Basic Math and Pre-Algebra For Dummies (38 page)

Every mixed number has both a whole number part and a fractional part. So the three numbers in a mixed number are

• The whole number
  
• The numerator
  
• The denominator
  

For example, in the mixed number
, the whole number part is 3 and the fractional part is
. So this mixed number is made up of three numbers: the whole number (3), the numerator (1), and the denominator (2). Knowing these three parts of a mixed number is helpful for converting back and forth between mixed numbers and improper fractions.

To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the denominator of the fractional part by the whole number, and add the result to the numerator.
   

   For example, suppose you want to convert the mixed number
   to an improper fraction. First, multiply 3 by 5 and add 2:
   

   

2. Use this result as your numerator, and place it over the denominator you already have.
   

   Place this result over the denominator:
   

   

   So the mixed number
   equals the improper fraction
   . This method works for all mixed numbers. Furthermore, if you start with the fractional part reduced, the answer is also reduced (see the earlier “Increasing and Reducing Terms of Fractions” section).
   

To convert an improper fraction to a mixed number, divide the numerator by the denominator (see Chapter
3
). Then write the mixed number in this way:

• The quotient (answer) is the whole-number part.
  
• The remainder is the numerator.
  
• The denominator of the improper fraction is the denominator.
  

For example, suppose you want to write the improper fraction
as a mixed number. First, divide 19 by 5:

Then write the mixed number as follows:

This method works for all improper fractions. And as is true of conversions in the other direction, if you start with a reduced fraction, you don't have to reduce your answer (see “Increasing and Reducing Terms of Fractions”).

Cross-multiplication is a handy little technique to know. You can use it in a few different ways, so I explain it here and then show you an immediate application.

To cross-multiply two fractions, follow these steps:

1. Multiply the numerator of the first fraction by the denominator of the second fraction and jot down the answer.
   
2. Multiply the numerator of the second fraction by the denominator of the first fraction and jot down the answer.
   

For example, suppose you have these two fractions:

When you cross-multiply, you get these two numbers: