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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

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
?
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
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
what is biological synthesis of nanoparticles
Sanket Reply
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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