Read me first!
To the left you have the options of chosing which area of mathematics you
would like to review. Most people need to review from time-to-time. This review will take
time, but is a good means of brushing up on what you may have forgotten. To get the most
from this review, do not take short-cuts and work all problems. Before you begin
your review you should remember that mathematics has a language of its own. Understanding
that language can help you solve math problems.
For instance, the word and usually means you will be
performing an addition problem.
Two and two equal four.
You have heard this since the first grade.
2 + 2 = 4
AND means ADD
So if you see the word and being used in a problem, it very likely could
be an addition problem.
The next important word used in the language of mathematics is the word
Difference. Difference means to subtract.
For instance, if you are asked what's the difference between 5 and 4, you would say
Without considering it, what you have done is subtract 4 from 5, leaving you
Difference means Subtract
Therefore, if you see the word Difference used in a problem you can
expect the problem to be a subtraction problem.
The next important set of words is by and of
. These words both mean to multiply.
You may be familiar with the use of "by." If we know a room is ten feet by
ten feet we can calculate the square footage by multiplying one side times the other.
10 X 10 = 100 square feet
Likewise, the term of means to multiply.
"Half of a dollar is fifty-cents." That says the same as:
1/2 X 1.00 = 1/2 = .50 (fifty cents)
BY and OF mean to multiply.
Therefore, if you see these words in a problem you should expect the problem to be a
Finally, the word per means to divide.
When we need to calculate miles per gallon we divide the number of miles by the
number of gallons. Miles per hour is found by dividing the number of miles by the
number of hours travelled.
When we use per-cent we use the word per together with the word,
cent, which means "100." The word "percent" just means
to divide by 100.
So if you see the word per used in a problem it will very likely be a
PER means Divide
Now let's move on to fractions
When we use fractions we are really
just working with a division problem. For instance,
3/4 is a form of a division problem where we are dividing the number
"3" by the number "4."
In our fraction the number 3 is named
the numerator and the number 4 is named the denominator.
Since most people don't like
division problems, it makes sense that most people don't like fractions. Still, they are a
necessary tool in the business world.
The first rule to remember about fractions is all
fractions must be reduced to their lowest form. This means we must check to see if we
can divide both the top and bottom numbers by "2" or "3" or
"5" etc. If we can, then that process is called Reducing the fraction.
4/10 (both numbers can be divided by
2) Reduces to 2/5
The next thing to remember is
always make a proper fraction out of an improper fraction. An
improper fraction occurs whenever the top number is larger than the bottom number. For
11/8 is an improper fraction. We
change it to a proper fraction by working out the division problem of 11
divided by 8. The answer would be 1-3/8. (8 goes into 11
one time with a remainder of 3).
Anytime the top number is larger than the bottom, we
must work the division.
When adding fractions we simply
add the top (numerator) numbers, and leave the bottom (denominator) numbers the same. For
3/16 + 4/16 = 7/16 -- We simply added
the "3" to the "4" to get our answer.
CAUTION: Sometimes when we add
fractions we end up with an improper fraction which must be divided out to get
the correct final answer. For example:
3/4 + 3/4 = 6/4 --The numerator is
larger than the denominator. We must divide "6" by "4" resulting in an
answer of 1-2/4. This must be reduced to 1-1/2.
Subtracting fractions works the
same as addition -- we simply subtract the smallest numerator from the largest numerator.
The good thing about subtracting fractions is that you'll never end up with an improper
fraction for an answer.
When we multiply fractions we must actually
multiply the two numerators, then multiply the two denominators. For instance:
2/3 x 3/4 = 6/12 (2x3=6 -- 3x4=12) Again, we must
begin reducing this fraction. Start with "2" -- 6 divided by 2
= (3) and 12 divided by 2 = (6).
We now have reduced 6/12 to 3/6. But, this fraction needs to be
reduced by dividing each number by "3" which gives us 1/2.
Also, remember, sometimes when we multiply we'll end up with
improper fractions too.
Finally, dividing fractions is not rocket
science either. We just turn second fraction up-side-down and mulitply like we did in the
last example. For instance:
5/8 / 1/3 -- Just turn the second number over -
5/8 / 3/1.
Then multiply - - 5/8 x 3/1 = (5x3=15 &
8x1=8) 15/8 or 1-7/8.
Mixed numbers are whole numbers like
"1" or "3" etc. attached to a fraction. For instance:
2-3/4 is a mixed number.
We must remember to change mixed numbers into fractions (even
improper fractions) before we can work a fraction problem. To change a mixed number to a
fraction simply Multiply the denominator by the whole number and add this to the
numerator. This gives you a new numerator.
Here is an example of a problem with a mixed
7/8 + 2-3/8 -- We must convert "2-3/8" to
an improper fraction by multiplying the whole number (2) times the denominator (8) which
is (16) and add that to the numerator(3) which make (19). We now have a new problem:
7/8 + 19/8 -- Now we just add (7) and (19) which is
(26). Our new answer is 26/8. This is an improper fraction so we must
divide (8) into (26) which gives us 3-2/8. We now must reduce our
fraction giving us a final answer of 3-1/4.
Last, but not least, we must mention the common
denominator which isn't of importance unless you are adding or subtracting
fractions. You don't need to worry about it if you are multiplying or dividing fractions.
You can always find the common denominator, sometimes it's easier than others.
When two fractions have a common denominator, both their
denominators are the same. The quickest way to find a common denominator is to multiply
the two denominators together, but that is not the most desirable method.
Let's say we're adding 3/8 to 1/4.
Notice that we have two different denominators. We need to make both either (8)
or (4). We can't reduce "3/8" down any more so we'll have to
"un"-reduce "1/4." If we multiply this fraction's numerator and
denominator by 2 we'll have 2/8, which is an improper fraction, but we
need it to be that way so that its denominator is the same as the other fraction.
Now, let's add 3/8 + 2/8 = 5/8. We couldn't have
added these numbers with dissimilar denominators. Is it OK to leave 5/8 as it is or does
it need to be reduced?
Did you say "Leave it?" Good if you
did. Ok, this concludes this review. If you feel confused click on the start button again
and go through this a second or third time.
If you feel confident, start working the problems by clicking on the
area of review to the left.
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