SOLUTION: This is actually more of a simple question, but it seems no one can explain to me why we do these things. You know how we have to make the denominators the same before we can a

Question 1027825: This is actually more of a simple question, but it seems no one can explain to me why we do these things.
You know how we have to make the denominators the same before we can add or subtract fractions? Why? Why do we have to make them the same?
It's something we do, but why?
Also, why is it that when the denominators are the same we only add the numerators? Why don't we ever add two denominators that are the same? Why only the numerators?

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
You know how we have to make the denominators the same before we can add or subtract fractions? Why? Why do we have to make them the same?
It's something we do, but why?
Also, why is it that when the denominators are the same we only add the numerators? Why don't we ever add two denominators that are the same? Why only the numerators?
=================
It's necessary to add or subtract.
Any other "method" will not get the correct answer.
eg, to add 1/2 + 1/8
A common DEN is the product, 16
--> 8/16 + 2/16 = 10/16
= 5/8
-----
The 2 fractions were converted to fractions with a common DEN, making both a number of 16ths.
Adding halves & eighths is similar to adding apples and oranges. They are not the same thing.
-----------
What other options are there?
1/2 + 1/8 = 2/10 is wrong.
1*1/(2*8) is wrong.
===========================
There might be some rule or law that shows how to do it, but the simplest reason is, you get the correct answer.
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