Basic Math and Pre-Algebra For Dummies (50 page)

1. Add the fractions.
   

   

2. Switch improper fractions to mixed numbers, write down the fractional part, and carry over the whole number.
   

   Because the result is an improper fraction, convert it to the mixed number
   and then reduce it to
   (for more on converting and reducing fractions, see Chapter
   9
   ). I recommend doing these calculations on a piece of scrap paper.
   

   Write down
   and carry the 2 to the whole number column.
   

3. Add the whole numbers.
   
   • 2 + 5 + 11 + 3 + 1 = 22
     

Here's how the problem looks after you solve it:

The most difficult type of mixed number addition is when the denominators of the fractions are different. This difference doesn't change Steps 2 or 3, but it does make Step 1 tougher.

For example, suppose you want to add
.

1. Add the fractions.
   

   Add
   . You can use any method from earlier in this chapter. Here, I use the easy way:
   

   

2. Switch improper fractions to mixed numbers, write down the fractional part, and carry over the whole number.
   

   This fraction is improper, so change it to the mixed number
   . Fortunately, the fractional part of this mixed number isn't reducible.
   

   Write down the
   and carry over the 1 to the whole number column.
   

3. Add the whole numbers.
   

   

Here's how the completed problem looks:

The basic way to subtract mixed numbers is close to the way you add them. Again, the subtraction looks more like what you're used to with whole numbers. Here's how to subtract two mixed numbers:

1. Find the difference of the fractional parts using any method you like.
   
2. Find the difference of the two whole number parts.
   

Along the way, though, you may encounter a couple more twists and turns. I keep you on track so that, by the end of this section, you can do any mixed-number subtraction problem.

As with addition, subtraction is much easier when the denominators are the same. For example, suppose you want to subtract
. Here's what the problem looks like in column form: