Adding and Subtracting Fractions

Date: 03/05/2002 at 14:50:21
From: Stacey
Subject: Adding and subtracting fractions

My math teacher was talking to us about adding and subtracting 
fractions. We all know how to do this, but he asked us if we knew why 
we do not add or subtract the denominators. I don't know, and I was 
wondering if you would be able to tell me why we don't add or subtract 
the denominators of a fraction in a problem.

Thanks,
Stacey

Date: 03/05/2002 at 15:52:19
From: Doctor Rick
Subject: Re: Adding and subtracting fractions

Hi, Stacey.

Adding 2/3 and 3/5 is like adding 2 apples and 3 oranges. Think of the 
denominator as the name of the things you're adding. (That's really 
where the word "denominator" comes from!) You can't add unless you're 
adding the same kind of thing; that's why we make the denominators the 
same first.

If we have 10/15 and 9/15, that's like adding 10 apples and 9 apples; 
we can do it. What do we get? 19 apples, of course. Or 19/15.

Do you see what we did - or what we didn't do? When we added 10 apples 
and 9 apples, we didn't get 19 double-apples; we just kept the same 
"name" for the 19 things as for the 10 and 9 things. When we added 
10/15 and 9/15, we didn't add the denominators to get 19/30; we kept 
the same denominator for the sum.

If apples and oranges are too trite, or too unmathematical, you can 
set up an analogy using dimes and quarters (7/10 + 3/4 = 7 dimes and 
3 quarters), or feet and yards (showing that denominators are like 
units). Both of these analogies are interesting in terms of word 
origins. We say that dimes and quarters are different "denominations" 
of currency; this word is obviously related to "denominator." And the 
Romans didn't have a formal system of fractions; instead, if they 
needed to express a quantity less than one, they used a smaller unit. 
The words "inch" and "ounce" are both derived from the Roman word 
"uncia," meaning a twelfth. There's a strong connection between 
denominators and units!

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/   

Date: 03/06/2002 at 16:37:05
From: stacey
Subject: fractions/Thanks for the help!

Question submitted via WWW:
i want to thank you very much and I was glad to hear from someone in 
such a short period of time... it was less than 24 hours.The answer  
helped greatly and i am glad that you could help me.  Thanks again 
and i plan on writing again.
      Thanks
           Stacey