Mixed Expressions and Complex Fractions

After studying this lesson, you will be able to:

• Simplify mixed expressions and complex fractions.

Example 1

	We need to convert the first fraction to a common denominator
	Multiply before adding
	Add the numerators and keep the denominator

Example 2

This is a complex fraction. It can be read as "two-thirds divided by one-fifth". Remember the rule for dividing fractions is to multiply by the reciprocal:

Example 3

	First we convert the mixed numbers to improper fractions: Remember the rule for dividing fractions is to multiply by the reciprocal:

Example 4

This is a complex fraction. The best way to approach this problem is to work only with the numerator first. After we have completely simplified the numerator, we will work on the denominator. Then, the final step will be to divide the fractions.

First, we're only going to work with the numerator:

The common denominator will be xy. We multiply the first fraction by and the second fraction by :

This will give us . Now we add to get

Now we go back and work with the denominator:

Add the opposite:

The common denominator will be xy. We multiply the first fraction by and the second fraction by :

This will give us Now we add to get

We have now simplified the numerator and the denominator to get:

Now we have one fraction being divided by another. The rule for dividing fractions is to multiply by the reciprocal.

Now we multiply. (the xy and the xy will cancel)