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Sample set a

The diagrams in the following problems are illustrations of fractions.

A whole circle.
A whole circle
A whole circle divided into 3 equal parts.
The whole circle divided into 3 equal parts
A whole circle divided into 3 equal parts. One of the parts is shaded.
1 of the 3 equal parts

The fraction one-third. This would be read, 1 of 3 equal parts.

The fraction 1 3 size 12{ { {1} over {3} } } {} is read as "one third."

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A rectangle.
A whole rectangle
A rectangle divided into five equal parts by vertical bars.
The whole rectangle divided into 5 equal parts
A rectangle divided into five equal parts by vertical bars. The three leftmost bars are shaded.
3 of the 5 equal parts

The fraction three-fifths. This would be read, 3 of 5 equal parts.

The fraction 3 5 "is read as "three fifths."

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A number line with two marks, 0 and 1.
The number line between 0 and 1
A number line with two marks, 0, and 1, and six hash marks in between.
The number line between 0 and 1 divided into 7 equal parts
A number line with two marks, 0, and 1, and six hash marks in between. There is an arrow drawn from the zero to the first hash mark, and then from that hash mark to the next, until the sixth hash mark, where the arrows stop.
6 of the 7 equal parts

The fraction six-sevenths. This would be read, 6 of the 7 equal parts.

The fraction 6 7 is read as "six sevenths."

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A whole circle.
A whole circle
A whole circle divided into four equal parts.
The whole circle divided into 4 equal parts
A whole circle divided into four equal parts. All four parts are shaded.
4 of the 4 equal parts

The fraction four-fourths. This would be read, 4 of the 4 equal parts.

When the numerator and denominator are equal, the fraction represents the entire quantity, and its value is 1.

nonzero whole number same nonzero whole number = 1

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Practice set a

Specify the numerator and denominator of the following fractions.

4 7 size 12{ { {4} over {7} } } {}

4, 7

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5 8 size 12{ { {5} over {8} } } {}

5, 8

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10 15 size 12{ { {"10"} over {"15"} } } {}

10, 15

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

1, 9

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0 2 size 12{ { {0} over {2} } } {}

0, 2

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Reading and writing fractions

In order to properly translate fractions from word form to number form, or from number form to word form, it is necessary to understand the use of the hyphen .

Use of the hyphen

One of the main uses of the hyphen is to tell the reader that two words not ordinarily joined are to be taken in combination as a unit. Hyphens are always used for numbers between and including 21 and 99 (except those ending in zero).

Sample set b

Write each fraction using whole numbers.

Fifty three-hundredths. The hyphen joins the words three and hundredths and tells us to consider them as a single unit. Therefore,
fifty three-hundredths translates as 50 300 size 12{ { {"50"} over {"300"} } } {}

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Fifty-three hundredths. The hyphen joins the numbers fifty and three and tells us to con­sider them as a single unit. Therefore,
fifty-three hundredths translates as 53 100 size 12{ { {"53"} over {"100"} } } {}

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Four hundred seven-thousandths. The hyphen joins the words seven and thousandths and tells us to consider them as a single unit. Therefore,
four hundred seven-thousandths translates as 400 7,000 size 12{ { {"400"} over {"7000"} } } {}

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Four hundred seven thousandths. The absence of hyphens indicates that the words seven and thousandths are to be considered individually.
four hundred seven thousandths translates as 407 1000 size 12{ { {"407"} over {"1000"} } } {}

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Write each fraction using words.

21 85 size 12{ { {"21"} over {"85"} } } {} translates as twenty-one eighty-fifths.

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200 3,000 size 12{ { {"200"} over {"3000"} } } {} translates as two hundred three-thousandths. A hyphen is needed between the words three and thousandths to tell the reader that these words are to be considered as a single unit.

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203 1,000 size 12{ { {"203"} over {"1000"} } } {} translates as two hundred three thousandths.

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Practice set b

Write the following fractions using whole numbers.

one tenth

1 10 size 12{ { {1} over {"10"} } } {}

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eleven fourteenths

11 14 size 12{ { {"11"} over {"14"} } } {}

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sixteen thirty-fifths

16 35 size 12{ { {"16"} over {"35"} } } {}

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eight hundred seven-thousandths

800 7, 000 size 12{ { {"800"} over {7,"000"} } } {}

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Write the following using words.

3 8 size 12{ { {3} over {8} } } {}

three eighths

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1 10 size 12{ { {1} over {"10"} } } {}

one tenth

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3 250 size 12{ { {3} over {"250"} } } {}

three two hundred fiftieths

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114 3,190 size 12{ { {"114"} over {"3190"} } } {}

one hundred fourteen three thousand one hundred ninetieths

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Name the fraction that describes each shaded portion.

A whole circle divided into eight equal parts, with three parts shaded.

3 8 size 12{ { {3} over {8} } } {}

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A whole circle divided into sixteen equal parts, with one part shaded.

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

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In the following 2 problems, state the numerator and denominator, and write each fraction in words.

The number 5 9 size 12{ { {5} over {9} } } {} is used in converting from Fahrenheit to Celsius.

5, 9, five ninths

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A dime is 1 10 size 12{ { {1} over {"10"} } } {} of a dollar.

1, 10, one tenth

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Exercises

For the following 10 problems, specify the numerator and denominator in each fraction.

3 4 size 12{ { {3} over {4} } } {}

numerator, 3; denominator, 4

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9 10 size 12{ { {9} over {"10"} } } {}

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1 5 size 12{ { {1} over {5} } } {}

numerator, 1; denominator, 5

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

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7 7 size 12{ { {7} over {7} } } {}

numerator, 7; denominator, 7

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4 6 size 12{ { {4} over {6} } } {}

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0 12 size 12{ { {0} over {"12"} } } {}

numerator, 0; denominator, 12

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25 25 size 12{ { {"25"} over {"25"} } } {}

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18 1 size 12{ { {"18"} over {1} } } {}

numerator, 18; denominator, 1

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0 16 size 12{ { {0} over {"16"} } } {}

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For the following 10 problems, write the fractions using whole numbers.

four fifths

4 5 size 12{ { {4} over {5} } } {}

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fifteen twentieths

15 20 size 12{ { {"15"} over {"20"} } } {}

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forty-seven eighty-thirds

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ninety-one one hundred sevenths

91 107 size 12{ { {"91"} over {"107"} } } {}

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twenty-two four hundred elevenths

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six hundred five eight hundred thirty-fourths

605 834 size 12{ { {"658"} over {"134"} } } {}

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three thousand three forty-four ten-thousandths

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ninety-two one-millionths

92 1, 000 , 000 size 12{ { {"92"} over {1,"000","000"} } } {}

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For the following 10 problems, write the fractions using words.

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

five ninths

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6 10 size 12{ { {6} over {"10"} } } {}

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

eight fifteenths

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10 13 size 12{ { {"10"} over {"13"} } } {}

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75 100 size 12{ { {"75"} over {"100"} } } {}

seventy-five one hundredths

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86 135 size 12{ { {"86"} over {"135"} } } {}

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916 1,014 size 12{ { {"916"} over {"1014"} } } {}

nine hundred sixteen one thousand fourteenths

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501 10,001 size 12{ { {"501"} over {"10001"} } } {}

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18 31,608 size 12{ { {"18"} over {"31608"} } } {}

eighteen thirty-one thousand six hundred eighths

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1 500,000 size 12{ { {1} over {"500000"} } } {}

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For the following 4 problems, name the fraction corresponding to the shaded portion.

A whole circle divided into two equal parts, with one part shaded.

1 2 size 12{ { {1} over {2} } } {}

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A rectangle divided into seven equal parts, with four parts shaded.

4 7 size 12{ { {4} over {7} } } {}

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For the following 4 problems, shade the portion corresponding to the given fraction on the given figure.

State the numerator and denominator and write in words each of the fractions appearing in the state­ments for the following 10 problems.

A contractor is selling houses on 1 4 size 12{ { {1} over {4} } } {} acre lots.

Numerator, 1; denominator, 4; one fourth

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The fraction 22 7 size 12{ { {"22"} over {7} } } {} is sometimes used as an approximation to the number π . (The symbol is read “pi.")

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The fraction 4 3 size 12{ { {4} over {3} } } {} is used in finding the volume of a sphere.

Numerator, 4; denominator, 3; four thirds

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One inch is 1 12 size 12{ { {1} over {"12"} } } {} of a foot.

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About 2 7 size 12{ { {2} over {7} } } {} of the students in a college statistics class received a “B” in the course.

Numerator, 2; denominator, 7; two sevenths

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The probability of randomly selecting a club when drawing one card from a standard deck of 52 cards is 13 52 size 12{ { {"13"} over {"52"} } } {} .

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In a box that contains eight computer chips, five are known to be good and three are known to be defective. If three chips are selected at random, the probability that all three are defective is 1 56 size 12{ { {1} over {"56"} } } {} .

Numerator, 1; denominator, 56; one fifty-sixth

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In a room of 25 people, the probability that at least two people have the same birthdate (date and month, not year) is 569 1000 size 12{ { {"569"} over {"1000"} } } {} .

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The mean (average) of the numbers 21, 25, 43, and 36 is 125 4 size 12{ { {"125"} over {4} } } {} .

Numerator, 125; denominator, 4; one hundred twenty-five fourths

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If a rock falls from a height of 20 meters on Jupiter, the rock will be 32 25 size 12{ { {"32"} over {"25"} } } {} meters high after 6 5 size 12{ { {6} over {5} } } {} seconds.

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Exercises for review

( [link] ) Use the numbers 3 and 11 to illustrate the commutative property of addition.

3 + 11 = 11 + 3 = 14 size 12{3+"11"="11"+3="14"} {}

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( [link] ) Find the quotient. 676 ÷ 26 size 12{"676" div "26"} {}

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( [link] ) Write 7 7 7 7 7 size 12{7 cdot 7 cdot 7 cdot 7 cdot 7} {} using exponents.

7 5 size 12{7 rSup { size 8{5} } } {}

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( [link] ) Find the value of 8 6 + 20 8 + 3 6 + 16 22 size 12{ { {8 cdot left (6+"20" right )} over {8} } + { {3 cdot left (6+"16" right )} over {"22"} } } {} .

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( [link] ) Find the least common multiple of 12, 16, and 18.

144

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Questions & Answers

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
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
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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