Basic Mathematics for College Students

3.7 Order of Operations and Complex Fractions 289

Self Check 7

Simplify:

Now TryProblem 35



5

8



1

3

3

4



1

3

Solution

Write the division indicated by the main fraction bar using

a symbol.

Use the rule for dividing fractions: Multiply the first fraction

by the reciprocal of , which is.



5

8

Multiply the numerators.

 (^) Multiply the denominators.
1 # 5
4 # 2
5
2
2
5



1

4

#^5

2

1

4

2

5



1

4



2

5

EXAMPLE 7

Simplify:

StrategyRecall that a fraction bar is a type of grouping symbol. We will work
above and below the main fraction bar separately to write and as
single fractions.

WHYThe numerator and the denominator of the complex fraction must be
written as single fractions before dividing.

SolutionTo write the numerator as a single fraction, we build and to have
an LCD of 20, and then add. To write the denominator as a single fraction, we build
and to have an LCD of 10, and subtract.

Multiply in the numerator.

Multiply in the denominator.

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

2

To simplify, factor 20 as 2 10. Then remove

the common factors of 3 and 10 from the

numerator and denominator.

 

3

1

# 10

1

2 # 10

1

# 3

1

The product of two fractions with unlike

signs is negative. Multiply the numerators.

Multiply the denominators.

 

3 # 10

20 # 3

 103

 3 ^103

20

a

10

3

b

Write the division indicated by the main fraction

 (^) bar using a symbol.

3

20

a

3

10

b

In the numerator of the complex fraction,

add the fractions.

In the denominator, subtract the fractions.



3

20



3

10





5

20



8

20

5

10



8

10

The LCD for the numerator is 20. Build each

fraction so that each has a denominator of 20.

The LCD for the denominator is 10. Build each

fraction so that each has a denominator of 10.



1

4



2

5

1

2



4

5





1

4



5

5



2

5



4

4

1

2



5

5



4

5



2

2

4

5

1
2

2

 (^5)
1
4
1
2 
4
 (^5)
1
4 
2
5



1

4



2

5

1

2



4

5