How do you find the common denominator?

Answer 1

mulitply the denominators you are working with.

ex. 4/5 + 2/3
5 x 3=15


15 is the common denominator.
Now, we multiply the numerators by the old denominators


4 x 3 = 12
2 x 5 = 10


now add them


12 + 10 = 22


put it on the denominator


22/15, or 1 7/15
It's the same as finding the LCM.

Example: 5/30 and 6/42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Combine the factors, eliminating duplicates.

2 x 3 x 5 x 7 = 210, the LCM

5/30 = 35/210 6/42 = 30/210

Now you can add them.
By definition you write the multiples of each and find the one that is in both lists. the one that is always in both lists is the product of the denominators. That might give you one that is very large. That is why the least common multiple of the two denominators is the best to use.

Prime factor each denominator.

Choose each factor that was used the most. and multiply them,

5/18 + 7/27

18=2x3x3

27=3x3x3

common denominator or LCM=2x3x3x3 or 54