Adding and Subtracting Unlike Fractions
Finding the Common Denominator
Free lesson plan from HomeschoolMath.net

How do we add unlike fractions? The principle is quite easy:

First convert the unlike fractions to like fractions. Then add.

In this lesson we study how to do this conversion.

Like fractions have the same kind of parts: they have a same denominator. When we add unlike fractions, we need to decide into what kinds of parts we can convert them so that the converted fractions have the same denominator.

We call this denominator the common denominator, because it will be common (or the same) to all of the fractions we add (after the conversion).

After you know what denominator to use (into what kind of parts to convert to), use the principles of equivalent fractions to do the actual conversion.

The rule for finding a common denominator

The common denominator has to be a multiple of each of the denominators.

In other words, the common denominator has to be in the multiplication table of the individual denominators. Or, the individual denominators have to "go into" the common denominator, just like 5 goes into 30.

Examples:

2  3  + 1  5  =       15 +       15	The common denominator must be a multiple of 5, and also a multiple of 3. Fifteen will work because 5 goes into 15 and 3 goes into 15.
3  8  + 1  6  =       24 +       24	We need to find a number that is both a multiple of 8 and a multiple of 6. Let's check multiples of 8. From the list 8, 16, 24, 32, etc., we note that 24 is a multiple of 6 too, so 24 works.
7  8  + 3  4  = 7  8  +       8	We need a number that 4 can "go into" and 8 can "go into". Actually, 8 is the smallest such number. In this case, 7/8 does not need converted at all; you only convert 3/4 into 8th parts.

You can always multiply the denominators to get a common denominator. That is one possibility. But, often you can find a common denominator that is smaller than the one you get by multiplying the denominators. Just think of the multiplication tables of the denominators.