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Determine whether each equation is a proportion:

  1. 4 9 = 12 28
  2. 17.5 37.5 = 7 15

Solution

To determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.

.
Find the cross products. 28 4 = 112 9 12 = 108
.

Since the cross products are not equal, 28 · 4 9 · 12 , the equation is not a proportion.

.
Find the cross products. 15 17.5 = 262.5 37.5 7 = 262.5
.

Since the cross products are equal, 15 · 17.5 = 37.5 · 7 , the equation is a proportion.

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Determine whether each equation is a proportion:

  1. 7 9 = 54 72
  2. 24.5 45.5 = 7 13

  1. ⓐ no
  2. ⓑ yes

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Determine whether each equation is a proportion:

  1. 8 9 = 56 73
  2. 28.5 52.5 = 8 15

  1. ⓐ no
  2. ⓑ no

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Solve proportions

To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the Least Common Denominator (LCD) using the Multiplication Property of Equality .

Solve: x 63 = 4 7 .

Solution

.
To isolate x , multiply both sides by the LCD, 63. .
Simplify. .
Divide the common factors. .
Check: To check our answer, we substitute into the original proportion.
.
. .
Show common factors. .
Simplify. .
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Solve the proportion: n 84 = 11 12 .

77

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Solve the proportion: y 96 = 13 12 .

104

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When the variable is in a denominator, we’ll use the fact that the cross products    of a proportion are equal to solve the proportions.

We can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques.

Solve: 144 a = 9 4 .

Solution

Notice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal.

.
Find the cross products and set them equal. .
Simplify. .
Divide both sides by 9. .
Simplify. .

Check your answer.

.
. .
Show common factors.. .
Simplify. .

Another method to solve this would be to multiply both sides by the LCD, 4 a . Try it and verify that you get the same solution.

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Solve the proportion: 91 b = 7 5 .

65

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Solve the proportion: 39 c = 13 8 .

24

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Solve: 52 91 = −4 y .

Solution

Find the cross products and set them equal. .
.
Simplify. .
Divide both sides by 52. .
Simplify. .
Check:
.
. .
Show common factors. .
Simplify. .
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Solve the proportion: 84 98 = −6 x .

−7

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Solve the proportion: −7 y = 105 135 .

−9

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Solve applications using proportions

The strategy for solving applications that we have used earlier in this chapter, also works for proportions, since proportions are equations. When we set up the proportion    , we must make sure the units are correct—the units in the numerators match and the units in the denominators match.

When pediatricians prescribe acetaminophen to children, they prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of the child’s weight. If Zoe weighs 80 pounds, how many milliliters of acetaminophen will her doctor prescribe?

Solution

Identify what you are asked to find. How many ml of acetaminophen the doctor will prescribe
Choose a variable to represent it. Let a = ml of acetaminophen.
Write a sentence that gives the information to find it. If 5 ml is prescribed for every 25 pounds, how much will be prescribed for 80 pounds?
Translate into a proportion. .
Substitute given values—be careful of the units. .
Multiply both sides by 80. .
Multiply and show common factors. .
Simplify. .
Check if the answer is reasonable.
Yes. Since 80 is about 3 times 25, the medicine should be about 3 times 5.
Write a complete sentence. The pediatrician would prescribe 16 ml of acetaminophen to Zoe.

You could also solve this proportion by setting the cross products equal.

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Questions & Answers

so some one know about replacing silicon atom with phosphorous in semiconductors device?
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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
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
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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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