Examples of complex fractions

This lesson will provide you with good examples of complex fractions. But what is a complex fraction? Complex fractions are fractions whose numerator, denominator, or both are also fractions.

Another way to put it is to say that a complex fraction is a ratio of two fractions. All the fractions above are complex fractions.

Complex fractions can look quite sophisticated and scary sometimes. Take a look at the following. When I was in the 7th grade, the teacher put something that looked like the one you see below and then asked us to solve it. I was scared!


The strategy is to break the complex fractions into smaller pieces that you can easily solve as shown below:


Compute the smaller pieces:

Here is how to add piece #1: 3/2 + 3/2 = 6/2 = 3

Here is how to add piece #2: 1/4 + 1/2 = 1/4 + 2/4 = 3/4

Here is how to add piece #3: 2/4 + 1 = 2/4 + 4/4 = 6/4

Break this fraction again in smaller pieces, two to be more precise. Call the two pieces piece #1 and piece #2 again.

Compute the smaller pieces:

Here is how to divide piece #1: 3 ÷ (3/4) = (3/1)÷(3/4) = (3/1)×(4/3) = 12/3 = 4

Finally, just do 4 ÷ (6/4) = 4/1 × 4/6 = 16/6