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Solve: a + 3 4 = 3 8 a 1 2 .

a = −2

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Solve: c + 3 4 = 1 2 c 1 4 .

c = −2

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In [link] , we’ll start by using the Distributive Property. This step will clear the fractions right away!

Solve: 1 = 1 2 ( 4 x + 2 ) .

Solution

.
Distribute. .
Simplify. Now there are no fractions to clear! .
Subtract 1 from both sides. .
Simplify. .
Divide by 2. .
Simplify. .
Check: Let x = 0 .
.
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Solve: −11 = 1 2 ( 6 p + 2 ) .

p = −4

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Solve: 8 = 1 3 ( 9 q + 6 ) .

q = 2

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Many times, there will still be fractions, even after distributing.

Solve: 1 2 ( y 5 ) = 1 4 ( y 1 ) .

Solution

.
Distribute. .
Simplify. .
Multiply by the LCD, 4. .
Distribute. .
Simplify. .
Collect the y terms to the left. .
Simplify. .
Collect the constants to the right. .
Simplify. .
Check: Substitute 9 for y .
.
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Solve: 1 5 ( n + 3 ) = 1 4 ( n + 2 ) .

n = 2

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Solve: 1 2 ( m 3 ) = 1 4 ( m 7 ) .

m = −1

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Solve equations with decimal coefficients

Some equations have decimals in them. This kind of equation will occur when we solve problems dealing with money and percent. But decimals are really another way to represent fractions. For example, 0.3 = 3 10 and 0.17 = 17 100 . So, when we have an equation with decimals, we can use the same process we used to clear fractions—multiply both sides of the equation by the least common denominator .

Solve: 0.8 x 5 = 7 .

Solution

The only decimal in the equation is 0.8 . Since 0.8 = 8 10 , the LCD is 10 . We can multiply both sides by 10 to clear the decimal.

.
Multiply both sides by the LCD. .
Distribute. .
Multiply, and notice, no more decimals! .
Add 50 to get all constants to the right. .
Simplify. .
Divide both sides by 8. .
Simplify. .
Check: Let x = 15 .
.
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Solve: 0.6 x 1 = 11 .

x = 20

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Solve: 1.2 x 3 = 9 .

x = 10

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Solve: 0.06 x + 0.02 = 0.25 x 1.5 .

Solution

Look at the decimals and think of the equivalent fractions.

0.06 = 6 100 , 0.02 = 2 100 , 0.25 = 25 100 , 1.5 = 1 5 10

Notice, the LCD is 100 .

By multiplying by the LCD we will clear the decimals.

.
Multiply both sides by 100. .
Distribute. .
Multiply, and now no more decimals. .
Collect the variables to the right. .
Simplify. .
Collect the constants to the left. .
Simplify. .
Divide by 19. .
Simplify. .
Check: Let x = 8 .
.

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Solve: 0.14 h + 0.12 = 0.35 h 2.4 .

h = 12

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Solve: 0.65 k 0.1 = 0.4 k 0.35 .

k = −1

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The next example uses an equation that is typical of the ones we will see in the money applications in the next chapter. Notice that we will distribute the decimal first before we clear all decimals in the equation.

Solve: 0.25 x + 0.05 ( x + 3 ) = 2.85 .

Solution

.
Distribute first. .
Combine like terms. .
To clear decimals, multiply by 100. .
Distribute. .
Subtract 15 from both sides. .
Simplify. .
Divide by 30. .
Simplify. .
Check: Let x = 9 .
.
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Solve: 0.25 n + 0.05 ( n + 5 ) = 2.95 .

n = 9

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Solve: 0.10 d + 0.05 ( d 5 ) = 2.15 .

d = 16

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Key concepts

  • Solve equations with fraction coefficients by clearing the fractions.
    1. Find the least common denominator of all the fractions in the equation.
    2. Multiply both sides of the equation by that LCD. This clears the fractions.
    3. Solve using the General Strategy for Solving Linear Equations.

Questions & Answers

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
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
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.
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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