Pharmaceutical Calculations for Technicians Everyday Applications

Transcription

1 Page 1 PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS Every Day Applications Kevin McCarthy, RPh 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. PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS Every Day Applications Kevin McCarthy, RPh 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. PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS: EVERYDAY APPLICATIONS PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS: EVERYDAY APPLICATIONS Accreditation: Pharmacy Technicians: 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 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 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.

2 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 kevin@freece.com

3 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

4 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 $ 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

5 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 METRIC SYSTEM 1 ounce (oz) = grains = 28.4 g 16 ounces = 1 pound (lb) 1 g = 15.4 grains (gr) 1 gr = 65 mg 1 lb = 454 g 1 fluid ounce = 30 ml 1 pt = 16 ounces = 480 ml 1 gallon = 3840 ml 1 kg = 2.2 lb 1 oz = 28.4 g

6 Page 6 HOUSEHOLD EQUIVALENTS THE WEDDING COOKIE CHALLENGE! 1 teaspoonful (tsp) = 5 ml 1 tablespoonful (tbsp) = 15 ml 1 ounce = 30 ml 1 cup = 8 ounces 1 pt = 480 ml 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!

7 Page 7 COOKIE RECIPE CONVERSIONS COOKIE RECIPE CONVERSIONS 340 gm 28.4gm 28.4x = 340 = x = ozs x 1 ounce 90 gm 28.4gm 28.4x = 90 = x = 3.17 ozs x 1 ounce 12 oz 8 oz 8x = 12 = x = 1.5 cups x 1 cup 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 min. Do not brown. Cool slightly, then roll in the extra confectioners' sugar.

8 Page 8 TEMPERATURE CONVERSION ( C x 9/5) + 32 = F ( F - 32) x 5/9 = C ( C x 1.8) + 32 = F ( F - 32) = C 1.8 FORMULAS TEMPERATURE CONVERSION Problem: Convert 165 degrees Centigrade to Fahrenheit. F = (1.8 x C) + 32 F = (1.8 x 165) + 32 F = 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 %

9 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 PERCENTAGES/FRACTIONS Solving our problem: Round $3199 up to $3200 Subtract 25% from 100% ( = 75) 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% Multiply 75% times $3200 (0.75 x $3,200 = $2,400)

10 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. TWO TRICKS TO ALWAYS UNDERSTAND CONVERSION OF FRACTIONS TO DECIMALS 1. A calculator 2. Use the example of a fraction/decimal that you know. Your discount on your beloved TV is $800 off leaving you a price of $2,400. 1/2 = 50% But why?.50 move decimal 2 places right % 50% = 50/100 = 1/2

11 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 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? 18 lbs 2.2 lbs 2.2x = 18 = x = 8.18 kg x kg 1 kg 15mg x x = 15 x 8.18 = x = mg 1 kg 8.18 kg

12 Page 12 LINEAR CALCULATIONS 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? Notice the units of measure are crossed out mg LINEAR CALCULATIONS Problem: LINEAR CALCULATIONS. 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?

13 Page 13 QUESTIONS? COMMENTS? KEVIN MCCARTHY, RPh PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS Every Day Applications Kevin McCarthy, RPh 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. PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS: EVERYDAY APPLICATIONS PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS: EVERYDAY APPLICATIONS Accreditation: Pharmacy Technicians: 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 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 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.

14 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 kevin@freece.com

15 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

16 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 $ 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

17 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 METRIC SYSTEM 1 ounce (oz) = grains = 28.4 g 16 ounces = 1 pound (lb) 1 g = 15.4 grains (gr) 1 gr = 65 mg 1 lb = 454 g 1 fluid ounce = 30 ml 1 pt = 16 ounces = 480 ml 1 gallon = 3840 ml 1 kg = 2.2 lb 1 oz = 28.4 g

18 Page 18 HOUSEHOLD EQUIVALENTS THE WEDDING COOKIE CHALLENGE! 1 teaspoonful (tsp) = 5 ml 1 tablespoonful (tbsp) = 15 ml 1 ounce = 30 ml 1 cup = 8 ounces 1 pt = 480 ml 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!

19 Page 19 COOKIE RECIPE CONVERSIONS COOKIE RECIPE CONVERSIONS 340 gm 28.4gm 28.4x = 340 = x = ozs x 1 ounce 90 gm 28.4gm 28.4x = 90 = x = 3.17 ozs x 1 ounce 12 oz 8 oz 8x = 12 = x = 1.5 cups x 1 cup 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 min. Do not brown. Cool slightly, then roll in the extra confectioners' sugar.

20 Page 20 TEMPERATURE CONVERSION ( C x 9/5) + 32 = F ( F - 32) x 5/9 = C ( C x 1.8) + 32 = F ( F - 32) = C 1.8 FORMULAS TEMPERATURE CONVERSION Problem: Convert 165 degrees Centigrade to Fahrenheit. F = (1.8 x C) + 32 F = (1.8 x 165) + 32 F = 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 %

21 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 PERCENTAGES/FRACTIONS Solving our problem: Round $3199 up to $3200 Subtract 25% from 100% ( = 75) 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% Multiply 75% times $3200 (0.75 x $3,200 = $2,400)

22 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. TWO TRICKS TO ALWAYS UNDERSTAND CONVERSION OF FRACTIONS TO DECIMALS 1. A calculator 2. Use the example of a fraction/decimal that you know. Your discount on your beloved TV is $800 off leaving you a price of $2,400. 1/2 = 50% But why?.50 move decimal 2 places right % 50% = 50/100 = 1/2

23 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 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? 18 lbs 2.2 lbs 2.2x = 18 = x = 8.18 kg x kg 1 kg 15mg x x = 15 x 8.18 = x = mg 1 kg 8.18 kg

24 Page 24 LINEAR CALCULATIONS 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? Notice the units of measure are crossed out mg LINEAR CALCULATIONS Problem: LINEAR CALCULATIONS. 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?

25 Page 25 QUESTIONS? COMMENTS? PHARMACEUTICAL CALCULATIONS FOR TECHNICIANS: EVERYDAY APPLICATIONS Accreditation: Pharmacy Technicians: L04-T CE Credits: 1.0 contact hour Target Audience: Pharmacy Technicians KEVIN MCCARTHY, RPh 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 PHARMACY AND NASCAR??? 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 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.

26 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 TOPICS Ratios Proportions Conversions (Metric & Avoirdupois) Percentages Linear calculations Send your pic to kevin@freece.com

27 Page 27 RATIOS RATIO AS A MEASURE OF BEAUTY 1:1.6 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 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

28 Page 28 PROPORTIONS PROPORTIONS 20mg 10mg 20x = 10 = = x =.5 tab 1 tab x tab 20mg 5mg 20x = 5 = = x =.25 tab 1 tab x tab 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 $ 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

29 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) = grains = 28.4 g 16 ounces = 1 pound (lb) METRIC SYSTEM HOUSEHOLD EQUIVALENTS 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 1 teaspoonful (tsp) = 5 ml 1 tablespoonful (tbsp) = 15 ml 1 ounce = 30 ml 1 cup = 8 ounces 1 pt = 480 ml

30 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? COOKIE RECIPE CONVERSIONS 340 gm 28.4gm 28.4x = 340 = x = ozs x 1 ounce 12 oz 8 oz 8x = 12 = x = 1.5 cups x 1 cup Hint: There are 8 ounces in a cup!

31 Page 31 COOKIE RECIPE CONVERSIONS 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 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 min. Do not brown. Cool slightly, then roll in the extra confectioners' sugar. TEMPERATURE CONVERSION ( C x 9/5) + 32 = F ( F - 32) x 5/9 = C ( C x 1.8) + 32 = F ( F - 32) = C 1.8 FORMULAS

32 Page 32 TEMPERATURE CONVERSION Problem: Convert 165 degrees Centigrade to Fahrenheit. F = (1.8 x C) + 32 F = (1.8 x 165) + 32 F = 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%

33 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. PERCENTAGES Solving our problem: Round $3199 up to $3200 Subtract 25% from 100% ( = 75) It s only three days until the Super Bowl and they finally got around to having a 25% off sale. 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%

34 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 % 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 50% = 50/100 = 1/2

35 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 = 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? mg

36 Page 36 LINEAR CALCULATIONS LINEAR CALCULATIONS Problem: You receive a prescription for Metronidazole 250mg/5ml qid 240ml. Notice the units of measure are crossed out. 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 kevin@freece.com