Basic Math and Pre-Algebra For Dummies (49 page)

One way to add and subtract mixed numbers is to convert them to improper fractions, much as I describe earlier in this chapter in “Multiplying and dividing mixed numbers,” and then to add or subtract them using a method from the “All Together Now: Adding Fractions” or “Take It Away: Subtracting Fractions” sections. Doing so is a perfectly valid way of getting the right answer without learning a new method.

Unfortunately, teachers just love to make people add and subtract mixed numbers in their own special way. The good news is that a lot of folks find this way easier than all the converting stuff.

Adding mixed numbers looks a lot like adding whole numbers: You stack them one on top of the other, draw a line, and add. For this reason, some students feel more comfortable adding mixed numbers than adding fractions. Here's how to add two mixed numbers:

1. Add the fractional parts using any method you like; if necessary, change this sum to a mixed number and reduce it.
   
2. If the answer you found in Step 1 is an improper fraction, change it to a mixed number, write down the fractional part, and carry the whole number part to the whole number column.
   
3. Add the whole number parts (including any number carried).
   

You may also need to reduce your answer to lowest terms (see Chapter
9
). In the examples that follow, I show you everything you need to know.

As with any problem involving fractions, adding is always easier when the denominators are the same. For example, suppose you want to add
. Doing mixed number problems is often easier if you place one number above the other:

As you can see, this arrangement is similar to how you add whole numbers, but it includes an extra column for fractions. Here's how you add these two mixed numbers step by step:

1. Add the fractions.
   

   

2. Switch improper fractions to mixed numbers; write down your answer.
   

   Because
   is a proper fraction, you don't have to change it.
   

3. Add the whole number parts.
   
   • 3 + 5 = 8
     

Here's how your problem looks in column form:

This problem is about as simple as they get. In this case, all three steps are pretty easy. But sometimes, Step 2 requires more attention. For example, suppose you want to add
. Here's how you do it:

1. Add the fractions.
   

   

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

   Because the sum is an improper fraction, convert it to the mixed number
    (flip to Chapter
   9
   for more on converting improper fractions to mixed numbers). Write down
   and carry the 1 over to the whole number column.
   

3. Add the whole number parts, including any whole numbers you carried over when you switched to a mixed number.
   
   • 1 + 8 + 6 = 15
     

Here's how the solved problem looks in column form. (Be sure to line up the whole numbers in one column and the fractions in another.)

As with any other problems involving fractions, sometimes you need to reduce at the end of Step 1.

The same basic idea works no matter how many mixed numbers you want to add. For example, suppose you want to add
: