Adding and Subtracting Fractions and Rational Expressions

You can add or subtract fractions as long as they have the same (common) denominator:

 

If the denominators are different, you first have to find the LEAST COMMON DENOMINATOR.

That's the smallest number that BOTH denominators will go into evenly:

For example: 

Denominators 3, 4 ; Common denominator is 12 because 3 and 4 both go into 12.

Denominators 15 and 20 ; Common denominator is 60 because 15 and 20 both go into 60.

15*20 = 300, which would be a common denominator but not the smallest one. So you'd have to simplify a lot later.

15 = 3*5

20 = 2*2*5

So the LEAST COMMON DENOMINATOR is 3*5*2*2 = 60.

  

More examples:

 Rational Expressions work the same way. If you already have a common denominator, just add or subtract (whichever it says to do) the numerators, combine any like terms, and simplify if possible:

 If the denominators are not common, you need to find the least common denominator that includes all the factors of both denominators.

This is just like with number fractions!