pharmaceutical calculations for technicians everyday applications

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.

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


TECHNICIANS


_____

Kevin McCarthy, RPh


education





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



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




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 ???

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

[email protected]




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




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




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




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!




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


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


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


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%

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%





Thirds

1/3 = 33.3% 2/3 = 66.6%

Quarters

1/4 = 25% 2/4 = 1/2 = 50%

3/4 = 75%


Just a refresher!




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.


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



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




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

.




QUESTIONS ? COMMENTS?

KEVIN MCCARTHY, RPh

[email protected]


TECHNICIANS


_____

Kevin McCarthy, RPh


education





brought to you by

PharmCon



Accreditation:









Objectives:





by PharmCon




to you by PharmCon















mailto:[email protected]





PROGRAM OBJECTIVES








method

Send your pic to

[email protected]




TOPICS

Ratios

Proportions


Percentages

Linear calculations

RATIOS









1:1.6 PROPORTIONS



For example

1 4

__ = __

5 20




PROPORTIONS




stop.





__ 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




cocaine.

POLL QUESTION # 1






a. $20.25

b. $50

c. $25

d. Not enough






Seldom used

Avoirdupois system



Metric system









AVOIRDUPOIS WEIGHTS

1 ounce (oz) = 437.5 grains = 28.4 g


METRIC SYSTEM


1 gr = 65 mg

1 lb = 454 g

1 kg = 2.2 lb

1 oz = 28.4 g



1 gallon = 3840 ml







1 ounce = 30 ml

1 cup = 8 ounces

1 pt = 480 ml



Ingredients



5 g salt





CONVERSION PROBLEMS


many cups?


how many cups?






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


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


20 ml 5 ml

_____ = ______

x 1 tsp

5x = 20



DIRECTIONS





mix well.









FORMULAS

(°C x 9/5) + 32 = °F

(°F - 32) x 5/9 = °C

(°C x 1.8) + 32 = °F

(°F - 32) = °C

1.8



F = (1.8 x C) + 32

F = (1.8 x 165) + 32

F = 297 + 32

F = 329 degrees

PERCENTAGES

Gross margin



Markup



Markdown


PERCENTAGES

Basic Concepts




%




PERCENTAGES



For example:



100% - 25% = 75%

PERCENTAGES







PERCENTAGES


Round $3199 up to $3200


(100 – 25 = 75)


(0.75 x $3,200 = $2,400)


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%





Thirds

1/3 = 33.3% 2/3 = 66.6%

Quarters

1/4 = 25% 2/4 = 1/2 = 50%

3/4 = 75%


Just a refresher!








Round $3199 to $3200.


that 1/4 of 32 is 8. 1/4 of $3,200 is $800.


leaving you a

price of $2,400.



1. A calculator


know.

1/2 = 50% But why?


2 1.00 50%

50% = 50/100 = 1/2




POLL QUESTION # 2






a. Too easy

b. Too difficult

c. About right


CALCULATIONS





next step



answer

LINEAR CALCULATIONS

Problem:




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





122.7 mg

LINEAR CALCULATIONS


LINEAR CALCULATIONS

Problem:





How many tablets do


the entire order?

LINEAR CALCULATIONS

.





KEVIN MCCARTHY, RPh

[email protected]



Accreditation:









Objectives:





by PharmCon




to you by PharmCon




















PROGRAM OBJECTIVES








method

Send your pic to

[email protected]

TOPICS

Ratios

Proportions


Percentages

Linear calculations




RATIOS









1:1.6

PROPORTIONS



For example

1 4

__ = __

5 20

PROPORTIONS




stop.





__ 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




cocaine.

POLL QUESTION # 1






a. $20.25

b. $50

c. $25

d. Not enough



Seldom used

Avoirdupois system



Metric system












AVOIRDUPOIS WEIGHTS

1 ounce (oz) = 437.5 grains = 28.4 g


METRIC SYSTEM


1 gr = 65 mg

1 lb = 454 g

1 kg = 2.2 lb

1 oz = 28.4 g



1 gallon = 3840 ml




1 ounce = 30 ml

1 cup = 8 ounces

1 pt = 480 ml






Ingredients



5 g salt





CONVERSION PROBLEMS


many cups?


how many cups?



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





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


20 ml 5 ml

_____ = ______

x 1 tsp

5x = 20



DIRECTIONS





mix well.






FORMULAS

(°C x 9/5) + 32 = °F

(°F - 32) x 5/9 = °C

(°C x 1.8) + 32 = °F

(°F - 32) = °C

1.8






F = (1.8 x C) + 32

F = (1.8 x 165) + 32

F = 297 + 32

F = 329 degrees

PERCENTAGES

Gross margin



Markup



Markdown


PERCENTAGES

Basic Concepts




%

PERCENTAGES



For example:



100% - 25% = 75%




PERCENTAGES







PERCENTAGES


Round $3199 up to $3200


(100 – 25 = 75)


(0.75 x $3,200 = $2,400)


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%


Thirds

1/3 = 33.3% 2/3 = 66.6%

Quarters

1/4 = 25% 2/4 = 1/2 = 50%

3/4 = 75%





Just a refresher!








Round $3199 to $3200.


that 1/4 of 32 is 8. 1/4 of $3,200 is $800.


leaving you a

price of $2,400.



1. A calculator


know.

1/2 = 50% But why?


2 1.00 50%

50% = 50/100 = 1/2

POLL QUESTION # 2






a. Too easy

b. Too difficult

c. About right





CALCULATIONS





next step



answer

LINEAR CALCULATIONS

Problem:




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





122.7 mg




LINEAR CALCULATIONS


LINEAR CALCULATIONS

Problem:





How many tablets do


the entire order?

LINEAR CALCULATIONS

.


KEVIN MCCARTHY, RPh

[email protected]


pharmaceutical calculations for technicians everyday applications

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