CHAPTER 5
Ratios and Proportions
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LEARNING OBJECTIVES
Upon completion of this chapter, the learner will
be able to:
1.
2.
3.
4.
5.
Define the key terms that relate to the chapter.
Identify the proper way to set up ratios.
Demonstrate how to set up a proportion.
Solve for “X.”
Calculate word problems.
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Key Terms
1.
2.
3.
4.
5.
6.
Algebra
Cross Multiplication
Extremes
Means
Proportion
Ratio
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RATIO
• Ratio is a comparison between two objects or
similar amounts.
• Health care uses ratios to determine:




Medication dosages
Additives to IV solutions
Laboratory values
Disease statistics
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WRITING RATIOS
As a fraction
15
7
2. With the use of a colon to separate the items
15:7
3. In word problems, place the word “to” between the
two items
of comparison
15 to 7
1.
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RATIO OF SUSPENSIONS
What is the ratio of medication?
Erythromycin label.
From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians:
A worktext, St. Louis, 2007, Saunders.
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MEDICATION DOSAGE AS A RATIO
What is the ratio?
KAON-CL label
From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians:
A worktext, St. Louis, 2007, Saunders.
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RATIO OF LIQUIDS
What is the ratio?
Robinul Injectable label.
From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians:
A worktext, St. Louis, 2007, Saunders.
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RATIO OF TABLETS
What is the dose per tablet?
Pravachol label.
From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians:
A worktext, St. Louis, 2007, Saunders.
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RATIO OF TABLETS
What is the ratio for each tablet?
Voltaren label.
From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians:
A worktext, St. Louis, 2007, Saunders.
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RATIO PER TABLET
What is the ratio of each tablet?
Glucophage label.
From Fulcher RM, Fulcher E: Math calculations for pharmacy technicians:
A worktext, St. Louis, 2007, Saunders.
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WRITING A PROPORTION
• A proportion is a mathematical equation that
compares two equal ratios.
• Example:
 In one second grade class there is one boy for
every two girls. In another second grade class
there are three boys for every six girls. Are these
proportions equal?
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WRITING A PROPORTION, cont.
• Proportions can be set up as fractions with an
equal sign (=) between the ratios.
1 boy = 3 boys
 13
2 girls
6 girls
2
•
6
Proportions can be set up with double colons
(::) between the ratios.
1:2::3:6
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WRITING A PROPORTION, cont.
• Read the problem.
• Identify the known information.
• Write the proportion so that the same units appear in
the same location for each proportion.
• Solve the problem using cross multiplication if your
proportion is written as a fraction.

Solve in linear fashion by multiplying the means together and
the extremes together.
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WRITING A PROPORTION, cont.
• Example, cont.:
1/2 = 3/6
1x6=2x3
6=6
1:2::3:6
1 x 6::2 x 3
6::6
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SOLVING FOR “X”
1.
2.
3.
4.
5.
Read the problem.
Identify the known information.
Write the known information on the left side of the
equation.
Identify the unknown information.
Represent the unknown information with the letter
“X.”
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SOLVING FOR “X,” cont.
6.
7.
8.
Write the unknown information on the right side of
the equation. Make sure you have the same
measurements in identical positions for each portion.
Reduce any fractions before performing
computations.
Solve the problem using cross multiplication. If you
have forgotten how to cross multiply, refer to the
slide “Cross Multiplication.”
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SOLVING FOR “X,” cont.
9.
10.
Check your answer by substituting your answer for
“X.” You should obtain equal results for this to be a
true proportion.
Label your answer.
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CROSS MULTIPLICATION
•
Example:
2/3 = X/4
1.
Set up the problem with the same measurements
in the same location on both sides of the
proportion.
2=X
3 4
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CROSS MULTIPLICATION, cont.
Multiply the numerator from the left side of
the equation with the denominator of the right
side of the equation.
2x4
3. Multiply the numerator from the right side of
the equation with the denominator of the left
side of the equation.
3x X
2.
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CROSS MULTIPLICATION, cont.
4.
To isolate “X,” you must divide both sides of the equation
by the number being multiplied to the “X.”
3xX=2x4
X=
5.
or 2.666666666666, which rounded to the nearest tenth is 2.7.
Label your answer.
21
3
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CHECK YOUR ANSWER
Insert your answer to replace the “X” in the
proportion.
2. Perform the mathematical calculations.
3. Your answer is correct if the solutions of
both proportions are equal.
1.
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WRITING A PROPORTION WITH
LINEAR FORMAT
1.
2.
3.
4.
5.
Read the problem.
Identify the known information.
Write the known information on the left side
of the equation.
Identify the unknown information.
Represent the unknown information with the
letter “X.”
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WRITING A PROPORTION WITH LINEAR
FORMAT, cont.
Write the unknown information on the right side of
the equation. Make sure you have the same
measurements in identical positions for each portion.
7. Solve the problem by multiplying the means (“inside”
numbers) and the extremes (“outside” numbers).
8. Isolate “X” by dividing both sides of the equation with
the number that is being multiplied by “X.”
9. Check your answer.
10. Label your answer.
6.
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WRITING A PROPORTION WITH
LINEAR FORMAT, cont.
Human Error box 5-2:
•
•
•
Incorrect setup is the most common error with
proportion problems.
The units of measurement should be in the same
location on both sides of the problem.
Incorrect computation is the next most common
human error.
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WRITING A PROPORTION WITH
LINEAR FORMAT, cont.
•
Example: There are 15 boys for every 20 girls
in your college class. If there are 360 girls in
the class, how many boys are in the class?
15:20::X:360
Solve the problem.
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WRITING A PROPORTION WITH
LINEAR FORMAT, cont.
• Example :
The patient weighs 210 pounds. The
doctor orders 50 mg of medication for
every 10 pounds. How much medication
would you give?
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WRITING A PROPORTION WITH
LINEAR FORMAT, cont.
• Example:
50 mg = X mg
10 lb 210 lb
10X = 50 x 210
10X = 10,500
10
10
X = 1050 mg
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MEDICATION FORMULAS
• Dosage ordered x Known dosage form = Amount to give
Dosage available
• Known dosage available
Known dosage form
=
Dosage ordered_
Amount to be given
• What do you know? = What do you want?
What do you need?
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DOSAGE FORMULA
D (desire) x Q (quantity) = Amount
H (have)
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CONCLUSION
• There are many different ways to solve proportion problems.

Choose the method that works best for you.
• There are many formulas to determine drug dosages.

Choose the method that works best for you.
• Work carefully when preforming any type of mathematical
computation.

Errors may occur if you become rushed or distracted.
Errors may occur by incorrectly setting up the proportion.
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