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Translate and solve. The quotient of n and 2 3 is 5 12 .

n 2 3 = 5 12 ; n = 5 18

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Translate and solve The quotient of c and 3 8 is 4 9 .

c 3 8 = 4 9 ; c = 1 3

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Translate and solve: The sum of three-eighths and x is three and one-half.

Solution

Translate. .
Use the Subtraction Property of Equality to subtract 3 8 from both sides. .
Combine like terms on the left side. .
Convert mixed number to improper fraction. .
Convert to equivalent fractions with LCD of 8. .
Subtract. .
Write as a mixed number. .

We write the answer as a mixed number because the original problem used a mixed number.

Check:

Is the sum of three-eighths and 3 1 8 equal to three and one-half?

3 8 + 3 1 8 = ? 3 1 2
Add. 3 4 8 = ? 3 1 2
Simplify. 3 1 2 = 3 1 2

The solution checks.

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Translate and solve: The sum of five-eighths and x is one-fourth.

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

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Translate and solve: The difference of one-and-three-fourths and x is five-sixths.

1 3 4 x = 5 6 ; x = 11 12

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Key concepts

  • Determine whether a number is a solution to an equation.
    1. Substitute the number for the variable in the equation.
    2. Simplify the expressions on both sides of the equation.
    3. Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.
  • Addition, Subtraction, and Division Properties of Equality
    • For any numbers a, b, and c,
      if a = b , then a + c = b + c . Addition Property of Equality
    • if a = b , then a - c = b - c . Subtraction Property of Equality
    • if a = b , then a c = b c , c 0 . Division Property of Equality
  • The Multiplication Property of Equality
    • For any numbers a b and c , a = b , then a c = b c .
    • If you multiply both sides of an equation by the same quantity, you still have equality.

Practice makes perfect

Determine Whether a Fraction is a Solution of an Equation

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

x 2 5 = 1 10 :

  1. x = 1
  2. x = 1 2
  3. x = 1 2

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y 1 3 = 5 12 :

  1. y = 1
  2. y = 3 4
  3. y = 3 4

  1. no
  2. yes
  3. no

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h + 3 4 = 2 5 :

  1. h = 1
  2. h = 7 20
  3. h = 7 20

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k + 2 5 = 5 6 :

  1. k = 1
  2. k = 13 30
  3. k = 13 30

  1. no
  2. yes
  3. no

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Solve Equations with Fractions using the Addition, Subtraction, and Division Properties of Equality

In the following exercises, solve.

h + 5 6 = 1 6

h = 2 3

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c 1 4 = 5 4

c = −1

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x ( 3 20 ) = 11 20

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z ( 5 12 ) = 7 12

z = −1

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p 3 10 = 5 8

p = 37 40

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s + ( 1 2 ) = 8 9

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k + ( 1 3 ) = 4 5

k = 7 15

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−9 v = 33

v = 11 3

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Solve Equations with Fractions Using the Multiplication Property of Equality

In the following exercises, solve.

k = 17 20

k = 17 20

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5 12 v = −15

v = 36

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Mixed Practice

In the following exercises, solve.

q + 5 6 = 1 12

q = 3 4

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2 3 = y + 3 8

y = 25 24

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8 15 = d

d = 8 15

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Translate Sentences to Equations and Solve

In the following exercises, translate to an algebraic equation and solve.

n divided by eight is −16 .

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n divided by six is −24 .

n 6 = −24 ; n = −144

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m divided by −9 is −7 .

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m divided by −7 is −8 .

m −7 = −8 ; m = 56

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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.
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How do i figure this problem out.
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linda Reply
why surface tension is zero at critical temperature
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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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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