math 116
posted by Rosetta .
Is it always necessary to have a common denominator to add and subtract fractions? Why? What about multiplication and division with fractions?

yes it is...can't explain it but that's how it's always been. It's a rule.
For the multiplication and division of fractions it is not necessary.
Just cross multiply. 
I'm not good at explaining but here goes.
Yes, because you need to have the right proportion. Lets say you have 1/2 + 1/3. You have half a cake plus a third of a cake. If you added them togther, you will not know how much you have left over or if you have too much (in numbers that is)
But if you added them to a common demominator, you will get 3/6 + 2/6, so you know you will have 1/6 of the cake left.
Muliplication you dont
1/2 x 1/3 = 1/6
It all works out. One third of one half is one sixth. Try it out.
Dividing fractions, all you do is flip the fraction around.
1/2 (divide) 1/3 is 1/2 x 3 
This is the reason, using 1/2 + 1/3 as example:
the denominator means the number of equal parts you divide the whole thing into.
1/2 means you divide the whole thing into 2 equal parts and you take one part.
1/3 means you divide the same whole thing into 3 equal parts and you take one part.
in both cases, you take one part, but the size of each part is different, that's the reason you can add or subtract, they are not of the same size.
we can add 1/4 to 2/4 because each part is of the same size. 
Wow Qun is good, I sooooo got that explanation!
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