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The quotient of f and −3 is −18 .

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The quotient of f and −4 is −20 .

f −4 = −20 ; f = 80

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The quotient of g and twelve is 8 .

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The quotient of g and nine is 14 .

g 9 = 14 ; g = 126

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Three-fourths of q is 12 .

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Two-fifths of q is 20 .

2 5 q = 20 ; q = 50

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Seven-tenths of p is −63 .

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Four-ninths of p is −28 .

4 9 p = −28 ; p = −63

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m divided by 4 equals negative 6 .

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The quotient of h and 2 is 43 .

h 2 = 43

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Three-fourths of z is the same as 15 .

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The quotient of a and 2 3 is 3 4 .

a 2 3 = 3 4

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The sum of five-sixths and x is 1 2 .

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The sum of three-fourths and x is 1 8 .

3 4 + x = 1 8 ; x = 5 8

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The difference of y and one-fourth is 1 8 .

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The difference of y and one-third is 1 6 .

y 1 3 = 1 6 ; y = 1 6

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Everyday math

Shopping Teresa bought a pair of shoes on sale for $48 . The sale price was 2 3 of the regular price. Find the regular price of the shoes by solving the equation 2 3 p = 48

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Playhouse The table in a child’s playhouse is 3 5 of an adult-size table. The playhouse table is 18 inches high. Find the height of an adult-size table by solving the equation 3 5 h = 18 .

30 inches

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Writing exercises

[link] describes three methods to solve the equation y = 15 . Which method do you prefer? Why?

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Richard thinks the solution to the equation 3 4 x = 24 is 16 . Explain why Richard is wrong.

Answers will vary.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?

Chapter review exercises

Visualize Fractions

In the following exercises, name the fraction of each figure that is shaded.

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

In the following exercises, convert the improper fraction to a mixed number.

In the following exercises, convert the mixed number to an improper fraction.

Find three fractions equivalent to 2 5 . Show your work, using figures or algebra.

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Find three fractions equivalent to 4 3 . Show your work, using figures or algebra.

Answers may vary.

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In the following exercises, locate the numbers on a number line.

1 4 , 1 4 , 1 1 3 , −1 1 3 , 7 2 , 7 2


A number line is shown. Integers from negative 4 to 4 are labeled. Between negative 4 and negative 3, negative 7 halves is labeled and marked with a red dot. Between negative 2 and negative 1, negative 1 and 1 third is labeled and marked with a red dot. Between negative 1 and 0, negative 1 fourth is labeled and marked with a red dot. Between 0 and 1, 1 fourth is labeled and marked with a red dot. Between 1 and 2, 1 and 1 third is labeled and marked with a red dot. Between 3 and 4, 7 halves is labeled and marked with a red dot.

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In the following exercises, order each pair of numbers, using < or >.

Multiply and Divide Fractions

In the following exercises, simplify.

In the following exercises, multiply.

In the following exercises, find the reciprocal.

Fill in the chart.

Opposite Absolute Value Reciprocal
5 13
3 10
9 4
−12

In the following exercises, divide.

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( 3 x 5 ) ÷ ( 2 y 3 )

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Multiply and Divide Mixed Numbers and Complex Fractions

In the following exercises, perform the indicated operation.

−5 7 12 · 4 4 11

268 11

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In the following exercises, translate the English phrase into an algebraic expression.

the quotient of V and the difference of h and 6

V h 6

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In the following exercises, simplify the complex fraction

In the following exercises, simplify.

8 · 4 5 2 3 · 12

7 36

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8 · 7 + 5 ( 8 10 ) 9 · 3 6 · 4

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Add and Subtract Fractions with Common Denominators

In the following exercises, add.

In the following exercises, subtract.

31 30 7 30

19 15

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11 15 5 15 ( 2 15 )

8 15

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Add and Subtract Fractions with Different Denominators

In the following exercises, find the least common denominator.

In the following exercises, change to equivalent fractions using the given LCD.

3 8 and 5 6 , LCD = 24

9 24 and 20 24

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9 16 and 5 12 , LCD = 48

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1 3 , 3 4 and 4 5 , LCD = 60

20 60 , 15 60 and 48 60

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In the following exercises, perform the indicated operations and simplify.

11 36 11 20

77 90

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y 10 1 3

3 y 10 30

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2 5 + ( 3 n 8 ) ( 2 9 n )

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( 2 3 ) 2 ( 5 8 ) 2

256 225

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( 11 12 + 3 8 ) ÷ ( 5 6 1 10 )

In the following exercises, evaluate.

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y 4 5 when

  1. y = 4 5
  2. y = 1 4

  1. 8 5
  2. 11 20

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6 m n 2 when m = 3 4 and n = 1 3

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Add and Subtract Mixed Numbers

In the following exercises, perform the indicated operation.

9 13 20 4 11 20

5 1 10

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Solve Equations with Fractions

In the following exercises, determine whether the each number is a solution of the given equation.

x 1 2 = 1 6 :

  • x = 1
  • x = 2 3
  • x = 1 3

  1. no
  2. yes
  3. no

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y + 3 5 = 5 9 :

  1. y = 1 2
  2. y = 52 45
  3. y = 2 45

In the following exercises, solve the equation.

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n + 9 11 = 4 11

n = 5 11

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h ( 7 8 ) = 2 5

h = 51 40

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In the following exercises, translate and solve.

The sum of two-thirds and n is 3 5 .

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The difference of q and one-tenth is 1 2 .

q 1 10 = 1 2 ; q = 3 5

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The quotient of p and −4 is −8 .

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Three-eighths of y is 24 .

3 8 y = 24 ; y = 64

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Chapter practice test

Convert the improper fraction to a mixed number.

19 5

Convert the mixed number to an improper fraction.

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Locate the numbers on a number line.

1 2 , 1 2 3 , −2 3 4 , and 9 4

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In the following exercises, simplify.

−36 u ( 4 9 )

16 u

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( −15 5 6 ) ÷ ( −3 1 6 )

5

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3 13 + ( 4 13 )

7 13

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3 4 ÷ x 3

9 4 x

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Evaluate.

x + 1 3 when

  1. x = 2 3
  2. x = 5 6

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In the following exercises, solve the equation.

f + ( 2 3 ) = 5 12

f = 13 12

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2 3 c = 18

c = −27

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Translate and solve: The quotient of p and −4 is −8 . Solve for p .

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Questions & Answers

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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
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
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Good
Berger describes sociologists as concerned with
Mueller Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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