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Fraction Basics

Date: 7/21/96 at 2:24:48
From: Anonymous
Subject: Fraction Basics

To Dr. Math,

    I don't understand how to do any type of fractions. Can you please 
help me in easy form?

Thank you!

Date: 7/25/96 at 14:49:8
From: Doctor Mike
Subject: Re: Fraction Basics

Hello Karina,

Thanks for your question. Lots of people have problems when they
start learning about fractions. I cannot tell from your question
exactly what is giving you problems right now, so I will give you a
few pointers, and you can write back if you still need more. Okay?
Basically, fractions are about "parts of a whole."  For instance, if a 
sandwich is cut exactly down the middle so that two people could have 
the same amount, then the whole amount on the plate is 2 portions, and
each person gets 1 of them. So, each person gets 1/2 or one half.
If there are 30 people in a room and 20 of them are women, then the
fraction 20/30 tells what part of the entire group are women. Also,
the part of the whole group that are men is 10/30.
One common problem with fractions is multiplying them. There is a 
simple rule for this. When you multiply 2 fractions (some people use
the term Rational Numbers, since a/b is the Ratio of a to b) you get
another fraction. This new fraction has a numerator that comes from
multiplying the other 2 numerators, and it has a denominator that 
comes from multiplying the other 2 denominators. Using symbols ....
            A     B       A*B
           --- * ---  =  -----
            C     D       C*D
Let's go back to the 30 people in the room. You might have thought
that 20/30 looks a lot like 2 thirds. Well, it is, and here is why.
The numerator 20 is the same as 2 times 10. The denominator is the 
same as 3 times 10. So, we can use the simple rule for multiplying to 
            20       2*10       2     10       2          2  
           ----  =  ------  =  --- * ----  =  --- * 1  = --- 
            30       3*10       3     10       3          3  
You might wonder why I changed 10/10 to one. The denominator of 10
means that the whole consists of 10 parts. The numerator of 10 means
that you have all 10 of those parts. So, if you have all of the 
parts of the whole, you have one (1) whole thing. 

By the way, what I have shown you above with the 20/30 and 2/3 is the 
"long way".  It is important for you to understand the long way.  When 
you REALLY understand the long way, you can then use the "short way" 
which is often called Cancellation. But be careful; it can be tricky! 
Another common problem with fractions is adding them. The simple 
rule for this in symbols is
            N     M       N+M
           --- + ---  =  -----
            D     D        D  
Note that in this rule the denominators are all the same. It MUST be
that way for the rule to work. If the denominators are not the same,
you must MAKE them the same before you use the rule. This process of
making them the same involves finding a Common Denominator. This is
the process of taking the fractions you want to add, and changing them
to two other fractions which mean the same, but that have the same

I will show this with an example.  3/8 equals 9/24 and 1/6 equals 
4/24.  The common denominator here is 24. 
             3   1   3 3   1 4   3*3   1*4   9    4    13
             - + - = -*- + -*- = --- + --- = -- + -- = --
             8   6   8 3   6 4   8*3   6*4   24   24   24
I hope this helps to give you a good start. Write back when and if
you need more. Specific questions are easier for the doctors here to
answer, because then we understand exactly what you need to know. 
-Doctor Mike,  The Math Forum
 Check out our web site!   
Associated Topics:
Elementary Fractions
Middle School Fractions

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