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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

Application of nanotechnology in medicine
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August 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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