This also works with subtraction: 
Again,
you’re just subtracting
the numerators. This works because each fraction has a common denominator, in
this
case 8. It’s the same as saying 1 apple + 3 apples = 4 apples. Since
we’re dealing
only with apples, you can add them together without any problems.
Exercises
Solve the following problems.
...with different denominators :
We’ve seen how simple it is to add or subtract a fraction with a common
denominator,
but what do we do if the denominators are different? Unfortunately,
common
denominators are required for addition and subtraction of fractions.
Before you can
proceed, you’ll have to change each fraction into an equivalent fraction so the
two
equivalent fractions have common denominators so they can be added. Below is a
quick lesson on how to do this.
Equivalent Fractions
Equivalent fractions are those fractions that may not look the same, but they do
have
the same value. For example, 1/2 and 2/4 are equivalent fractions because the
numerator
and denominator of each fraction are in the same ratio; 1 is half of 2 and 2 is
half of 4.
Therefore, 3/6 is also equivalent to 1/2 since 3 is half of 6. 4/8 , 10/20 , and
25/50 are also equivalent
to the fraction 1/2 . Every fraction has infinitely many fractions that are
equivalent to it.
All you really need to do to find an equivalent fraction is to multiply the
numerator
and denominator of a fraction by the same number. For example we have already
stated 1/2 and 2/4 are equivalent. Notice that 
We just multiplied the numerator
and denominator by 2 and found an equivalent fraction. Look at the other
fractions
equivalent to 1/2 and convince yourself that the numerator and denominator of
these
equivalent fractions are simply
Now that we know what equivalent fractions are, the next
step in adding or subtracting
fractions without common denominators is to make new equivalent fractions
where the denominators equal one another. To accomplish this we must first find
the
least common multiple or LCM of the denominators. This is known as the
least
common denominator or LCD. It may help to list the multiples of each
denominator
until you find the least common multiple, meaning the smallest number that both
denominators will divide evenly.
For example: Lets add 
We would start by
listing the multiples of the denominators,
in this case 6 and 8 respectively.
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, etc.
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, etc.
You’ll notice that 24 and 48 are multiples of both denominators. These are
called
common multiples. Since 24 is smaller than 48, 24 is the least common multiple
of the
denominators. Thus our least common denominator is 24. Now we want to make new
fractions equivalent to 1/6 and 7/8 with 24 as the denominator. Remember from
earlier
that in equivalent fractions both the numerator and denominator must be
multiplied
by the same number.
To get 24 from 6 you
have to multiply by 4. So we must also multiply the
numerator (the 1) by 4.
We do the same thing with 7/8 .
To get 24 from 8 you
have to multiply by 3. So we must also multiply the
numerator (the 7) by 3.
We now have fractions equivalent to the original fractions
and these fractions have
a common denominator, so we can just add the numerators as we discussed before.
In
this case,
Exercises
Reduce the following fractions.
Solve the following problems.
...with mixed numbers
A mixed number is a combination of a whole number and a proper fraction. (i.e.
). A proper fraction is a fraction whose
numerator is smaller than the denominator.
A mixed number is actually a sum (two things being added). It is very important
to
understand this. The mixed number actually
means the whole number 4 plus the
fraction 3/4 or 
When adding mixed numbers
that have a common denominator
in the fractional part, just add the whole numbers together, then add the
fractions
together as previously discussed.
For example, 
because 4 + 9 = 13 AND
When subtracting a
mixed number from another mixed number, we do basically the same thing. We can
subtract the whole numbers and, some of the time, we can subtract the fractions,
BUT
BE CAREFUL!
Why?
For example:
because 12 − 5 = 7 and
But what if you were subtracting
Subtracting 12 − 5 is no problem,
but what about 
Since 7 is larger than 4 we
can not perform this subtraction
via this method. We need another method to subtract when the fraction in the
second
mixed number is larger than the fraction in the first mixed number. Luckily,
there is
another method. This involves converting mixed numbers to improper fractions.
Improper Fractions
An improper fraction is a fraction in which the numerator is larger than or
equal
to the denominator. 5/4 is an improper fraction because the numerator (5) is
larger than
the denominator (4). It is very important to know that all improper fractions
can
be converted to an equivalent mixed number and that any mixed number
(or whole number) can be converted into an equivalent improper fraction.
To convert a mixed number into an improper fraction:
1) Multiply the denominator of the fraction times the whole number.
2) Add the numerator to the product (answer) from step one.
3) Put the sum (answer) from step 2 in the numerator of a fraction whose
denominator
is the same as the denominator of the original mixed number.
whole number
Now how do we use this to subtract
We we can convert
to 
and
convert 
to
. Now all we have to do is subtract the
equivalent improper fractions.
Since the denominators are the same we simply subtract numerators:
To convert an improper fraction into a mixed number:
Our answer to the previous problem is an improper fraction. Normally we do not
leave answers as improper fractions. Instead we convert them to mixed numbers.
This
is done by dividing the numerator of the improper fraction by the denominator of
the
improper fraction.
The process has us divide the numerator by the
denominator. The quotient (the number
above the division box [the 6]) will become the whole number in our mixed
number.
The remainder (the 8) will be the numerator in the fractional part of the mixed
number
and the denominator from the improper fraction remains the denominator for the
mixed number.
Mixed Numbers with Different Denominators
Finally, adding mixed numbers with different denominators is no different than
adding
mixed numbers with the same denominators. We still simply add the whole numbers
and then add the fractions. Only now we must use the techniques mentioned above
for
adding fractions with different denominators. For example, if we were trying to
add 
and 
, we would still just add 6+3, but we
must first change the fractional parts into
equivalent fractions with common denominators before we can add here. The LCD
this time is 8. So we want to change 3/4 and 5/8 into equivalent fractions with
8 as the
denominator. 5/8 already has 8 as the denominator so we do not make any changes.
3/4
is equivalent to 6/8
Now our mixed numbers become
and 
,
and we can simply add the whole numbers
together and then the numerators. Since 6 + 3 = 9 and 6
,we
are left with
an answer of 
But that’s not the end of it.
Since 11/8 is an improper fraction, this
is not a mixed number in its proper form. Remember a mixed number is defined to
be
a whole number and a proper fraction. We convert the improper fraction
11/8 to the
mixed number 
by the method previously
mentioned.
And finally...
Subtracting mixed numbers with different denominators is
the same idea. Subtract the
second whole number from the first, find the LCD of the denominators, make
equivalent
fractions with the LCD as the denominator, then subtract the second fraction
from the first. Be aware that after you have found equivalent fractions with
common
denominators, you may have to convert these mixed numbers to improper fractions
as
discussed before when subtracting if the second fraction is bigger than the
first!
Exercises
Change the improper fraction into a mixed number.
Change the mixed number into an improper fraction.
Solve the following problems.
Multiplying Fractions
...a fraction by a whole number:
Now that we’ve discussed adding and subtracting fractions, it’s time to talk
about
multiplication of fractions. But don’t worry, multiplying fractions is much
easier than
adding or subtracting them. Multiplying a fraction by a whole number is actually
quite
simple. All you have to do is multiply the numerator by the whole number. DO
NOT
CHANGE THE DENOMINATOR. For example: If you wanted to multiply 3 by
2/7 , just multiply 3 × 2 = 6. This is the numerator of your answer. The
denominator
does not change, giving you 6/7 .
Reminder: If the numerator is larger than the denominator, change it into
a mixed
number.
...a mixed number by a whole number:
Multiplying a mixed number by a whole number is actually very similar to
multiplying
a whole number and fraction together. In this case, you must multiply both the
whole number in front of the fraction AND the numerator by the other whole
number.
For example: In order to multiply 
, you must
first multiply 2 × 4 to give you 8
and then multiply that same 
, to give
you
giving you an answer of
Notice again that the denominator does not change.
...a fraction by a fraction:
When multiplying two fractions together (no matter if they are proper or
improper, or
have common denominators or not), you simply multiply the numerators together
and
then multiply the denominators together.
For example: To multiply 3/4 by 7/11 , first multiply the numerators, 3 × 7 =
21. Then
multiply the denominators, 4 × 11 = 44. This gives you a new fraction of 21/44
or
If you have more than two fractions, just multiply all the
numerators together and all
the denominators together.
For example: If you wanted to multiply
...a fraction by a mixed number or a mixed number by a
mixed number:
In order to multiply a mixed number by either a fraction or another mixed
number,
you’ll need to first change the mixed number or mixed numbers into an improper
fraction(s) .
For example: If we wanted to multiply 
, we
first must change both mixed
numbers into improper fractions.
Now we apply
the previously mentioned method (remembering that it applies to improper
fractions as
well!). Multiply the numerators together, then the denominators.
Finally, you can change it back to a mixed number.
Exercises
Solve the following problems.
Dividing Fractions
Just like multiplication, division of fractions does not require common
denominators.
It does require knowledge of something called “the reciprocal of a fraction.”
The reciprocal
of a fraction is simply a fraction with the numerator and denominator switched.
For example, the reciprocal of the fraction 2/3 is the fraction 3/2 . The
reciprocal of 7/11 is 11/7 .
You may be asking, “Where does the reciprocal of a fraction come into the
division of
fractions?” It comes from the fact that we can change any division problem
involving
any fractions into a multiplication problem (which we have already discussed how
to
solve) by changing the fraction we are dividing by to its reciprocal.
For example:
Division involving a Whole Number and a Fraction
If you want to divide a fraction (proper or improper) by a whole number or
divide
a whole number by a fraction, you’ll need to turn the whole number “into a
fraction.”
This is easily accomplished by putting the whole number into the numerator of a
fraction
whose denominator is 1. For example: the whole number
Now
we apply this to dividing a fraction by a whole number. For instance:
Division involving a Mixed Number(s)
If a division problem involves mixed numbers, we must first change the mixed
number
to its equivalent improper fraction. We then use the same method discussed
above.
For example: Let’s say you wanted to divide 
by 
. The first thing we do is convert
into the improper fraction
and convert
to 7/5 . Now we have
Decimals
A decimal is a number written in three parts:
1) The whole number part
2) The decimal point
3) The decimal part
In the decimal 143.216 (pronounced one hundred forty-three AND two hundred
sixteen
thousandths) the 143 is the whole number part and the 216 is the decimal part.
The whole number part can be zero or any whole number. The decimal point and the
decimal part represent a number greater than 0 but smaller than 1.
Adding Decimals
Now that we’ve learned to add, subtract, multiply and divide fractions, we’ll do
the
same with decimals, starting with addition. The key thing to remember about
adding
with decimals is to keep the decimal points lined up , as in the example below:
Notice that the decimals are all stacked on top of one
another, perfectly aligned. This
will ensure that we add the whole number part (the part of a decimal to the left
of a
decimal point) to the other whole-number parts and add the decimal parts (the
part
to the right of a decimal point) to the other decimal parts. Note too that
although
the number 58 does not have a decimal, because of place value and how decimal
are
defined, we know that the decimal comes at the end of the whole number. Thus, 58
could be written as 58.0. So as long as you keep the decimals in their proper
places,
the rest is basic addition.
Subtracting Decimals
Subtracting decimals is very similar to adding. You just line up the decimal
points and
subtract. You may fill in zeros where there are not the same amount of digits
after a
decimal.
For example if we are to subtract 13.56 - 8.674. We would write this vertically,
lining
up our decimal points, fill in any empty spaces to the right of the decimal
point with
zeros, and finally subtract as we would if they were whole numbers.
Exercises
Solve the following problems.
Multiplying Decimals
Multiplication of decimals works a little differently than addition or
subtraction, as
you don’t necessarily line the decimals up. First, we’ll show you how to
multiply large
numbers together, without decimal places. Below is an example of how to do this:
You begin by multiplying the bottom-right most number by
all numbers on the top
row. So, to begin, 7 multiplied by 628 is 4,396. Next, multiply 5 by 628, which
is 3,140.
This number is placed below the 4,396 that you had before. Notice also that the
last
digit of your answer (3140) is always directly below the number you’re
multiplying by
on the bottom row (in this case 5). Just keep in mind that each row of answers
is
shifted one place over to the left from previous row. Next, multiply 2 by 628 to
give
you 1,256. Finally, once you have all of your answers, add them all together,
row by
row, to give you the final answer of 161,396.
Multiplying with decimals works the same way, the only difference being the
decimal
place itself. Below is an example of multiplying with a decimal:
Begin by multiplying as you did before. The next question
is where to put the decimal.
Since there are three decimal places (2 in the first number, 1 in the second),
the answer
will have three decimal places as well. Since we’ve already said that the
decimal place
comes at the end of a whole number, move the decimal three spaces to the left.
This
gives you the correct answer of 161.396.
Exercises
Solve the following problems.
5. Rachel has to make 12,000 copies of a document for
Student Development. If
each copy costs 3 cents per sheet, how much will Student Development owe?
Dividing Decimals
As with multiplication, we’ll start by showing you how to divide without
decimals.
Start out by dividing each digit in the dividend (1798) by
the divisor (5). Since 1 won’t
go into 5, divide 17 by 5. 5 will go evenly into 15 3 times, leaving you with 2
left over.
Place the 2 right beside the 9, then try to divide 5 by 29.
5 will go into 25 5 times, so then you’re left with 4.
After placing the leftover 4 in front of the 8, divide 5
by 48. 5 will go evenly into 45 9
times, so you’re left with a remainder of 3.
When the Dividend Contains a Decimal
If the dividend contains a decimal, just place it directly above the dividend in
the
quotient. An example of this can be found below:
When the Divisor Contains a Decimal
If the divisor contains a decimal, it isn’t a simple matter of lining up the
decimals.
However, there is a simple solution to the problem. Just move the decimal as
many
places as needed so that both the dividend and the divisor are whole numbers.
For example:
First, the decimal in .02 was moved over 2 places to the
right in order to turn it into the
whole number 2. Then, the decimal in the dividend (14) must also be moved over
the
same amount of places. Remember that there is a decimal after the 14, even
though it
isn’t written. Move the decimal after 14 two spaces to the right to make the
number
1400. Then, divide 2 into 1400 as you normally would, giving you an answer of
700.
Note: Even if the dividend and divisor both contain decimals, you can still use
the
method described above. Remember too that only the divisor needs to be changed
into a whole number.
For example:
All you need to do is move the decimal in front of the 6
one place to the right in order
to make it the whole number 6. Then, move the decimal in .0018 one place to the
right as well, making it 0.018. After that, just place the decimal in the
quotient above
the decimal in the dividend (as described in the previous section ”When the
Dividend
Contains a Decimal”) and divide as you normally would.
Exercises
Solve the following problems.
Fraction/Decimal Conversions
Decimals into Fractions
Now that we’ve talked extensively about both fractions and decimals, let’s take
a
minute to talk about how they relate to one another. The truth is, a decimal is
a
fraction whose denominator isn’t written but is instead assumed to be a power of
10.
For example:
The astute reader will notice that the number of digits
after the decimal is directly
related to the number of zeros in the denominator. If we move the decimal place
three
places to the right in order to change .123 into the whole number 123, we must
move
the decimal place after the assumed 1 in the denominator three places to the
right,
making it 1,000.
Exercises
Convert the decimal into a fraction
1. 0.9
2. 0.35
3. 0.0005
4. 1.5 5. 80.0
Converting Fractions into Decimals
If we wanted to convert a fraction into a decimal, we just divide the numerator
of
the fraction by the denominator of the fraction. For example if we wanted to
convert
3/5 into a decimal we simply divide 3 by 5. But we make use of the fact that 3 =
3.0000000... (as many zeros as we want!)
To convert a mixed number to a decimal you must first
change the mixed number to
an improper fraction, then change the improper fraction to a decimal by dividing
as
previously mentioned.
Now we change this to a decimal by dividing the numerator
(43) by the denominator
(8). (And remember, we can put a decimal point and as many zeros after 43 as we
need.)
Exercises
Convert the fraction into a decimal.
Percent
A percent is defined to be the ratio of a number to the number 100. For example
the
percent 50% means fifty parts of 100. Percents cn easily be converted to
decimals and
fractions.
Converting a percent to a decimal:
To convert a percent to a decimal simply “drop off” the percent sign and move
the
decimal two place to the left. 53% = 53.0% = .53 (move the decimal point two
places
to the left).
25% = .25
100% = 1.00 = 1
3.75% = .0375
4300% = 43.00 = 43
Notice in all cases, you simply drop the percent sign and move the decimal two
place
to the right.
Exercises
Convert the percent to a decimal.
Converting a decimal to a percent:
To convert a decimal to a percent you simply do the opposite of what we just
discussed.
You move the decimal 2 places to the right, and then you just add a percent
sign.
Notice again that all we are doing is simply moving the
decimal point two places to
the right, and then adding the percent sign.
Converting a percent to a fraction:
This is easily done if we remember that percent mean parts of 100. The number
in front of the percent sign is the numerator of a fraction whose denominator is
100.
So
and
Exercises
Convert the percent to a fraction.
1. 13%
2. 47%
3. 69%
4. 88.45%
5. 
Where do we use percent?
A percentage is used to determine the relationship between two numerical values .
For
example 36 is 50% of 72. In this example, 72 is the called the base (the base
always
follows the word “of”). 36 is the amount that is 50% of this base. The
following
equation applies to all of these types of percent problems:
Amount = Base × Percent
In these types of problems, two of the three values will be known and you must
find
the third value. For example, you may know the percent and the base and will
have
to find the amount as in the problem:
What is 25% of 60?
Always remember that the number beside of the word “of” is
the base. So the base
is 60. The percent is obviously 25% because of the percent sign. We substitute
these
values into our equation: Amount = Base × Percent
Amount = 60 × 25% To multiply this we must first convert the percent to either a
decimal or a fraction. It is your preference, but most people like working with
decimals
more.
Amount = 60 × .25
Amount = 15
You may know the percent and amount and have to find the base:
13 is 50% of what number?
Here we know 50 is the percent, but beside the word “of” it says “what number.”
This means the other number, 13, is the amount. Often times the amount will be
beside the word “is.”
Amount = Base × Percent
13 = Base × 50%
13 = Base × .5 At this point we have the unknown number we are looking for (the
base) times .5 is equal to 13. To find what the base is, we divide 13 by .5.
13÷.5 = Base
26 = Base
And finally sometimes you will know the base and amount
but will not know the
percent.
What percent of 80 is 25?
Beside the word “of” is 80, so 80 is the base. We don’t know the percent. Beside
the word “is” we find the number 25. So 25 is the amount.
Amount = Base × Percent
25 = 80 × Percent At this point we have the number we are trying to find (the
percent) times 80 is equal to 25. To find what the percent is, we divide 25 by
80.
25 ÷ 80 = Percent
.3125 = Percent Now we have the percent represented as a decimal. WE MUST
CHANGE THIS TO A PERCENT BEFORE WE ARE FINISHED!
Recall from above to change a decimal to a percent, we move the decimal point 2
places to the right and add a percent sign.
So Percent = .3125 = 31.25%.
Percent Increase or Decrease
In the real world, percentages are most often used to express an increase or
decrease
in some value. The most common example of a percent decrease occurs when a store
is selling something for a discount. We’ve all seen the signs, “get this really
cool pair
of jeans for 30% off,” but what exactly does 30% off mean? Basically, it means
taking
30% of the original price and then subtracting that price from the original
price. It
sounds a little confusing, I know, but let me give you an example.
Example: A pair of jeans is originally priced at $45.00, but is on sale for 30%
off.
The first thing we must do is find out what 30% of 45 is. Remember that 30% can
be expressed in decimal form as .3 (just move the decimal two places to the
left) and
that 45 is the base since it is beside the word “of.” Multiply 45 by .3 and you
should
get 13.5 (refer to the section “Multiplying Decimals”). 13.5 in this case means
$13.50.
This is the amount that you save due to the discount. Next, you have to subtract
that
amount from the original price. $13.50 off of the original $45 is $45 - $13.50 =
$31.50.
So you get a $45 pair of jeans for only $31.50!
Next, we’ll talk about percent increases. The two most common examples of
percent
increases are when dealing with taxes and tipping. Let’s use taxes as an example
(since everyone has to pay them!).
Example: You go into a convenience store and purchase a bag of potato chips for
$1.75, but you only have $2 on you. That would be fine, except the food tax in
your
state is 6.5%. Do you have enough money to cover the cost? Start like you did
before.
Multiply 1.75 by .065 (we changed the percent to a decimal), giving you 0.11375.
Since
we’re dealing with money, this represent cents, so we’ll have to round to 0.11.
Add the
11 cents to the original $1.75 for a grand total of $1.86. Since you had $2.00,
it looks
like you’ll be having your chips and eating them too!
Exercises
Solve the following problems.
1. Lisa bought a blouse. The original cost of the blouse was $42.50, but she
bought it
at a 23.5% discount. How much did she end up paying for the blouse?
2. Jamie bought a TV dinner for $1.63. If she had to pay 6% state tax plus 3%
food tax, how much did the TV dinner actually cost?
3. There are approximately 9,000 students attending Surry Community College,
3,000
of which are curriculum students. What percent are non-curriculum?
ANSWERS
Adding and Subtracting Fractions with a Common Denominator
Equivalent Fractions
Adding and Subtracting Fractions with Different
Denominators
Converting Improper Fractions to Mixed Numbers
Converting Mixed Numbers to Improper Fractions
Adding and Subtracting Mixed Numbers
Multiplying Fractions
Dividing Fractions
Adding and Subtracting Decimals
Multiplying Decimals
5. Rachel has to make 12,000 copies of a document for
Student Development. If
each copy costs 3 cents per sheet, how much will Student Development owe?
12, 000 × $0.03 = $360
Dividing Decimals
Converting Decimals into Fractions
Converting Fractions into Decimals
Converting a Percentage to a Decimal
Converting a Percentage to a Fraction
Percent Increase or Decrease
1. Lisa bought a blouse. The original cost of the blouse was $42.50, but she
bought it
at a 23.5% discount. How much did she end up paying for the blouse?
$42.50 × .235 = $9.9875 ≈ $9.99
Now subtract the discount from the original amount. $42.50 - $9.99 = $32.51
Note: When dealing with money, always round to the hundredths place
(cents).
2. Jamie bought a TV dinner for $1.63. If she had to pay
6% state tax plus 3% food
tax, how much did the TV dinner actually cost?
6% + 3% = 9%; $1.63 × 0.09 = 0.1467≈ 0.15
Now add in the tax to the amount of the original item. $1.63 + $0.15 = $1.78
3. There are approximately 9,000 students attending Surry Community College,
3,000
of which are curriculum students. What percent are non-curriculum?
9,000 - 3,000 = 6,000; 6000/9000 are not curriculum.
