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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Back to Basics: A Simple
Guide to Calculations for
Pharmacy Technicians
By: Kevin McCarthy, R.Ph
This program has been brought to you by PharmCon
PharmCon is accredited by the Accreditation Council for Pharmacy Education as a provider of continuing
pharmacy education
Legal Disclaimer: The material presented here does not necessarily reflect the views of Pharmaceutical Education Consultants (PharmCon) or
the companies that support educational programming. A qualified healthcare professional should always be consulted before using any
therapeutic product discussed. Participants should verify all information and data before treating patients or employing any therapies
described in this educational activity.
Copyright PharmCon 2010
Back to Basics: A Simple Guide to Calculations
for Pharmacy Technicians
Speakers: Kevin McCarthy, RPh is a graduate of the University of Maryland School of Pharmacy.
His professional background includes being a Trustee of the Maryland Pharmacists Association,
and President of the Southern Maryland Pharmacists Association. In addition to owning his own
pharmacy, he has worked in management in both chain and independent pharmacies. His most
recent position prior to PharmCon was Director of Managed Care for Safeway Inc., and Regional
Director of Sales for the pharmacy benefits manager, SMCRx, now known as Avia Partners, Inc.
Speaker Disclosure: Kevin McCarthy have no actual or potential conflicts of interest in relation
to this program
Back to Basics: A Simple Guide to Calculations
for Pharmacy Technicians
Accreditation:
Pharmacy Technicians: 0798-0000-10-039-L04-T
CE Credits: 1.0 contact hour
Target Audience: Pharmacy Technicians
Program Overview: Brushing up on the basics of math is something that is essential for every pharmacy technician.
Pharmaceutical calculations are a part of everyday life in the pharmacy practice, and your duty as a technician.
These calculations are not too difficult, but require swift work, and accuracy that is no less than perfection. This
program will also refresh the memory of important rules to help reduce errors throughout the calculation
processes. By giving sample problems, and working through them, this program will also help build confidence in
using these basic math skills.
Objectives:
• Define the three common systems of measurement
• Explain and show how the processes of proportion, ratios, and percentages apply to pharmacy
calculations
• Distinguish and solve for Flow Rate, Drip Rate and Drip Factor
This program has been brought to you by PharmCon
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Objectives
• Define the three common systems of measurement
• Explain and show how the processes of proportion,
ratios, and percentages apply to pharmacy
calculations
• Distinguish and solve for Flow Rate, Drip Rate and
Drip Factor
This program has been brought to you by PharmCon
PharmCon is accredited by the Accreditation Council for Pharmacy Education as a provider of continuing
pharmacy education
Legal Disclaimer: The material presented here does not necessarily reflect the views of Pharmaceutical Education Consultants (PharmCon) or
the companies that support educational programming. A qualified healthcare professional should always be consulted before using any
therapeutic product discussed. Participants should verify all information and data before treating patients or employing any therapies
described in this educational activity.
Copyright PharmCon 2010
Copyright PharmCon 2010
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Lets Get to the Point: Decimals!
The Three General Rules When Dealing With
Decimals
1) NEVER add zeros to the right of the decimal point,
Unless you are working with money
- The end signifies the accuracy of the number
- 2.3 not 2.300
2) The answer you get can be only as accurate as the least
accurate number used in the calculation
3) NEVER leave a decimal point “uncovered”
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- Too easy to misread
and make a mistake .2 or 0.2?
Rounding Numbers
If the number following the place you are
rounding to is 4 or lower, round down.
If the number following the place you are
rounding to is 5 or higher, round up.
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Decimal Examples
1.4593 ≠ 1.45930
1.4593 = 1.4593
1.5 x 1.5 is less accurate than 1.52 x 1.5
because 1.52 is more accurate than 1.5
.432 is covered 0.432 is covered and correct
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Lets Try Some Rounding
7.847 to tenths
7.8
0.347 to hundredths
0.35
7.9372 to thousandths
7.937
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Roman Numerals
Roman Numerals…Decoded
• Used to write prescriptions
ss = One Half
I = One
V = Five
X = Ten
L = Fifty
C = One Hundred
M = One Thousand
• Used in directions to the patient
• Used to specify the amounts of ingredients
and the quantity being dispensed
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Copyright PharmCon 2010
III Rules of Roman Numerals
Lets give it a try…
1) If a symbol follows another symbol of lower
value, the lower value is subtracted from the
higher value XL = 40
2) If a symbol follows another symbol of equal or
greater value, the two symbols are added
together
VI = 6
3) First perform any necessary subtraction, then
add the resulting values together to get a final
answer
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Question 1:
VII = ?
Question 2:
CXXXII = ?
Question 3:
17 = ?
Type your answers in the Chat Box
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Lets give it a try…
Question 1:
VII = 7
Question 2:
CXXXII = 132
Question 3:
17 = XVII
Roman Numerals In Real Life
#2
#1
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Copyright PharmCon 2010
Systems of Measurement
Metric System Conversion Factors
There are three systems of measurement
•Metric
•Avoirdupois
(household system)
•Apothecary
•
•
•
•
•
Micro – One Millionth
Milli – One Thousandth
Centi – One Hundredth
Deci – One Tenth
Kilo – One Thousand
(rarely used)
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Metric System Conversions
•
•
•
•
Avoirdupois Conversion Factors
•
•
•
•
•
1000mcg = 1mg
1000mg = 1g
1000g = 1kg
1000ml = 1L
Metrics are expressed in decimal form, such as
500ml = 0.5L
3 tsp = 1 tbsp
2 tbsp = 1 oz
16 oz = 1 pt
2 pt = 1 qt
4 qt = 1 G
*16 oz = 1 lb*
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Copyright PharmCon 2010
Conversions Between Systems
Ending Conversion Confusion
1 tsp = 5 ml
1 tbsp = 15 ml
1 oz = 30 ml (29.57 ml)
1 pt = 480 ml (473 ml)
1 G = 3840 ml (3784 ml)
1 g = 15.4 gr
1 gr = 60 mg (64.8mg)
1 kg = 2.2 lb
1 lb = 454 g
1 oz = 30 g
8.3 oz = ___ ml
Units should be arranged so that they will cancel
and solve for the unknown unit
Value x Conversion Factor = Answer
8.3 oz x 30 ml = 249 ml
1 oz
The ounces cancel, which leaves you with milliliters
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Lets give it a try…
Lets give it a try…
Convert:
4.1 kg to grams
Convert:
4.1 kg x 2.2 lb x 454 g = 4,095.08 g
1 kg
1 lb
4.1 kg to grams
OR
approximately 4,100g
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Copyright PharmCon 2010
Convert This
Convert This…Answers!
Lets say you receive a prescription for Amoxil
250mg/5mls with directions to take 1 tsp by
mouth twice daily for 10 days.
A) How much drug in milligrams, is in one tsp?
B) How much Amoxil in milliliters do you have to
give the patient to last the full 10 days?
• How much drug in milligrams, is in one tsp?
250 mg x 5mls = 250mg
5mls
1tsp
1tsp
• How much Amoxil in mls do you have to give the patient to
last the full 10 days?
1 tsp x 2 doses per day x 10 days = 20tsp
20tsp x 5mls = 100mls
1tsp
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Copyright PharmCon 2010
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Ratios
Ratios
Ratios are the relations between like numbers,
values or ways to express fractional part of a
whole.
Ratios can be written as:
• Using “per” such as 1 milligram per three
hours (1mg/3hr)
• With the colon or ratio sign 1:3
• A fraction 1/3
Strengths or concentrations of drugs can be
expressed as ratios. Read the label of a drug
and find the strength or concentration. Then,
express this strength/concentration in
fractional form. Here are a few examples.
– Epinephrine injection, 1:1000  1/1000
– Albuterol Solution, 0.83 mg per ml  0.83/1ml
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Proportion
Proportion
• Proportions are used when two expressions
are directly related to each other.
– Example: A 2kg drug costs $10. How much drug
can you get for $20?
• Proportions are your most used calculation in
the pharmacy
• Used to solve most dosage calculations
• Every day life calculations
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Proportions consist of two equal ratios and is
a statement of equality for the two ratios.
Example:
_3_
5
=
_6_
10
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Proportion & Ratio
Proportion & Ratio
Example 1:
A Doctor orders digoxin 0.25 mg by mouth. You have a 0.5 mg tablet of digoxin. How
much of the tablet would you give the patient?
Example 1:
A Doctor orders digoxin 0.25 mg by mouth.
You have a 0.5 mg tablet of digoxin. How
much of the tablet would you give the
patient?
0.5 mg
1 tab
=
0.25 mg
X
0.5 mg (X) = (1 tab) (0.25 mg)
X = 0.25
0.5
X = 0.5 tablet
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Copyright PharmCon 2010
Proportion & Ratio
Proportion & Ratio
Example 2:
You have a 40 ml vial of a drug labeled “100
mg per 2ml”
How many milliliters must be injected to
administer a dose of 500 mg?
Example 2:
You have a 40 ml vial of a drug labeled “100 mg per 2 ml”
How many milliliters must be injected to administer a dose of 500 mg?
_100 mg_ = _500 mg_
2 ml
X ml
100 mg (X) = (2 ml) (500 mg)
X = 1000
100
X = 10 ml
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Proportion and Ratio
A formula calls for 37 capsules of
300 mg drug. How many
milligrams would be required to
make 15 capsules?
Proportion & Ratio
A formula calls for 37 capsules of 300 mg drug. How many
milligrams would be required to make 15 capsules?
300 mg = __X__
37 caps 15 caps
37 caps (X) = (300 mg) (15 caps)
X= 4,500
37
X = 121.6 mg
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Percentages
There are three ways to prepare percentages:
• Percent volume-in-volume (v/v)
– X milliliters / 100 milliliters
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Percentages
• Example:
How much NaCl in grams is needed to prepare
a 1 liter of 0.9% normal saline solution?
• Percent weight-in-weight (wt/wt)
– X grams / 100 grams
• Percent weight-in-volume (wt/v)
– X grams / 100 milliliters
• Most Common
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Percentages
•
Example:
How much NaCl in grams is needed to prepare a 1 liter of 0.9% normal
saline solution?
0.9% = 0.9 g / 100 ml
1 liter = 1000ml
So: 0.9 g = X g
100 ml 1000 ml
100 (X) = (0.9)(1000)
X = 900
100
X = 9 g NaCl
Parenteral Calculations
• Parenteral Calculations deal with the
administration of IV fluids
• 3 Main concepts you will learn
– Flow rate
– Drip rate
– Dose per time
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Flow Rate
Give it a try
• Flow rate is the rate of speed that the IV solution
is being delivered
• This is a function of Volume per Time
– Usually ml/hour
A patient receives 1 L of IV solution over a 5 hour
period. Calculate the flow rate in ml/hour.
First, we need to convert Liters to milliliters:
1 L = 1000 ml
• Formula: Volume ÷ Time = Flow Rate
Volume ÷ Time = Flow Rate
**Always double check what time and volume you are solving
for! ml/hour, L/min..etc**
1000 ml ÷ 5 hours = 200 ml/hr
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Another Flow Rate Problem
A patient receives 0.5 L of IV solution
over a 3 hour period. Calculate the
flow rate in ml/hr
Another Flow Rate Problem
A patient receives 0.5 L of IV solution over a 3
hour period. Calculate the flow rate in ml/hr
Again, convert Liters to milliliters
0.5 L X 1000 ml = 500 ml
1L
500 ml ÷ 3 hours = 167 ml/hr
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Manipulating the Formula
Lets Try Solving for Time
By manipulating the formula that we have for
flow rate, we can also solve for time or
volume.
Solving for time would make the formula:
Volume ÷ Flow Rate = Time
Say you have an IV running at 138
ml/hr. How long will 1 L last the
patient?
Solving for Volume would make the formula
Rate x Time = Volume
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Lets Try Solving for Time
Now, Solve for Volume
Say you have an IV running at 138 ml/hr. How long will 1
L last the patient?
How many ml of solution would be
required to run an IV for 8 hours, at a
rate of 60 ml/hr?
Again, Convert L to ml.
1 L = 1000 ml
Volume ÷ Flow Rate = Time
1000 ml (volume)
138 ml/hour (flow rate)
= 7 Hours
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Copyright PharmCon 2010
Now, Solve for Volume
Drip Rate
How many ml of solution would be required to
run an IV for 8 hours, at a rate of 48 ml/hr?
• Drip Rate is the number of drops the IV solutions
is dripping during a specified time period
• Function of drops per minute
Remember: Rate x Time = Volume
60ml X 8 hours = 480 ml
1 hr
1
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– Reported as gtt/min
• Drip Factor is the tubing found on the
manufacturer’s packaging
– Reported as gtt/ml
• Formula: (Volume/Time) X drip factor = drip rate
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Finding Drip Rate
Finding Drip Rate
The physician orders IV fluids D5NS 4 liters
over 24 hours. The package says the drip
factor of the tubing is 15 gtt/ml. What is
the drip rate?
The physician orders IV fluids D5NS 4 liters over 24 hours. The package
says the drip factor of the tubing is 15 gtt/ml. What is the drip rate?
First, we need to convert liters to milliliters & hours to minutes
4L X 1000ml = 4000 ml
24 hours X 60 min = 1440 min
1L
1 hour
Now, “plug and chug” the formula
(V/T) X drip factor = drip rate
(4000 ml / 1440 min) X 15 gtt/ml = 41.66 gtt/ml
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ITS TIME FOR….
THE PHARMACY TECH CHALLENGE!!!
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This is Troy Polamalu!! His is number
43. What would his number be in
Roman Numerals??
How about a friendly competition?
Type your answers into the chat box and try to
win a PHARMCON KOOZIE!!
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Rounding
1) 0.85937 to tenths
2) 0.73683 to hundredths
3) 3.93749 to thousandths
When measuring __?___ and ___?___ in a
tuberculin syringe, the number of units will
ALWAYS equal an equivalent number of
hundredths of a milliliter. Therefore these two
drugs will ALWAYS be rounded in hundredths
in calculations.
Hint: One deals with glucose, and the other one is an
anticoagulant
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Remember, flow rate is measured in ml/hr. But,
just for fun, use your conversion skills and tell
us:
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Convert the numerical expression
Decimal
What is the flow rate in tsp/sec if 0.75 L of 0.9%
Sodium Chloride solution is given over a 7
hour period?
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0.6
Fraction
Percent
?
Ratio
?
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?
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Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Convert the numerical expression
Decimal
Fraction
?
Percent
7/20
A) This could be written as 20 mg/__lb/day. ?
Ratio
?
A child’s amoxicillin dose is 20 mg/kg/day
in divided doses, every 8 hours
?
B) How many grams of amoxicillin would a 44 lb
child receive daily?
C) How many milligrams per dose?
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Notes
Notes
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