Adding and Subtracting FractionsDate: 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 |
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