OpenStax-CNX module: m34941
1
Addition and Subtraction of
Fractions, Comparing Fractions,
and Complex Fractions: Complex
Fractions
∗
Wade Ellis
Denny Burzynski
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0
†
Abstract
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr.
module discusses complex fractions.
This
By the end of the module students should be able to distinguish
between simple and complex fractions and convert a complex fraction to a simple fraction.
1 Section Overview
•
•
Simple Fractions and Complex Fractions
Converting Complex Fractions to Simple Fractions
2 Simple Fractions and Complex Fractions
Simple Fraction
A simple fraction is any fraction in which the numerator is any whole number and the denominator is any
nonzero whole number. Some examples are the following:
1
2
,
4
3
763
,
1,000
Complex Fraction
A complex fraction is any fraction in which the numerator and/or the denominator is a fraction; it is a
fraction of fractions. Some examples of complex fractions are the following:
3
4
5
6
,
1
3
2
∗ Version
,
6
9
10
,
4+ 38
7− 65
1.2: Aug 18, 2010 8:06 pm -0500
† http://creativecommons.org/licenses/by/3.0/
http://cnx.org/content/m34941/1.2/
OpenStax-CNX module: m34941
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3 Converting Complex Fractions to Simple Fractions
The goal here is to convert a complex fraction to a simple fraction. We can do so by employing the methods
of adding, subtracting, multiplying, and dividing fractions. Recall from here1 that a fraction bar serves as
a grouping symbol separating the fractional quantity into two individual groups. We proceed in simplifying
a complex fraction to a simple fraction by simplifying the numerator and the denominator of the complex
fraction separately. We will simplify the numerator and denominator completely before removing the fraction
bar by dividing. This technique is illustrated in problems 3, 4, 5, and 6 of Section 3.1 (Sample Set A).
3.1 Sample Set A
Convert each of the following complex fractions to a simple fraction.
Example 1
3
8
15
16
Convert this complex fraction to a simple fraction by performing the indicated division.
3
8
3
8
=
15
16
1
15
16
15
=
1·2
1·5
15
The divisor is 16 .Invert 16 and multiply.
2
)3
)8
=
÷
·
)16
)15
1
2
5
=
5
Example 2
4
9
6
Write 6 as 1 and divide.
6
4
9
6
1
4
9
=
÷
6
1
2
)4
9
=
·
1
)6
2·1
9·3
=
2
=
27
3
Example 3
5+ 43
Simplify the numerator.
46
4·5+3
4
=
46
23
4
46
20+3
23
=
4
46
23
=
4
1
46
Write 46 as 1
4
46
÷
46
=
1·1
4·2
.
1
1
)23
4
=
·
1
)46
1
8
=
2
Example 4
1
3
4+8
1
13
2 + 24
5
8
=
2
3
8+8
12 + 13
24 24
1
÷
25
24
=
3
)5
)8
·
1
=
4·6+5
6
7·3−1
3
)24
)25
=
5
8
=
12+13
24
1·3
1·5
5
8
=
25
24
÷
25
24
3
5
=
5
Example 5
4+ 65
7− 13
2+3
8
=
=
29
6
20
29
=
20
÷
6
3
3
1
=
29
)6
·
)3
20
=
29
40
2
Example 6
3
11+ 10
4 45
=
11·10+3
10
4·5+4
5
=
110+3
10
20+4
5
=
113
10
24
5
=
113
10
÷
24
5
1 "Introduction to Fractions and Multiplication and Division of Fractions: Fractions of Whole Numbers"
<http://cnx.org/content/m34908/latest/>
http://cnx.org/content/m34941/1.2/
OpenStax-CNX module: m34941
3
1
113
10
÷
24
5
=
113
)10
·
)5
24
=
113·1
2·24
=
113
48
= 2 17
48
2
3.2 Practice Set A
Convert each of the following complex fractions to a simple fraction.
Exercise 1
(Solution on p. 6.)
4
9
8
15
Exercise 2
(Solution on p. 6.)
7
10
28
Exercise 3
(Solution on p. 6.)
Exercise 4
(Solution on p. 6.)
5+ 25
3+ 35
7
1
8+8
3
6− 10
Exercise 5
(Solution on p. 6.)
Exercise 6
(Solution on p. 6.)
1
5
6+8
1
5
9−4
2
16−10 3
7
11 5
6 −7 6
4 Exercises
Simplify each fraction.
Exercise 7
(Solution on p. 6.)
3
5
9
15
Exercise
8
1
3
1
9
Exercise 9
(Solution on p. 6.)
1
4
5
12
Exercise
10
8
9
4
15
Exercise 11
(Solution on p. 6.)
6+ 41
11+ 1
4
Exercise
12
1
2+ 2
7+ 12
Exercise 13
(Solution on p. 6.)
5+ 31
2
2+ 15
Exercise
14
1
9+ 2
8
1+ 11
Exercise 15
10
4+ 13
12
39
http://cnx.org/content/m34941/1.2/
(Solution on p. 6.)
OpenStax-CNX module: m34941
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Exercise
16
1
2
3+7
26
21
Exercise 17
(Solution on p. 6.)
5
1
6−4
1
12
Exercise
18
4
3
10 + 12
19
90
Exercise 19
9
(Solution on p. 6.)
7
16 + 3
139
48
Exercise
20
1
288
8
3
9 − 16
Exercise 21
(Solution on p. 6.)
27
429
5
1
11 − 13
Exercise
22
2
1
3+5
3
17
5 + 45
Exercise 23
9
(Solution on p. 6.)
5
70 + 42
13 − 1
30 21
Exercise
24
1
1
16 + 14
13
2
3 − 60
Exercise 25
(Solution on p. 6.)
3
11
20 + 12
19 −1 11
7
35
Exercise
26
2
1
2 3 −1 2
1
1
4 +1 16
Exercise 27
(Solution on p. 6.)
3 15 +3 13
6
15
5 − 63
Exercise
28
1
1 +15
2
5 1 −3 5
4
12
1
8 −4 1
3
2
11 2
−5 11
3
12
Exercise 29
(Solution on p. 6.)
5 3 +3 1
4
5
2 1 +15 7
5
10
1
9 −4 1
2
6
1 +2 1
8
120
4.1 Exercises for Review
Exercise 30
( here2 ) Find the prime factorization of 882.
Exercise 31
(Solution on p. 6.)
62
( here3 ) Convert 7 to a mixed number.
2 "Exponents, Roots, Factorization of Whole Numbers: Prime Factorization of Natural Numbers"
<http://cnx.org/content/m34873/latest/>
3 "Introduction to Fractions and Multiplication and Division of Fractions: Proper Fractions, Improper Fractions, and Mixed
Numbers" <http://cnx.org/content/m34912/latest/>
http://cnx.org/content/m34941/1.2/
OpenStax-CNX module: m34941
Exercise 32
( here4 ) Reduce
114
342
5
to lowest terms.
Exercise 33
( here5 ) Find the value of
(Solution on p. 6.)
6 38 − 4 56 .
Exercise 34
1
3
4
( here6 ) Arrange from smallest to largest: 2 , 5 , 7 .
4 "Introduction to Fractions and Multiplication and Division of Fractions: Equivalent Fractions, Reducing Fractions to
Lowest Terms, and Raising Fractions to Higher Terms" <http://cnx.org/content/m34927/latest/>
5 "Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Addition and Subtraction of
Mixed Numbers" <http://cnx.org/content/m34936/latest/>
6 "Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Comparing Fractions"
<http://cnx.org/content/m34937/latest/>
http://cnx.org/content/m34941/1.2/
OpenStax-CNX module: m34941
Solutions to Exercises in this Module
Solution to Exercise (p. 3)
5
6
Solution to Exercise (p. 3)
1
40
Solution to Exercise (p. 3)
3
2
Solution to Exercise (p. 3)
10
57
Solution to Exercise (p. 3)
2 13
22
Solution to Exercise (p. 3)
5
1 11
Solution to Exercise (p. 3)
1
Solution to Exercise (p. 3)
3
5
Solution to Exercise (p. 3)
5
9
Solution to Exercise (p. 3)
5
2
Solution to Exercise (p. 3)
31
2
Solution to Exercise (p. 4)
7
Solution to Exercise (p. 4)
1
Solution to Exercise (p. 4)
1
6
Solution to Exercise (p. 4)
52
81
Solution to Exercise (p. 4)
16
21
Solution to Exercise (p. 4)
686
101
Solution to Exercise (p. 4)
1
3
Solution to Exercise (p. 4)
8 67
Solution to Exercise (p. 5)
1 13
24
or
37
24
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