suppose you want to add 1/4 + 1/2 . Easy enough, because it's 1/4 plus another 2 quarters.
-- the common denominator is 4, or one quarter. We added one quarter to two quarters by changing the 1/2 into quarters.
But suppose you want to add,say, 2/5 + 1/3. The problem is that 5 and 3 don't have any common factors. We get round this,if you like, by multiplying 5 and 3 to get fifteenths as our common denominator. So we are just adding some 'fifteenths' together.
So we change 2/5 into fifteenths and we change 1/3 into fifteenths and then add them together.This is all we are doing when we find the common denominator.
2/5 = 6/15 and 1/3 = 5/15 .Now adding the numerators we get (6 + 5)/15 = 11/15
Another one.
Let's add 2/3 + 1/7. The common denominator is 3 x 7 = 21.This time we are just adding twentyfirsts of something.Last time it was fifteenths. Same idea.
So 2/3 = 14/21 and 1/7 = 3/21 and the answer is (14 + 3)/ 21 = 17/21
In general,the common denominator of two fractions a/x + b/y is xy.
Finally,let's add a/x + b/y so you really understand.
Common denominator is xy.
so we have (ay + bx) /xy as the answer. I multiply a/x by the common denominator xy to get ay and then I multiply b/y by the same to get bx. Check this by dividing both ay and bx by the common denominator,and you get back to a/x + b/y. Just do some practice.It's not hard.
