Basic Mathematics for College Students

Chapter 3 Summary and Review 309

A complex fraction is a fraction whose
numerator or denominator, or both, contain
one or more fractions or mixed numbers.

Complex fractions:

 7

1

4

2 

1

9

2

5



1

3

3

7



1

5

9

10

27

5

The method for simplifying complex fractions
is based on the fact that the main fraction bar
indicates division.

Simplify:

Use the rule for dividing fractions: Multiply the

first fraction by the reciprocal of , which is.

Multiply the remaining factors in the numerator.

 Multiply the remaining factors in the denominator.

1

6

To simplify, factor 10 as 25 and 27 as 39.

Then remove the common factors of 9 and 5

from the numerator and denominator.



9

1

 5

1

2  5

1

 3  9

1

Multiply the numerators.

 Multiply the denominators.

9  5

10  27

5

27

27

5



9

10



5

27

Write the division indicated by the

main fraction bar using a symbol.

9

10

27

5



9

10



27

5

9

10

27

5

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.

Simplify:

Use the rule for dividing fractions:

Multiply the first fraction by the

reciprocal of , which is.

Multiply the remaining factors

in the numerator.

Multiply the remaining factors

in the denominator.



7

66

To simplify, factor 35 as 57 and 15 as 35.

Then remove the common factor of 5 from

the numerator and denominator.



1  5

1

 7

3  5

1

 22

Multiply the numerators.

 Multiply the denominators.

1  35

15  22

35

22

22

35



1

15



35

22

Write the division indicated by the main

 fraction bar using a symbol.

1

15



22

35

Subtract the numerators and write the

difference over the common denominator 15.

Add the numerators and write the sum

over the common denominator 35.



1

15

22

35

Multiply the numerators.

 Multiply the denominators.

6

15



5

15

15

35



7

35

In the numerator, build each fraction so

that each has a denominator of 15.

In the denominator, build each fraction so

that each has a denominator of 35.

2

5



1

3

3

7



1

5



2

5



3

3



1

3



5

5

3

7



5

5



1

5



7

7

2

5



1

3

3

7



1

5