Strategies for finding common denominators (also see video links for more help!)

Finding common denominators - Reasons:
(1) To accurately compare the relative value of 2 fractions (when denominator is same - same sized pieces- the one with the bigger numerator is larger...has more of these same sized pieces!) or
(2) to add & subtract fractions finding common denominators becomes essential because you need to be adding up (or subtracting) the same sized pieces or your answer won't make any sense!

Strategy/Example #1:

1/3 + 2/9 = _____
- Hmmm, well, since the denominator of the 1st fraction is a FACTOR of the second I should be able to use multiplication to create my common denom. because 3x3=9! Don't forget, to get an EQUIVALENT fraction (we don't want to add up a non-equivalent fraction, that would change the actual value of the problem!) we need to multiply the numerator and the denominator by the same #

1 x 3
__ = 3/9 and now we just substitute 3/9 into our original problem for 1/3
3 x 3


3/9 + 2/9 = 5/9 (remember, only add the denominators because that is how many pieces you
are adding - if you added the denominators you'd be changing the size of
your pieces which would, in effect, be making your sum of less value!)

Strategy/example #2:

1/5 + 2/4 = ____ well, neither denominator is a factor of the other so we have to find a
common multiple of both - easiest way to do this is to multiply 2
numbers together!! Here, like this:

1 x 4
___ = 4/20
5 x 4


2 x 5
__ = 10/20
4 x 5


Now, we can substitute our new, fancy equivalent fractions with common denominators in for the old ones and we get

4/20 + 10/20 = 14/20 which reduces to 7/10

Note: you can also use division to reduce fractions in order to find a common denominator - make sure you divide the numerator and the denominator by the same # and that the they are both divisible by that number!