pharmaceutical calculations for technicians everyday applications
TRANSCRIPT
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 1
PHARMACEUTICAL CALCULATIONS FOR
TECHNICIANS
Every Day Applications
_____
Kevin McCarthy, RPh
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.
This program has been
brought to you by
PharmCon
PHARMACEUTICAL CALCULATIONS FOR
TECHNICIANS
Every Day Applications
_____
Kevin McCarthy, RPh
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.
This program has been
brought to you by
PharmCon
PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS:
EVERYDAY APPLICATIONS
Accreditation:
Pharmacy Technicians: 0798-0000-11-091-L04-T
CE Credits: 1.0 contact hour
Target Audience: Pharmacy Technicians
Program Overview: This program will briefly take technicians through some common pharmaceutical
weight, volume, and temperature conversions. Then, these conversions will be done for a recipe utilizing
ratios and proportions to show the relevance of pharmaceutical math to daily life. We’ll also review the
relationship between percentages and fractions to demonstrate common non-pharmaceutical applications
for this concept. This presentation is for technicians only, be ready to learn…and laugh!
Objectives:
• Explain ratios and proportions and show their applications in both pharmacy and everyday calculations
• Demonstrate an alternative perspective of looking at and utilizing percentages
• Solve calculations using both successive proportions and a continuous linear method
This program has been brought to you
by PharmCon
PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS:
EVERYDAY APPLICATIONS
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.
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
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 2
PHARMACY AND NASCAR ???
PROGRAM OBJECTIVES
Explain ratios and proportions and show
their applications in both pharmaceutical
and every day calculations
Demonstrate an alternative perspective
for looking at and utilizing percentages
Solve calculations using both successive
proportions and a continuous linear
method
Send your pic to
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 3
TOPICS
Ratios
Proportions
Conversions (Metric & Avoirdupois)
Percentages
Linear calculations
RATIOS
Ratios are a way of expressing the relationship
between two quantities.
They can be written with a colon, as a fraction, or
in the case of an IV or injectable using “per”.
6:12 Stated as “6 out of 12”
6/12 Stated as “six twelfths”
6ml/12 hours Stated as “6 mls per 12 hours”
RATIO AS A MEASURE OF BEAUTY
1:1.6 PROPORTIONS
A proportion is the expression of equality of two
ratios or fractions to each other
For example
1 4
__ = __
5 20
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 4
PROPORTIONS
Your friend’s dog is prescribed 10 mgs of
Prednisone daily for three days, 5 mgs daily for
three days, 2.5 mgs daily for three days, then
stop.
The veterinarian only has a 10 count box of 20mg
tablets in stock. How much of a tablet will the
dog be given for each of the
three different doses?
__ tab qd x 3 days;
__ tab qd x 3 days;
__ tab qd x 3 days
PROPORTIONS
20mg 10mg 20x = 10
____ = ____ = x = .5 tab
1 tab x tab
20mg 5mg 20x = 5
____ = ____ = x = .25 tab
1 tab x tab
PROPORTIONS
20mg 2.5mg 20x = 2.5
____ = _____ x = .125 tab !!!!
1 tab x tab
Challenge question
for audience: how
would you divide that
small tablet into eight even
quantities? Hint, think
cocaine.
POLL QUESTION # 1
Click what you think is the right answer and hit
the “submit” button.
Your hourly salary is $20.00. Because you took this
CE class, you are being give a 25% raise. What is
your new hourly wage?
a. $20.25
b. $50
c. $25
d. Not enough
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 5
SYSTEMS OF MEASUREMENT
Apothecaries’ system
Seldom used
Avoirdupois system
Used only for measuring weight
Typically used in US households
Metric system
Used throughout the world for pharmaceutical and
medical calculations
Adopted and mandated in the United States
APOTHECARIES’ FLUID MEASURES
Most commonly used of THIS system:
16 fluid ounces = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
AVOIRDUPOIS WEIGHTS
1 ounce (oz) = 437.5 grains = 28.4 g
16 ounces = 1 pound (lb)
METRIC SYSTEM
1 g = 15.4 grains (gr)
1 gr = 65 mg
1 lb = 454 g
1 kg = 2.2 lb
1 oz = 28.4 g
1 fluid ounce = 30 ml
1 pt = 16 ounces = 480 ml
1 gallon = 3840 ml
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 6
HOUSEHOLD EQUIVALENTS
1 teaspoonful (tsp) = 5 ml
1 tablespoonful (tbsp) = 15 ml
1 ounce = 30 ml
1 cup = 8 ounces
1 pt = 480 ml
THE WEDDING COOKIE CHALLENGE!
ITALIAN WEDDING COOKIE RECIPE
Ingredients
340 g unsalted butter
90 g confectioners' sugar
5 g salt
215 g finely ground almonds
20 ml vanilla extract
375 g sifted all-purpose flour
40 g confectioners' sugar for rolling
CONVERSION PROBLEMS
340 gm of unsalted butter equals how
many cups?
90 gm of confectioners sugar equals
how many cups?
Hint: There are 8 ounces in a cup!
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 7
COOKIE RECIPE CONVERSIONS
340 gm 28.4gm 28.4x = 340
_____ = ______ x = 11.97 ozs
x 1 ounce
12 oz 8 oz 8x = 12
____ = ____ x = 1.5 cups
x 1 cup
COOKIE RECIPE CONVERSIONS
90 gm 28.4gm 28.4x = 90
_____ = ______ x = 3.17 ozs
x 1 ounce
3 oz 8 oz 8x = 3
____ = ____ x = 3/8 cup
x 1 cup
COOKIE RECIPE CONVERSIONS
20 ml 5 ml
_____ = ______
x 1 tsp
5x = 20
x = 4 tsps vanilla extract
ITALIAN WEDDING COOKIE
DIRECTIONS
Preheat oven to 165 degrees C.
Cream butter or margarine in a bowl, gradually add
confectioners' sugar and salt. Beat until light and fluffy.
Add almonds and vanilla. Blend in flour gradually and
mix well.
Shape into balls (or crescents) using about 1 teaspoon for
each cookie. Place on ungreased cookie sheets, and bake
for 15-20 min. Do not brown. Cool slightly, then roll in
the extra confectioners' sugar.
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 8
TEMPERATURE CONVERSION
FORMULAS
(°C x 9/5) + 32 = °F
(°F - 32) x 5/9 = °C
(°C x 1.8) + 32 = °F
(°F - 32) = °C
1.8
TEMPERATURE CONVERSION
Problem: Convert 165 degrees Centigrade to Fahrenheit.
F = (1.8 x C) + 32
F = (1.8 x 165) + 32
F = 297 + 32
F = 329 degrees
PERCENTAGES
Gross margin
Interchangeable with gross profit
Selling price minus purchase price
Markup
Selling price less the cost
Interchangeable with gross margin and gross profit
Markdown
A reduction in the selling price
PERCENTAGES
Basic Concepts
In dealing with discounts, the percentage off and the percentage you pay always add up to 100%
Percentages directly equate to fractions
You can usually choose to use either a fraction or a percentage
%
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 9
PERCENTAGES
In dealing with discounts, both
percentages always add up to 100%
For example:
If a sweater is 25% off, that means
you’re paying 75% of the full price
100% - 25% = 75%
PERCENTAGES
You go into Mr. Big Box store, and that “famous”
name brand 50” LED HDTV with 1080p
resolution, Dolby digital surround sound, and 3D
capabilities was selling for $3,199.
It’s only three days until the Super Bowl and
they finally got around to having a 25% off sale.
PERCENTAGES
Solving our problem:
Round $3199 up to $3200
Subtract 25% from 100%
(100 – 25 = 75)
Multiply 75% times $3200
(0.75 x $3,200 = $2,400)
PERCENTAGES/FRACTIONS
1/8 = 12.5% 2/8 = 1/4 = 25%
3/8 = 37.5% 4/8 = 1/2 = 50%
5/8 = 62.5% 6/8 = 3/4 = 75%
7/8 = 87.5%
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 10
PERCENTAGES/FRACTIONS
Thirds
1/3 = 33.3% 2/3 = 66.6%
Quarters
1/4 = 25% 2/4 = 1/2 = 50%
3/4 = 75%
PERCENTAGES/FRACTIONS
Just a refresher!
You go into Mr. Big Box store, and that “famous”
name brand 50” LED HDTV with 1080p
resolution, Dolby digital surround sound, and 3D
capabilities that you’ve been eyeing is $3199.
It’s three days before the Super Bowl and they
finally got around to having a 25% off sale.
PERCENTAGES/FRACTIONS
Round $3199 to $3200.
From basic elementary school math, we know
that 1/4 of 32 is 8. 1/4 of $3,200 is $800.
Your discount on your beloved TV is $800 off
leaving you a
price of $2,400.
TWO “TRICKS” TO ALWAYS UNDERSTAND
CONVERSION OF FRACTIONS TO DECIMALS
1. A calculator
2. Use the example of a fraction/decimal that you
know.
1/2 = 50% But why?
.50 move decimal 2 places right
2 1.00 50%
50% = 50/100 = 1/2
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 11
POLL QUESTION # 2
Click what you think is the right answer and hit
the “submit” button.
Help us with future presentations on this
topic. Do you feel the math level in this
presentation so far has been:
a. Too easy
b. Too difficult
c. About right
LINEAR APPROACH TO MULTI-STEP
CALCULATIONS
Many pharmaceutical calculations
require more than one step
It’s easy to get lost in the problem and
not know where you are or even the
next step
It’s easy to lose sight of the required
units of measurement for the final
answer
LINEAR CALCULATIONS
Problem:
An IV antibiotic is prescribed for a child
who weighs 18 lbs. The dose is 15mg/kg
twice daily. What amount of drug should
be given per dose?
LINEAR CALCULATIONS
18 lbs 2.2 lbs 2.2x = 18
_____ = ______ x = 8.18 kg
x kg 1 kg
↓ 15mg x x = 15 x 8.18
_____ = ______ x = 122.7 mg
1 kg 8.18 kg
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 12
LINEAR CALCULATIONS
An IV antibiotic is prescribed for a
child who weighs 18 lbs. The dose is
15mg/kg twice daily. What amount of
drug should be given per dose?
122.7 mg
LINEAR CALCULATIONS
Notice the units of measure are crossed out.
LINEAR CALCULATIONS
Problem:
You receive a prescription for Metronidazole
250mg/5ml qid 240ml.
You don’t have it in stock so you will need to
compound it using 500mg tablets.
How many tablets do
you need to use to fill
the entire order?
LINEAR CALCULATIONS
.
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 13
QUESTIONS ? COMMENTS?
KEVIN MCCARTHY, RPh
PHARMACEUTICAL CALCULATIONS FOR
TECHNICIANS
Every Day Applications
_____
Kevin McCarthy, RPh
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.
This program has been
brought to you by
PharmCon
PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS:
EVERYDAY APPLICATIONS
Accreditation:
Pharmacy Technicians: 0798-0000-11-091-L04-T
CE Credits: 1.0 contact hour
Target Audience: Pharmacy Technicians
Program Overview: This program will briefly take technicians through some common pharmaceutical
weight, volume, and temperature conversions. Then, these conversions will be done for a recipe utilizing
ratios and proportions to show the relevance of pharmaceutical math to daily life. We’ll also review the
relationship between percentages and fractions to demonstrate common non-pharmaceutical applications
for this concept. This presentation is for technicians only, be ready to learn…and laugh!
Objectives:
• Explain ratios and proportions and show their applications in both pharmacy and everyday calculations
• Demonstrate an alternative perspective of looking at and utilizing percentages
• Solve calculations using both successive proportions and a continuous linear method
This program has been brought to you
by PharmCon
PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS:
EVERYDAY APPLICATIONS
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.
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
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 14
PHARMACY AND NASCAR ???
PROGRAM OBJECTIVES
Explain ratios and proportions and show
their applications in both pharmaceutical
and every day calculations
Demonstrate an alternative perspective
for looking at and utilizing percentages
Solve calculations using both successive
proportions and a continuous linear
method
Send your pic to
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 15
TOPICS
Ratios
Proportions
Conversions (Metric & Avoirdupois)
Percentages
Linear calculations
RATIOS
Ratios are a way of expressing the relationship
between two quantities.
They can be written with a colon, as a fraction, or
in the case of an IV or injectable using “per”.
6:12 Stated as “6 out of 12”
6/12 Stated as “six twelfths”
6ml/12 hours Stated as “6 mls per 12 hours”
RATIO AS A MEASURE OF BEAUTY
1:1.6 PROPORTIONS
A proportion is the expression of equality of two
ratios or fractions to each other
For example
1 4
__ = __
5 20
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 16
PROPORTIONS
Your friend’s dog is prescribed 10 mgs of
Prednisone daily for three days, 5 mgs daily for
three days, 2.5 mgs daily for three days, then
stop.
The veterinarian only has a 10 count box of 20mg
tablets in stock. How much of a tablet will the
dog be given for each of the
three different doses?
__ tab qd x 3 days;
__ tab qd x 3 days;
__ tab qd x 3 days
PROPORTIONS
20mg 10mg 20x = 10
____ = ____ = x = .5 tab
1 tab x tab
20mg 5mg 20x = 5
____ = ____ = x = .25 tab
1 tab x tab
PROPORTIONS
20mg 2.5mg 20x = 2.5
____ = _____ x = .125 tab !!!!
1 tab x tab
Challenge question
for audience: how
would you divide that
small tablet into eight even
quantities? Hint, think
cocaine.
POLL QUESTION # 1
Click what you think is the right answer and hit
the “submit” button.
Your hourly salary is $20.00. Because you took this
CE class, you are being give a 25% raise. What is
your new hourly wage?
a. $20.25
b. $50
c. $25
d. Not enough
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 17
SYSTEMS OF MEASUREMENT
Apothecaries’ system
Seldom used
Avoirdupois system
Used only for measuring weight
Typically used in US households
Metric system
Used throughout the world for pharmaceutical and
medical calculations
Adopted and mandated in the United States
APOTHECARIES’ FLUID MEASURES
Most commonly used of THIS system:
16 fluid ounces = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
AVOIRDUPOIS WEIGHTS
1 ounce (oz) = 437.5 grains = 28.4 g
16 ounces = 1 pound (lb)
METRIC SYSTEM
1 g = 15.4 grains (gr)
1 gr = 65 mg
1 lb = 454 g
1 kg = 2.2 lb
1 oz = 28.4 g
1 fluid ounce = 30 ml
1 pt = 16 ounces = 480 ml
1 gallon = 3840 ml
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 18
HOUSEHOLD EQUIVALENTS
1 teaspoonful (tsp) = 5 ml
1 tablespoonful (tbsp) = 15 ml
1 ounce = 30 ml
1 cup = 8 ounces
1 pt = 480 ml
THE WEDDING COOKIE CHALLENGE!
ITALIAN WEDDING COOKIE RECIPE
Ingredients
340 g unsalted butter
90 g confectioners' sugar
5 g salt
215 g finely ground almonds
20 ml vanilla extract
375 g sifted all-purpose flour
40 g confectioners' sugar for rolling
CONVERSION PROBLEMS
340 gm of unsalted butter equals how
many cups?
90 gm of confectioners sugar equals
how many cups?
Hint: There are 8 ounces in a cup!
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 19
COOKIE RECIPE CONVERSIONS
340 gm 28.4gm 28.4x = 340
_____ = ______ x = 11.97 ozs
x 1 ounce
12 oz 8 oz 8x = 12
____ = ____ x = 1.5 cups
x 1 cup
COOKIE RECIPE CONVERSIONS
90 gm 28.4gm 28.4x = 90
_____ = ______ x = 3.17 ozs
x 1 ounce
3 oz 8 oz 8x = 3
____ = ____ x = 3/8 cup
x 1 cup
COOKIE RECIPE CONVERSIONS
20 ml 5 ml
_____ = ______
x 1 tsp
5x = 20
x = 4 tsps vanilla extract
ITALIAN WEDDING COOKIE
DIRECTIONS
Preheat oven to 165 degrees C.
Cream butter or margarine in a bowl, gradually add
confectioners' sugar and salt. Beat until light and fluffy.
Add almonds and vanilla. Blend in flour gradually and
mix well.
Shape into balls (or crescents) using about 1 teaspoon for
each cookie. Place on ungreased cookie sheets, and bake
for 15-20 min. Do not brown. Cool slightly, then roll in
the extra confectioners' sugar.
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 20
TEMPERATURE CONVERSION
FORMULAS
(°C x 9/5) + 32 = °F
(°F - 32) x 5/9 = °C
(°C x 1.8) + 32 = °F
(°F - 32) = °C
1.8
TEMPERATURE CONVERSION
Problem: Convert 165 degrees Centigrade to Fahrenheit.
F = (1.8 x C) + 32
F = (1.8 x 165) + 32
F = 297 + 32
F = 329 degrees
PERCENTAGES
Gross margin
Interchangeable with gross profit
Selling price minus purchase price
Markup
Selling price less the cost
Interchangeable with gross margin and gross profit
Markdown
A reduction in the selling price
PERCENTAGES
Basic Concepts
In dealing with discounts, the percentage off and the percentage you pay always add up to 100%
Percentages directly equate to fractions
You can usually choose to use either a fraction or a percentage
%
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 21
PERCENTAGES
In dealing with discounts, both
percentages always add up to 100%
For example:
If a sweater is 25% off, that means
you’re paying 75% of the full price
100% - 25% = 75%
PERCENTAGES
You go into Mr. Big Box store, and that “famous”
name brand 50” LED HDTV with 1080p
resolution, Dolby digital surround sound, and 3D
capabilities was selling for $3,199.
It’s only three days until the Super Bowl and
they finally got around to having a 25% off sale.
PERCENTAGES
Solving our problem:
Round $3199 up to $3200
Subtract 25% from 100%
(100 – 25 = 75)
Multiply 75% times $3200
(0.75 x $3,200 = $2,400)
PERCENTAGES/FRACTIONS
1/8 = 12.5% 2/8 = 1/4 = 25%
3/8 = 37.5% 4/8 = 1/2 = 50%
5/8 = 62.5% 6/8 = 3/4 = 75%
7/8 = 87.5%
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 22
PERCENTAGES/FRACTIONS
Thirds
1/3 = 33.3% 2/3 = 66.6%
Quarters
1/4 = 25% 2/4 = 1/2 = 50%
3/4 = 75%
PERCENTAGES/FRACTIONS
Just a refresher!
You go into Mr. Big Box store, and that “famous”
name brand 50” LED HDTV with 1080p
resolution, Dolby digital surround sound, and 3D
capabilities that you’ve been eyeing is $3199.
It’s three days before the Super Bowl and they
finally got around to having a 25% off sale.
PERCENTAGES/FRACTIONS
Round $3199 to $3200.
From basic elementary school math, we know
that 1/4 of 32 is 8. 1/4 of $3,200 is $800.
Your discount on your beloved TV is $800 off
leaving you a
price of $2,400.
TWO “TRICKS” TO ALWAYS UNDERSTAND
CONVERSION OF FRACTIONS TO DECIMALS
1. A calculator
2. Use the example of a fraction/decimal that you
know.
1/2 = 50% But why?
.50 move decimal 2 places right
2 1.00 50%
50% = 50/100 = 1/2
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 23
POLL QUESTION # 2
Click what you think is the right answer and hit
the “submit” button.
Help us with future presentations on this
topic. Do you feel the math level in this
presentation so far has been:
a. Too easy
b. Too difficult
c. About right
LINEAR APPROACH TO MULTI-STEP
CALCULATIONS
Many pharmaceutical calculations
require more than one step
It’s easy to get lost in the problem and
not know where you are or even the
next step
It’s easy to lose sight of the required
units of measurement for the final
answer
LINEAR CALCULATIONS
Problem:
An IV antibiotic is prescribed for a child
who weighs 18 lbs. The dose is 15mg/kg
twice daily. What amount of drug should
be given per dose?
LINEAR CALCULATIONS
18 lbs 2.2 lbs 2.2x = 18
_____ = ______ x = 8.18 kg
x kg 1 kg
↓ 15mg x x = 15 x 8.18
_____ = ______ x = 122.7 mg
1 kg 8.18 kg
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 24
LINEAR CALCULATIONS
An IV antibiotic is prescribed for a
child who weighs 18 lbs. The dose is
15mg/kg twice daily. What amount of
drug should be given per dose?
122.7 mg
LINEAR CALCULATIONS
Notice the units of measure are crossed out.
LINEAR CALCULATIONS
Problem:
You receive a prescription for Metronidazole
250mg/5ml qid 240ml.
You don’t have it in stock so you will need to
compound it using 500mg tablets.
How many tablets do
you need to use to fill
the entire order?
LINEAR CALCULATIONS
.
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 25
QUESTIONS ? COMMENTS?
KEVIN MCCARTHY, RPh
PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS:
EVERYDAY APPLICATIONS
Accreditation:
Pharmacy Technicians: 0798-0000-11-091-L04-T
CE Credits: 1.0 contact hour
Target Audience: Pharmacy Technicians
Program Overview: This program will briefly take technicians through some common pharmaceutical
weight, volume, and temperature conversions. Then, these conversions will be done for a recipe utilizing
ratios and proportions to show the relevance of pharmaceutical math to daily life. We’ll also review the
relationship between percentages and fractions to demonstrate common non-pharmaceutical applications
for this concept. This presentation is for technicians only, be ready to learn…and laugh!
Objectives:
• Explain ratios and proportions and show their applications in both pharmacy and everyday calculations
• Demonstrate an alternative perspective of looking at and utilizing percentages
• Solve calculations using both successive proportions and a continuous linear method
This program has been brought to you
by PharmCon
PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS:
EVERYDAY APPLICATIONS
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.
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
PHARMACY AND NASCAR ???
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 26
PROGRAM OBJECTIVES
Explain ratios and proportions and show
their applications in both pharmaceutical
and every day calculations
Demonstrate an alternative perspective
for looking at and utilizing percentages
Solve calculations using both successive
proportions and a continuous linear
method
Send your pic to
TOPICS
Ratios
Proportions
Conversions (Metric & Avoirdupois)
Percentages
Linear calculations
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 27
RATIOS
Ratios are a way of expressing the relationship
between two quantities.
They can be written with a colon, as a fraction, or
in the case of an IV or injectable using “per”.
6:12 Stated as “6 out of 12”
6/12 Stated as “six twelfths”
6ml/12 hours Stated as “6 mls per 12 hours”
RATIO AS A MEASURE OF BEAUTY
1:1.6
PROPORTIONS
A proportion is the expression of equality of two
ratios or fractions to each other
For example
1 4
__ = __
5 20
PROPORTIONS
Your friend’s dog is prescribed 10 mgs of
Prednisone daily for three days, 5 mgs daily for
three days, 2.5 mgs daily for three days, then
stop.
The veterinarian only has a 10 count box of 20mg
tablets in stock. How much of a tablet will the
dog be given for each of the
three different doses?
__ tab qd x 3 days;
__ tab qd x 3 days;
__ tab qd x 3 days
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 28
PROPORTIONS
20mg 10mg 20x = 10
____ = ____ = x = .5 tab
1 tab x tab
20mg 5mg 20x = 5
____ = ____ = x = .25 tab
1 tab x tab
PROPORTIONS
20mg 2.5mg 20x = 2.5
____ = _____ x = .125 tab !!!!
1 tab x tab
Challenge question
for audience: how
would you divide that
small tablet into eight even
quantities? Hint, think
cocaine.
POLL QUESTION # 1
Click what you think is the right answer and hit
the “submit” button.
Your hourly salary is $20.00. Because you took this
CE class, you are being give a 25% raise. What is
your new hourly wage?
a. $20.25
b. $50
c. $25
d. Not enough
SYSTEMS OF MEASUREMENT
Apothecaries’ system
Seldom used
Avoirdupois system
Used only for measuring weight
Typically used in US households
Metric system
Used throughout the world for pharmaceutical and
medical calculations
Adopted and mandated in the United States
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 29
APOTHECARIES’ FLUID MEASURES
Most commonly used of THIS system:
16 fluid ounces = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon (gal)
AVOIRDUPOIS WEIGHTS
1 ounce (oz) = 437.5 grains = 28.4 g
16 ounces = 1 pound (lb)
METRIC SYSTEM
1 g = 15.4 grains (gr)
1 gr = 65 mg
1 lb = 454 g
1 kg = 2.2 lb
1 oz = 28.4 g
1 fluid ounce = 30 ml
1 pt = 16 ounces = 480 ml
1 gallon = 3840 ml
HOUSEHOLD EQUIVALENTS
1 teaspoonful (tsp) = 5 ml
1 tablespoonful (tbsp) = 15 ml
1 ounce = 30 ml
1 cup = 8 ounces
1 pt = 480 ml
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 30
THE WEDDING COOKIE CHALLENGE!
ITALIAN WEDDING COOKIE RECIPE
Ingredients
340 g unsalted butter
90 g confectioners' sugar
5 g salt
215 g finely ground almonds
20 ml vanilla extract
375 g sifted all-purpose flour
40 g confectioners' sugar for rolling
CONVERSION PROBLEMS
340 gm of unsalted butter equals how
many cups?
90 gm of confectioners sugar equals
how many cups?
Hint: There are 8 ounces in a cup!
COOKIE RECIPE CONVERSIONS
340 gm 28.4gm 28.4x = 340
_____ = ______ x = 11.97 ozs
x 1 ounce
12 oz 8 oz 8x = 12
____ = ____ x = 1.5 cups
x 1 cup
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 31
COOKIE RECIPE CONVERSIONS
90 gm 28.4gm 28.4x = 90
_____ = ______ x = 3.17 ozs
x 1 ounce
3 oz 8 oz 8x = 3
____ = ____ x = 3/8 cup
x 1 cup
COOKIE RECIPE CONVERSIONS
20 ml 5 ml
_____ = ______
x 1 tsp
5x = 20
x = 4 tsps vanilla extract
ITALIAN WEDDING COOKIE
DIRECTIONS
Preheat oven to 165 degrees C.
Cream butter or margarine in a bowl, gradually add
confectioners' sugar and salt. Beat until light and fluffy.
Add almonds and vanilla. Blend in flour gradually and
mix well.
Shape into balls (or crescents) using about 1 teaspoon for
each cookie. Place on ungreased cookie sheets, and bake
for 15-20 min. Do not brown. Cool slightly, then roll in
the extra confectioners' sugar.
TEMPERATURE CONVERSION
FORMULAS
(°C x 9/5) + 32 = °F
(°F - 32) x 5/9 = °C
(°C x 1.8) + 32 = °F
(°F - 32) = °C
1.8
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 32
TEMPERATURE CONVERSION
Problem: Convert 165 degrees Centigrade to Fahrenheit.
F = (1.8 x C) + 32
F = (1.8 x 165) + 32
F = 297 + 32
F = 329 degrees
PERCENTAGES
Gross margin
Interchangeable with gross profit
Selling price minus purchase price
Markup
Selling price less the cost
Interchangeable with gross margin and gross profit
Markdown
A reduction in the selling price
PERCENTAGES
Basic Concepts
In dealing with discounts, the percentage off and the percentage you pay always add up to 100%
Percentages directly equate to fractions
You can usually choose to use either a fraction or a percentage
%
PERCENTAGES
In dealing with discounts, both
percentages always add up to 100%
For example:
If a sweater is 25% off, that means
you’re paying 75% of the full price
100% - 25% = 75%
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 33
PERCENTAGES
You go into Mr. Big Box store, and that “famous”
name brand 50” LED HDTV with 1080p
resolution, Dolby digital surround sound, and 3D
capabilities was selling for $3,199.
It’s only three days until the Super Bowl and
they finally got around to having a 25% off sale.
PERCENTAGES
Solving our problem:
Round $3199 up to $3200
Subtract 25% from 100%
(100 – 25 = 75)
Multiply 75% times $3200
(0.75 x $3,200 = $2,400)
PERCENTAGES/FRACTIONS
1/8 = 12.5% 2/8 = 1/4 = 25%
3/8 = 37.5% 4/8 = 1/2 = 50%
5/8 = 62.5% 6/8 = 3/4 = 75%
7/8 = 87.5%
PERCENTAGES/FRACTIONS
Thirds
1/3 = 33.3% 2/3 = 66.6%
Quarters
1/4 = 25% 2/4 = 1/2 = 50%
3/4 = 75%
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 34
PERCENTAGES/FRACTIONS
Just a refresher!
You go into Mr. Big Box store, and that “famous”
name brand 50” LED HDTV with 1080p
resolution, Dolby digital surround sound, and 3D
capabilities that you’ve been eyeing is $3199.
It’s three days before the Super Bowl and they
finally got around to having a 25% off sale.
PERCENTAGES/FRACTIONS
Round $3199 to $3200.
From basic elementary school math, we know
that 1/4 of 32 is 8. 1/4 of $3,200 is $800.
Your discount on your beloved TV is $800 off
leaving you a
price of $2,400.
TWO “TRICKS” TO ALWAYS UNDERSTAND
CONVERSION OF FRACTIONS TO DECIMALS
1. A calculator
2. Use the example of a fraction/decimal that you
know.
1/2 = 50% But why?
.50 move decimal 2 places right
2 1.00 50%
50% = 50/100 = 1/2
POLL QUESTION # 2
Click what you think is the right answer and hit
the “submit” button.
Help us with future presentations on this
topic. Do you feel the math level in this
presentation so far has been:
a. Too easy
b. Too difficult
c. About right
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 35
LINEAR APPROACH TO MULTI-STEP
CALCULATIONS
Many pharmaceutical calculations
require more than one step
It’s easy to get lost in the problem and
not know where you are or even the
next step
It’s easy to lose sight of the required
units of measurement for the final
answer
LINEAR CALCULATIONS
Problem:
An IV antibiotic is prescribed for a child
who weighs 18 lbs. The dose is 15mg/kg
twice daily. What amount of drug should
be given per dose?
LINEAR CALCULATIONS
18 lbs 2.2 lbs 2.2x = 18
_____ = ______ x = 8.18 kg
x kg 1 kg
↓ 15mg x x = 15 x 8.18
_____ = ______ x = 122.7 mg
1 kg 8.18 kg
LINEAR CALCULATIONS
An IV antibiotic is prescribed for a
child who weighs 18 lbs. The dose is
15mg/kg twice daily. What amount of
drug should be given per dose?
122.7 mg
Pharmaceutical Calculations for Technicians – Everyday Applications
© 2010 Pharmaceutical Education Consultants, Inc. unless otherwise noted. All rights reserved.
Reproduction in whole or in part without permission is prohibited.
Page 36
LINEAR CALCULATIONS
Notice the units of measure are crossed out.
LINEAR CALCULATIONS
Problem:
You receive a prescription for Metronidazole
250mg/5ml qid 240ml.
You don’t have it in stock so you will need to
compound it using 500mg tablets.
How many tablets do
you need to use to fill
the entire order?
LINEAR CALCULATIONS
.
QUESTIONS ? COMMENTS?
KEVIN MCCARTHY, RPh