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For example,

Equal Measurements Unit Fraction
1ft = 12in. size 12{"1ft"="12in"} {} 1ft 12in. or 12in. 1ft size 12{ { {"1ft"} over {"12in."} } "or" { {"12in."} over {"1ft"} } } {}
1pt = 16 fl oz size 12{"1pt"="16 fl oz"} {} 1pt 16 fl oz or 16 fl oz 1pt size 12{ { {"1pt"} over {"16 fl oz"} } " or " { {"16 fl oz"} over {"1pt"} } } {}
1wk = 7da size 12{"1wk"="7da"} {} 7da 1wk or 1wk 7da size 12{ { {"7da"} over {"1wk"} } " or " { {"1wk"} over {"7da"} } } {}

Sample set a

Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.

Convert 11 yards to feet.

Looking in the unit conversion table under length , we see that 1 yd = 3 ft size 12{1" yd "="3 ft"} {} . There are two corresponding unit fractions, 1 yd 3 ft size 12{ { {"1 yd"} over {"3 ft"} } } {} and 3 ft 1 yd size 12{ { {"3 ft"} over {"1 yd"} } } {} . Which one should we use? Look to see which unit we wish to convert to. Choose the unit fraction with this unit in the numerator . We will choose 3 ft 1 yd size 12{ { {"3 ft"} over {"1 yd"} } } {} since this unit fraction has feet in the numerator. Now, multiply 11 yd by the unit fraction. Notice that since the unit fraction has the value of 1, multiplying by it does not change the value of 11 yd.

11 yd = 11 yd 1 3 ft 1yd Divide out common units. = 11 yd 1 3 ft 1 yd (Units can be added, subtracted, multiplied, and divided, just as numbers can.) = 11 3 ft 1 = 33 ft

Thus, 11 yd = 33 ft .

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Convert 36 fl oz to pints.

Looking in the unit conversion table under liquid volume , we see that 1 pt = 16 fl oz size 12{"1 pt "=" 16 fl oz"} {} . Since we are to convert to pints, we will construct a unit fraction with pints in the numerator.

36 fl oz = 36 fl oz 1 1 pt 16 fl oz Divide out common units. = 36 fl oz 1 1 pt 16 fl oz = 36 1 pt 16 = 36 pt 16 Reduce. = 9 4 pt Convert to decimals: 9 4 = 2.25 .

Thus, 36 fl oz = 2 . 25 pt size 12{"36 fl oz "=" 2" "." "25 pt"} {} .

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Convert 2,016 hr to weeks.

Looking in the unit conversion table under time , we see that 1wk = 7da size 12{"1wk "="7da"} {} and that 1 da = 24 hr size 12{1" da "=" 24 hr"} {} . To convert from hours to weeks, we must first convert from hours to days and then from days to weeks. We need two unit fractions.

The unit fraction needed for converting from hours to days is 1 da 24 hr size 12{ { {"1 da"} over {"24 hr"} } } {} . The unit fraction needed for converting from days to weeks is 1 wk 7 da size 12{ { {"1 wk"} over {"7 da"} } } {} .

2,016 hr = 2,016 hr 1 1 da 24 hr 1 wk 7 da Divide out common units. = 2,016 hr 1 1 da 24 hr 1 wk 7 da = 2,016 1 wk 24 7 Reduce. = 12 wk

Thus, 2,016 hr = 12 wk size 12{"2,016 hr "=" 12 wk"} {} .

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Practice set a

Make the following conversions. If a fraction occurs, convert it to a decimal rounded to two decimal places.

Convert 18 ft to yards.

6 yd

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Convert 2 mi to feet.

10,560 ft

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Convert 26 ft to yards.

8.67 yd

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Convert 9 qt to pints.

18 pt

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Convert 52 min to hours.

0.87 hr

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Convert 412 hr to weeks.

2.45 wk

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Exercises

Make each conversion using unit fractions. If fractions occur, convert them to decimals rounded to two decimal places.

8 mi to inches

506,880 inches

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5 in. to yards

0.14 yard

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62 in. to miles

0.00 miles (to two decimal places)

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6 T to ounces

192,000 ounces

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15,000 oz to pounds

937.5 pounds

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9 tbsp to teaspoons

27 teaspoons

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5 pt to fluid ounces

80 fluid ounces

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5 fl oz to quarts

0.16 quart

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5 pt to teaspoons

480 teaspoons

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18 min to seconds

1,080 seconds

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3 hr to days

1 8 = 0 . 125 size 12{ { {1} over {8} } =0 "." "125"} {} day

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1 2 da to weeks

1 14 = 0 . 0714 size 12{ { {1} over {"14"} } =0 "." "0714"} {} week

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Exercises for review

( [link] ) Specify the digits by which 23,840 is divisible.

1,2,4,5,8

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( [link] ) Find 2 4 5 size 12{2 { {4} over {5} } } {} of 5 5 6 size 12{5 { {5} over {6} } } {} of 7 5 7 size 12{7 { {5} over {7} } } {} .

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( [link] ) Convert 0 . 3 2 3 size 12{0 "." 3 { {2} over {3} } } {} to a fraction.

11 30 size 12{ { {"11"} over {"30"} } } {}

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( [link] ) Use the clustering method to estimate the sum: 53 + 82 + 79 + 49 size 12{"53"+"82"+"79"+"49"} {} .

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( [link] ) Use the distributive property to compute the product: 60 46 size 12{"60" cdot "46"} {} .

60 ( 50 4 ) = 3, 000 240 = 2, 760 size 12{"60" \( "50" - 4 \) =3,"000" - "240"=2,"760"} {}

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Questions & Answers

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
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
?
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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