Basic Mathematics for College Students

Simplify complex fractions.

Fractions whose numerators and/or denominators contain fractions are called

complex fractions.Here is an example of a complex fraction:

A fraction in the numerator

The main fraction bar

A fraction in the denominator

Complex Fraction

A complex fractionis a fraction whose numerator or denominator, or both,

contain one or more fractions or mixed numbers.

Here are more examples of complex fractions:

Numerator

Main fraction bar

Denominator

To simplifya complex fraction means to express it as a fraction in simplified form.

The following method for simplifying complex fractions is based on the fact that

the main fraction bar indicates division.

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Simplifying a complex fraction

To simplify a complex fraction:

1. Add or subtract in the numerator and/or denominator so that the
   numerator is a single fraction and the denominator is a single fraction.


2. Perform the indicated division by multiplying the numerator of the
   complex fraction by the reciprocal of the denominator.


3. Simplify the result, if possible.

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4



2

5

The main fraction bar means

“divide the fraction in the

numerator by the fraction in

the denominator.”

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4

2

5

 

 

1

3



1

4

1

3



1

4

^1  

4



4

5

2

4

5





3

4

7

8



4

288 Chapter 3 Fractions and Mixed Numbers

Self Check 6

Simplify:

Now TryProblem 31

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6

3

8

EXAMPLE 6

Simplify:

Strategy We will perform the division indicated by the main fraction bar using

the rule for dividing fractions from Section 3.3.

WHYWe can skip step 1 and immediately divide because the numerator and the

denominator of the complex fraction are already single fractions.

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4

2

5