# 4.8 Exercise supplement

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Introduction to Fractions and Multiplication and Division of Fractions" and contains many exercise problems. Odd problems are accompanied by solutions.

## Fractions of whole numbers ( [link] )

For Problems 1 and 2, name the suggested fraction. $\frac{2}{6}$ or $\frac{1}{3}$ For problems 3-5, specify the numerator and denominator.

$\frac{4}{5}$

numerator, 4; denominator, 5

$\frac{5}{\text{12}}$

$\frac{1}{3}$

numerator, 1; denominator, 3

For problems 6-10, write each fraction using digits.

Three fifths

Eight elevenths

$\frac{8}{\text{11}}$

Sixty-one forty firsts

Two hundred six-thousandths

$\frac{\text{200}}{6,\text{000}}$

zero tenths

For problems 11-15, write each fraction using words.

$\frac{\text{10}}{\text{17}}$

ten seventeenths

$\frac{\text{21}}{\text{38}}$

$\frac{\text{606}}{\text{1431}}$

six hundred six, one thousand four hundred thirty-firsts

$\frac{0}{8}$

$\frac{1}{\text{16}}$

one sixteenth

For problems 16-18, state each numerator and denominator and write each fraction using digits.

One minute is one sixtieth of an hour.

In a box that contains forty-five electronic components, eight are known to be defective. If three components are chosen at random from the box, the probability that all three are defective is fifty-six fourteen thousand one hundred ninetieths.

numerator, 56; denominator, 14,190

About three fifths of the students in a college algebra class received a “B” in the course.

For problems 19 and 20, shade the region corresponding to the given fraction.

$\frac{1}{4}$  $\frac{3}{7}$ ## Proper fraction, improper fraction, and mixed numbers ( [link] )

For problems 21-29, convert each improper fraction to a mixed number.

$\frac{\text{11}}{4}$

$2\frac{3}{4}$

$\frac{\text{15}}{2}$

$\frac{\text{51}}{8}$

$6\frac{3}{8}$

$\frac{\text{121}}{\text{15}}$

$\frac{\text{356}}{3}$

$\text{118}\frac{2}{3}$

$\frac{3}{2}$

$\frac{5}{4}$

$1\frac{1}{4}$

$\frac{\text{20}}{5}$

$\frac{9}{3}$

3

For problems 30-40, convert each mixed number to an improper fraction.

$5\frac{2}{3}$

$\text{16}\frac{1}{8}$

$\frac{\text{129}}{8}$

$\text{18}\frac{1}{3}$

$3\frac{1}{5}$

$\frac{\text{16}}{5}$

$2\frac{9}{\text{16}}$

$\text{17}\frac{\text{20}}{\text{21}}$

$\frac{\text{377}}{\text{21}}$

$1\frac{7}{8}$

$1\frac{1}{2}$

$\frac{3}{2}$

$2\frac{1}{2}$

$8\frac{6}{7}$

$\frac{\text{62}}{7}$

$2\frac{9}{2}$

Why does $0\frac{1}{\text{12}}$ not qualify as a mixed number?

because the whole number part is zero

Why does 8 qualify as a mixed number?

## Equivalent fractions, reducing fractions to lowest terms, and raising fractions to higher term ( [link] )

For problems 43-47, determine if the pairs of fractions are equivalent.

$\frac{1}{2}$ , $\frac{\text{15}}{\text{30}}$

equivalent

$\frac{8}{9}$ , $\frac{\text{32}}{\text{36}}$

$\frac{3}{\text{14}}$ , $\frac{\text{24}}{\text{110}}$

not equivalent

$2\frac{3}{8}$ , $\frac{\text{38}}{\text{16}}$

$\frac{\text{108}}{\text{77}}$ , $1\frac{5}{\text{13}}$

not equivalent

For problems 48-60, reduce, if possible, each fraction.

$\frac{\text{10}}{\text{25}}$

$\frac{\text{32}}{\text{44}}$

$\frac{8}{\text{11}}$

$\frac{\text{102}}{\text{266}}$

$\frac{\text{15}}{\text{33}}$

$\frac{5}{\text{11}}$

$\frac{\text{18}}{\text{25}}$

$\frac{\text{21}}{\text{35}}$

$\frac{3}{5}$

$\frac{9}{\text{16}}$

$\frac{\text{45}}{\text{85}}$

$\frac{9}{\text{17}}$

$\frac{\text{24}}{\text{42}}$

$\frac{\text{70}}{\text{136}}$

$\frac{\text{35}}{\text{68}}$

$\frac{\text{182}}{\text{580}}$

$\frac{\text{325}}{\text{810}}$

$\frac{\text{65}}{\text{162}}$

$\frac{\text{250}}{\text{1000}}$

For problems 61-72, determine the missing numerator or denominator.

$\frac{3}{7}=\frac{?}{\text{35}}$

15

$\frac{4}{\text{11}}=\frac{?}{\text{99}}$

$\frac{1}{\text{12}}=\frac{?}{\text{72}}$

6

$\frac{5}{8}=\frac{\text{25}}{?}$

$\frac{\text{11}}{9}=\frac{\text{33}}{?}$

27

$\frac{4}{\text{15}}=\frac{\text{24}}{?}$

$\frac{\text{14}}{\text{15}}=\frac{?}{\text{45}}$

42

$\frac{0}{5}=\frac{?}{20}$

$\frac{\text{12}}{\text{21}}=\frac{\text{96}}{?}$

168

$\frac{\text{14}}{\text{23}}=\frac{?}{\text{253}}$

$\frac{\text{15}}{\text{16}}=\frac{\text{180}}{?}$

192

$\frac{\text{21}}{\text{22}}=\frac{\text{336}}{?}$

For problems 73-95, perform each multiplication and division.

$\frac{4}{5}\cdot \frac{\text{15}}{\text{16}}$

$\frac{3}{4}$

$\frac{8}{9}\cdot \frac{3}{\text{24}}$

$\frac{1}{\text{10}}\cdot \frac{5}{\text{12}}$

$\frac{1}{\text{24}}$

$\frac{\text{14}}{\text{15}}\cdot \frac{7}{5}$

$\frac{5}{6}\cdot \frac{\text{13}}{\text{22}}\cdot \frac{\text{11}}{\text{39}}$

$\frac{5}{\text{36}}$

$\frac{2}{3}÷\frac{\text{15}}{7}\cdot \frac{5}{6}$

$3\frac{1}{2}÷\frac{7}{2}$

1

$2\frac{4}{9}÷\frac{\text{11}}{\text{45}}$

$\frac{8}{\text{15}}\cdot \frac{3}{\text{16}}\cdot \frac{5}{\text{24}}$

$\frac{1}{\text{48}}$

$\frac{8}{\text{15}}÷3\frac{3}{5}\cdot \frac{9}{\text{16}}$

$\frac{\text{14}}{\text{15}}÷3\frac{8}{9}\cdot \frac{\text{10}}{\text{21}}$

$\frac{4}{\text{35}}$

$\text{18}\cdot 5\frac{3}{4}$

$3\frac{3}{7}\cdot 2\frac{1}{\text{12}}$

$\frac{\text{50}}{7}=7\frac{1}{7}$

$4\frac{1}{2}÷2\frac{4}{7}$

$6\frac{1}{2}÷3\frac{1}{4}$

2

$3\frac{5}{\text{16}}÷2\frac{7}{\text{18}}$

$7÷2\frac{1}{3}$

3

$\text{17}÷4\frac{1}{4}$

$\frac{5}{8}÷1\frac{1}{4}$

$\frac{1}{2}$

$2\frac{2}{3}\cdot 3\frac{3}{4}$

$\text{20}\cdot \frac{\text{18}}{4}$

90

$0÷4\frac{1}{8}$

$1÷6\frac{1}{4}\cdot \frac{\text{25}}{4}$

1

## Applications involving fractions ( [link] )

Find $\frac{8}{9}$ of $\frac{\text{27}}{2}$ .

What part of $\frac{3}{8}$ is $\frac{\text{21}}{\text{16}}$ ?

$\frac{7}{2}$ or $3\frac{1}{2}$

What part of $3\frac{1}{5}$ is $1\frac{7}{\text{25}}$ ?

Find $6\frac{2}{3}$ of $\frac{9}{\text{15}}$ .

4

$\frac{7}{\text{20}}$ of what number is $\frac{\text{14}}{\text{35}}$ ?

What part of $4\frac{1}{\text{16}}$ is $3\frac{3}{4}$ ?

$\frac{\text{12}}{\text{13}}$

Find $8\frac{3}{\text{10}}$ of $\text{16}\frac{2}{3}$ .

$\frac{3}{\text{20}}$ of what number is $\frac{\text{18}}{\text{30}}$ ?

4

Find $\frac{1}{3}$ of 0.

Find $\frac{\text{11}}{\text{12}}$ of 1.

$\frac{\text{11}}{\text{12}}$

what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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 ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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