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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to estimate by rounding fractions. By the end of the module students should be able to estimate the sum of two or more fractions using the technique of rounding fractions.

Section overview

  • Estimation by Rounding Fractions

Estimation by rounding fractions is a useful technique for estimating the result of a computation involving fractions. Fractions are commonly rounded to 1 4 size 12{ { {1} over {4} } } {} , 1 2 size 12{ { {1} over {2} } } {} , 3 4 size 12{ { {3} over {4} } } {} , 0, and 1. Remember that rounding may cause estimates to vary.

Sample set a

Make each estimate remembering that results may vary.

Estimate 3 5 + 5 12 size 12{ { {3} over {5} } + { {5} over {"12"} } } {} .

Notice that 3 5 size 12{ { {3} over {5} } } {} is about 1 2 size 12{ { {1} over {2} } } {} , and that 5 12 size 12{ { {5} over {"12"} } } {} is about 1 2 size 12{ { {1} over {2} } } {} .

Thus, 3 5 + 5 12 size 12{ { {3} over {5} } + { {5} over {"12"} } } {} is about 1 2 + 1 2 = 1 size 12{ { {1} over {2} } + { {1} over {2} } =1} {} . In fact, 3 5 + 5 12 = 61 60 size 12{ { {3} over {5} } + { {5} over {"12"} } = { {"61"} over {"60"} } } {} , a little more than 1.

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Estimate 5 3 8 + 4 9 10 + 11 1 5 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } } {} .

Adding the whole number parts, we get 20. Notice that 3 8 size 12{ { {3} over {8} } } {} is close to 1 4 size 12{ { {1} over {4} } } {} , 9 10 size 12{ { {9} over {"10"} } } {} is close to 1, and 1 5 size 12{ { {1} over {5} } } {} is close to 1 4 size 12{ { {1} over {4} } } {} . Then 3 8 + 9 10 + 1 5 size 12{ { {3} over {8} } + { {9} over {"10"} } + { {1} over {5} } } {} is close to 1 4 + 1 + 1 4 = 1 1 2 size 12{ { {1} over {4} } +1+ { {1} over {4} } =1 { {1} over {2} } } {} .

Thus, 5 3 8 + 4 9 10 + 11 1 5 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } } {} is close to 20 + 1 1 2 = 21 1 2 size 12{"20"+1 { {1} over {2} } ="21" { {1} over {2} } } {} .

In fact, 5 3 8 + 4 9 10 + 11 1 5 = 21 19 40 size 12{5 { {3} over {8} } +4 { {9} over {"10"} } +"11" { {1} over {5} } ="21" { {"19"} over {"40"} } } {} , a little less than 21 1 2 size 12{"21" { {1} over {2} } } {} .

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Practice set a

Use the method of rounding fractions to estimate the result of each computation. Results may vary.

5 8 + 5 12 size 12{ { {5} over {8} } + { {5} over {"12"} } } {}

Results may vary. 1 2 + 1 2 = 1 size 12{ { {1} over {2} } + { {1} over {2} } =1} {} . In fact, 5 8 + 5 12 = 25 24 = 1 1 24 size 12{ { {5} over {8} } + { {5} over {"12"} } = { {"25"} over {"24"} } =1 { {1} over {"24"} } } {}

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7 9 + 3 5 size 12{ { {7} over {9} } + { {3} over {5} } } {}

Results may vary. 1 + 1 2 = 1 1 2 size 12{1+ { {1} over {2} } =1 { {1} over {2} } } {} . In fact, 7 9 + 3 5 = 1 17 45 size 12{ { {7} over {9} } + { {3} over {5} } =1 { {"17"} over {"45"} } } {}

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8 4 15 + 3 7 10 size 12{8 { {4} over {"15"} } +3 { {7} over {"10"} } } {}

Results may vary. 8 1 4 + 3 3 4 = 11 + 1 = 12 size 12{8 { {1} over {4} } +3 { {3} over {4} } ="11"+1="12"} {} . In fact, 8 4 15 + 3 7 10 = 11 29 30 size 12{8 { {4} over {"15"} } +3 { {7} over {"10"} } ="11" { {"29"} over {"30"} } } {}

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16 1 20 + 4 7 8 size 12{"16" { {1} over {20} } +4 { {7} over {8} } } {}

Results may vary. 16 + 0 + 4 + 1 = 16 + 5 = 21. size 12{ left ("16"+0 right )+ left (4+1 right )="16"+5="21"} {} In fact, 16 1 20 + 4 7 8 = 20 37 40 size 12{"16" { {1} over {"20"} } +4 { {7} over {8} } ="20" { {"37"} over {"40"} } } {}

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Exercises

Estimate each sum or difference using the method of rounding. After you have made an estimate, find the exact value of the sum or difference and compare this result to the estimated value. Result may vary.

5 6 + 7 8 size 12{ { {5} over {6} } + { {7} over {8} } } {}

1 + 1 = 2   1 17 24 size 12{1+1=2 left (1 { {"17"} over {"24"} } right )} {}

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3 8 + 11 12 size 12{ { {3} over {8} } + { {"11"} over {"12"} } } {}

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9 10 + 3 5 size 12{ { {9} over {"10"} } + { {3} over {5} } } {}

1 + 1 2 = 1 1 2 1 1 2 size 12{1+ { {1} over {2} } =1 { {1} over {2} } left (1 { {1} over {2} } right )} {}

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13 15 + 1 20 size 12{ { {"13"} over {"15"} } + { {1} over {"20"} } } {}

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3 20 + 6 25 size 12{ { {3} over {"20"} } + { {6} over {"25"} } } {}

1 4 + 1 4 = 1 2 39 100 size 12{ { {1} over {4} } + { {1} over {4} } = { {1} over {2} } left ( { {"39"} over {"100"} } right )} {}

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

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15 16 + 1 12 size 12{ { {"15"} over {"16"} } + { {1} over {"12"} } } {}

1 + 0 = 1 1 1 48 size 12{1+0=1 left (1 { {1} over {"48"} } right )} {}

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29 30 + 11 20 size 12{ { {"29"} over {"30"} } + { {"11"} over {"20"} } } {}

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5 12 + 6 4 11 size 12{ { {5} over {"12"} } +6 { {4} over {"11"} } } {}

1 2 + 6 1 2 = 7   6 103 132 size 12{ { {1} over {2} } +6 { {1} over {2} } =7 left (6 { {"103"} over {"132"} } right )} {}

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3 7 + 8 4 15 size 12{ { {3} over {7} } +8 { {4} over {"15"} } } {}

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9 10 + 2 3 8 size 12{ { {9} over {"10"} } +2 { {3} over {8} } } {}

1 + 2 1 2 = 3 1 2 3 11 40 size 12{1+2 { {1} over {2} } =3 { {1} over {2} } left (3 { {"11"} over {"40"} } right )} {}

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19 20 + 15 5 9 size 12{ { {"19"} over {"20"} } +"15" { {5} over {9} } } {}

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8 3 5 + 4 1 20 size 12{8 { {3} over {5} } +4 { {1} over {"20"} } } {}

8 1 2 + 4 = 12 1 2 12 13 20 size 12{8 { {1} over {2} } +4="12" { {1} over {2} } left ("12" { {"13"} over {"20"} } right )} {}

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5 3 20 + 2 8 15 size 12{5 { {3} over {"20"} } +2 { {8} over {"15"} } } {}

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9 1 15 + 6 4 5 size 12{9 { {1} over {"15"} } +6 { {4} over {5} } } {}

9 + 7 = 16   15 13 15 size 12{9+7="16" left ("15" { {"13"} over {"15"} } right )} {}

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7 5 12 + 10 1 16 size 12{7 { {5} over {"12"} } +"10" { {1} over {"16"} } } {}

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3 11 20 + 2 13 25 + 1 7 8 size 12{3 { {"11"} over {"20"} } +2 { {"13"} over {"25"} } +1 { {7} over {8} } } {}

3 1 2 + 2 1 2 + 2 = 8   7 189 200 size 12{3 { {1} over {2} } +2 { {1} over {2} } +2=8 left (7 { {"189"} over {"200"} } right )} {}

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6 1 12 + 1 1 10 + 5 5 6 size 12{6 { {1} over {"12"} } +1 { {1} over {"10"} } +5 { {5} over {6} } } {}

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15 16 7 8 size 12{ { {"15"} over {"16"} } - { {7} over {8} } } {}

1 1 = 0   1 16 size 12{1 - 1=0 left ( { {1} over {"16"} } right )} {}

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12 25 9 20 size 12{ { {"12"} over {"25"} } - { {9} over {"20"} } } {}

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Exercises for review

( [link] ) The fact that
( a first number a second number ) a third number = a first number ( a second number a third number )
is an example of which property of multiplication?

associative

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( [link] ) Find the quotient: 14 15 ÷ 4 45 size 12{ { {"14"} over {"15"} } div { {4} over {"45"} } } {} .

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( [link] ) Find the difference: 3 5 9 2 2 3 size 12{3 { {5} over {9} } - 2 { {2} over {3} } } {} .

8 9 size 12{ { {8} over {9} } } {}

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( [link] ) Find the quotient: 4 . 6 ÷ 0 . 11 size 12{4 "." "6 " div " 0" "." "11"} {} .

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( [link] ) Use the distributive property to compute the product: 25 37 size 12{"25 " cdot " 37"} {} .

25 40 3 = 1000 75 = 925 size 12{"25" left ("40" - 3 right )="1000" - "75"="925"} {}

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Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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