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what is the common denominator of 3 over 5

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"Common" means something that applies to two or more of the same or similar things.  In this case, "common demoninator" means one denominator (bottom part of a fraction, or the divisor) that can be used by two or more fractions with denominators.  In your example, you only have ONE fraction and ONE denominator, so there is no "common denominator" except the denominator in the one fraction you gave:  5.

If you add a second fraction, for example:  5/6, then you can find a denominator that both fractions can use.  This means:  what same number can both denominators divide into evenly (leaves no remainder).  By trial and error, I think 30 is the only one that will work here - the only number that both 5 and 6 can divide into evenly (without having some remainder).  One way to always get a common denominator is to simply multiply both denominators - that guarantees the new denominator is common to both fractions.  In this example, 5x6 = 30, our common denominator.

How to use it to add or subtract fractions:  First, convert each fraction to use its new denominator, in this case, 30.  Whatever we multiply or divide either the numerator or denominator by, we must also do the same with the other one.  That's because we are scaling the fraction either up (multiplying) or down (dividing), and to keep the proportions the same, we have to do the same to both top and bottom. 

So 3/5 = x/30 (x is our unknown numerator).  If we had to multiply 5 X 6 to get 30, then we also must multiply the numerator 3 by 6, so 3x6 = X = 18, and our new fraction is 18/30.

If we want to add this to another fraction, such as 5/6, then we do the same for that one:  5/6 = x/30.  Since we had to multiply 5 X 5 to get 30, we must also multiply the numerator 5 X 5 = 25 to get our new numerator, so 5/6 = 25/30.  

Now we can easily add or subtract our two fractions:  25/30 + 18/30 = 43/30 (we only add numerators, keeping our common denoominator).  To subtract:  25/30 - 18/30 = 7/30 (we only subtract numerators, keeping our common denominator.  Hope this helps to understand fractions!