1. Home
  2. Fundamentals of mathematics
  3. Addition and subtraction of
  4. Complex fractions

5.5 Complex fractions

<< Chapter < Page
  Fundamentals of mathematics   Page 1 / 1
Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses complex fractions. 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.

Section overview

  • Simple Fractions and Complex Fractions
  • Converting Complex Fractions to Simple Fractions

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 size 12{ { {1} over {2} } } {} , 4 3 size 12{ { {4} over {3} } } {} , 763 1, 000 size 12{ { {"763"} over {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 size 12{ { { { {3} over {4} } } over { { {5} over {6} } } } } {} , 1 3 2 size 12{ { { { {1} over {3} } } over {2} } } {} , 6 9 10 size 12{ { {6} over { { {9} over {"10"} } } } } {} , 4 + 3 8 7 − 5 6 size 12{ { {4+ { {3} over {8} } } over {7 - { {5} over {6} } } } } {}

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 [link] 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 [link] .

Sample set a

Convert each of the following complex fractions to a simple fraction.

3 8 15 16 size 12{ { { { {3} over {8} } } over { { {"15"} over {"16"} } } } } {}

Convert this complex fraction to a simple fraction by performing the indicated division.

3 8 15 16 = 3 8 ÷ 15 16 The divisor is 15 16 . Invert 15 16 and multiply. = 3 1 8 1 ⋅ 16 2 15 5 = 1 ⋅ 2 1 ⋅ 5 = 2 5

Got questions? Get instant answers now!

4 9 6 Write 6 as 6 1 and divide.

4 9 6 1 = 4 9 ÷ 6 1 = 4 2 9 ⋅ 1 6 3 = 2 ⋅ 1 9 ⋅ 3 = 2 27

Got questions? Get instant answers now!

5 + 3 4 46 Simplify the numerator.

4 ⋅ 5 + 3 4 46 = 20 + 3 4 46 = 23 4 46 size 12{ { { { {4 cdot 5+3} over {4} } } over {"46"} } = { { { {"20"+3} over {4} } } over {"46"} } = { { { {"23"} over {4} } } over {"46"} } } {} Write 46 as 46 1 size 12{ { {"46"} over {1} } } {} .

23 4 46 1 = 23 4 ÷ 46 1 = 23 1 4 ⋅ 1 46 2 = 1 ⋅ 1 4 ⋅ 2 = 1 8

Got questions? Get instant answers now!

1 4 + 3 8 1 2 + 13 24 = 2 8 + 3 8 12 24 + 13 24 = 2 + 3 8 12 + 13 24 = 5 8 25 24 = 5 8 ÷ 25 24 size 12{ { { { {1} over {4} } + { {3} over {8} } } over { { {1} over {2} } + { {"13"} over {"24"} } } } = { { { {2} over {8} } + { {3} over {8} } } over { { {"12"} over {"24"} } + { {"13"} over {"24"} } } } = { { { {2+3} over {8} } } over { { {"12"+"13"} over {"24"} } } } = { { { {5} over {8} } } over { { {"25"} over {"24"} } } } = { {5} over {8} } ¸ { {"25"} over {"24"} } } {}

5 8 ÷ 25 24 = 5 1 8 1 ⋅ 24 3 25 5 = 1 ⋅ 3 1 ⋅ 5 = 3 5 size 12{ { {5} over {8} } ¸ { {"25"} over {"24"} } = { { { { {5}}} cSup { size 8{1} } } over { { { {8}}} cSub { size 8{1} } } } cdot { { { { {2}} { {4}}} cSup { size 8{3} } } over { { { {2}} { {5}}} cSub { size 8{5} } } } = { {1 cdot 3} over {1 cdot 5} } = { {3} over {5} } } {}

Got questions? Get instant answers now!

4 + 5 6 7 − 1 3 = 4 ⋅ 6 + 5 6 7 ⋅ 3 − 1 3 = 29 6 20 3 = 29 6 ÷ 20 3 = 29 6 2 ⋅ 3 1 20 = 29 40

Got questions? Get instant answers now!

11 + 3 10 4 4 5 = 11 ⋅ 10 + 3 10 4 ⋅ 5 + 4 5 = 110 + 3 10 20 + 4 5 = 113 10 24 5 = 113 10 ÷ 24 5 size 12{ { {"11"+ { {3} over {"10"} } } over {4 { {4} over {5} } } } = { { { {"11" cdot "10"+3} over {"10"} } } over { { {4 cdot 5+4} over {5} } } } = { { { {"110"+3} over {"10"} } } over { { {"20"+4} over {5} } } } = { { { {"113"} over {"10"} } } over { { {"24"} over {5} } } } = { {"113"} over {"10"} } ¸ { {"24"} over {5} } } {}

113 10 ÷ 24 5 = 113 10 2 ⋅ 5 1 24 = 113 ⋅ 1 2 ⋅ 24 = 113 48 = 2 17 48 size 12{ { {"113"} over {"10"} } ¸ { {"24"} over {5} } = { {"113"} over { { { {1}} { {0}}} cSub { size 8{2} } } } cdot { { { { {5}}} cSup { size 8{1} } } over {"24"} } = { {"113" cdot 1} over {2 cdot "24"} } = { {"113"} over {"48"} } =2 { {"17"} over {"48"} } } {}

Got questions? Get instant answers now!

Practice set a

Convert each of the following complex fractions to a simple fraction.

4 9 8 15 size 12{ { { { {4} over {9} } } over { { {8} over {"15"} } } } } {}

5 6 size 12{ { {5} over {6} } } {}

Got questions? Get instant answers now!

7 10 28 size 12{ { { { {7} over {"10"} } } over {"28"} } } {}

1 40 size 12{ { {1} over {"40"} } } {}

Got questions? Get instant answers now!

5 + 2 5 3 + 3 5 size 12{ { {5+ { {2} over {5} } } over {3+ { {3} over {5} } } } } {}

3 2 size 12{ { {3} over {2} } } {}

Got questions? Get instant answers now!

1 8 + 7 8 6 − 3 10 size 12{ { { { {1} over {8} } + { {7} over {8} } } over {6- { {3} over {"10"} } } } } {}

10 57 size 12{ { {"10"} over {"57"} } } {}

Got questions? Get instant answers now!

1 6 + 5 8 5 9 − 1 4 size 12{ { { { {1} over {6} } + { {5} over {8} } } over { { {5} over {9} } - { {1} over {4} } } } } {}

2 13 22 size 12{2 { {"13"} over {"22"} } } {}

Got questions? Get instant answers now!

16 − 10 2 3 11 5 6 − 7 7 6 size 12{ { {"16"-"10" { {2} over {3} } } over {"11" { {5} over {6} } -7 { {7} over {6} } } } } {}

1 5 11 size 12{1 { {5} over {"11"} } } {}

Got questions? Get instant answers now!

Exercises

Simplify each fraction.

3 5 9 15 size 12{ { { { {3} over {5} } } over { { {9} over {"15"} } } } } {}

1

Got questions? Get instant answers now!

1 3 1 9 size 12{ { { { {1} over {3} } } over { { {1} over {9} } } } } {}

Got questions? Get instant answers now!

1 4 5 12 size 12{ { { { {1} over {4} } } over { { {5} over {"12"} } } } } {}

3 5 size 12{ { {3} over {5} } } {}

Got questions? Get instant answers now!

8 9 4 15 size 12{ { { { {8} over {9} } } over { { {4} over {"15"} } } } } {}

Got questions? Get instant answers now!

6 + 1 4 11 + 1 4 size 12{ { {6+ { {1} over {4} } } over {"11"+ { {1} over {4} } } } } {}

5 9 size 12{ { {5} over {9} } } {}

Got questions? Get instant answers now!

2 + 1 2 7 + 1 2 size 12{ { {2+ { {1} over {2} } } over {7+ { {1} over {2} } } } } {}

Got questions? Get instant answers now!

5 + 1 3 2 + 2 15 size 12{ { {5+ { {1} over {3} } } over {2+ { {2} over {"15"} } } } } {}

5 2 size 12{ { {5} over {2} } } {}

Got questions? Get instant answers now!

9 + 1 2 1 + 8 11 size 12{ { {9+ { {1} over {2} } } over {1+ { {8} over {"11"} } } } } {}

Got questions? Get instant answers now!

4 + 10 13 12 39 size 12{ { {4+ { {"10"} over {"13"} } } over { { {"12"} over {"39"} } } } } {}

31 2 size 12{ { {"31"} over {2} } } {}

Got questions? Get instant answers now!

1 3 + 2 7 26 21 size 12{ { { { {1} over {3} } + { {2} over {7} } } over { { {"26"} over {"21"} } } } } {}

Got questions? Get instant answers now!

5 6 − 1 4 1 12 size 12{ { { { {5} over {6} } - { {1} over {4} } } over { { {1} over {"12"} } } } } {}

7

Got questions? Get instant answers now!

3 10 + 4 12 19 90 size 12{ { { { {3} over {"10"} } + { {4} over {"12"} } } over { { {"19"} over {"90"} } } } } {}

Got questions? Get instant answers now!

9 16 + 7 3 139 48 size 12{ { { { {9} over {"16"} } + { {7} over {3} } } over { { {"139"} over {"48"} } } } } {}

1

Got questions? Get instant answers now!

1 288 8 9 − 3 16 size 12{ { { { {1} over {"288"} } } over { { {8} over {9} } - { {3} over {"16"} } } } } {}

Got questions? Get instant answers now!

27 429 5 11 − 1 13 size 12{ { { { {27} over {"429"} } } over { { {5} over {11} } - { {1} over {"13"} } } } } {}

1 6 size 12{ { {1} over {6} } } {}

Got questions? Get instant answers now!

1 3 + 2 5 3 5 + 17 45 size 12{ { { { {1} over {3} } + { {2} over {5} } } over { { {3} over {5} } + { {"17"} over {"45"} } } } } {}

Got questions? Get instant answers now!

9 70 + 5 42 13 30 - 1 21 size 12{ { { { {9} over {"70"} } + { {5} over {"42"} } } over { { {"13"} over {"30"} } - { {1} over {"21"} } } } } {}

52 81 size 12{ { {"52"} over {"81"} } } {}

Got questions? Get instant answers now!

1 16 + 1 14 2 3 − 13 60 size 12{ { { { {1} over {"16"} } + { {1} over {"14"} } } over { { {2} over {3} } - { {"13"} over {"60"} } } } } {}

Got questions? Get instant answers now!

3 20 + 11 12 19 7 - 1 11 35 size 12{ { { { {3} over {"20"} } + { {"11"} over {"12"} } } over { { {"19"} over {7} } - 1 { {"11"} over {"35"} } } } } {}

16 21 size 12{ { {"16"} over {"21"} } } {}

Got questions? Get instant answers now!

2 2 3 − 1 1 2 1 4 + 1 1 16 size 12{ { {2 { {2} over {3} } -1 { {1} over {2} } } over { { {1} over {4} } +1 { {1} over {"16"} } } } } {}

Got questions? Get instant answers now!

3 1 5 + 3 1 3 6 5 − 15 63 size 12{ { {3 { {1} over {5} } +3 { {1} over {3} } } over { { {6} over {5} } - { {"15"} over {"63"} } } } } {}

686 101 size 12{ { {"686"} over {"101"} } } {}

Got questions? Get instant answers now!

1 1 2 + 15 5 1 4 − 3 5 12 8 1 3 − 4 1 2 11 2 3 − 5 11 12 size 12{ { { { {1 { {1} over {2} } +"15"} over {5 { {1} over {4} } -3 { {5} over {"12"} } } } } over { { {8 { {1} over {3} } -4 { {1} over {2} } } over {"11" { {2} over {3} } -5 { {"11"} over {"12"} } } } } } } {}

Got questions? Get instant answers now!

5 3 4 + 3 1 5 2 1 5 + 15 7 10 9 1 2 − 4 1 6 1 8 + 2 1 120 size 12{ { { { {5 { {3} over {4} } +3 { {1} over {5} } } over {2 { {1} over {5} } +"15" { {7} over {"10"} } } } } over { { {9 { {1} over {2} } - 4 { {1} over {6} } } over { { {1} over {8} } +2 { {1} over {"120"} } } } } } } {}

1 3 size 12{ { {1} over {3} } } {}

Got questions? Get instant answers now!

Exercises for review

( [link] ) Find the prime factorization of 882.

Got questions? Get instant answers now!

( [link] ) Convert 62 7 size 12{ { {"62"} over {7} } } {} to a mixed number.

8 6 7 size 12{8 { {6} over {7} } } {}

Got questions? Get instant answers now!

( [link] ) Reduce 114 342 size 12{ { {"114"} over {"342"} } } {} to lowest terms.

Got questions? Get instant answers now!

( [link] ) Find the value of 6 3 8 − 4 5 6 size 12{6 { {3} over {8} } - 4 { {5} over {6} } } {} .

1 13 24 size 12{1 { {"13"} over {"24"} } } {} or 37 24 size 12{ { {"37"} over {"24"} } } {}

Got questions? Get instant answers now!

( [link] ) Arrange from smallest to largest: 1 2 size 12{ { {1} over {2} } } {} , 3 5 size 12{ { {3} over {5} } } {} , 4 7 size 12{ { {4} over {7} } } {} .

Got questions? Get instant answers now!

Questions & Answers

I'm interested in biological psychology and cognitive psychology
Tanya Reply
what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask