Page 1 Back to Basics: A Simple Guide to Calculations for Pharmacy Technicians By: Kevin McCarthy, R.Ph 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. 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. 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 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 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.
Page 2 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 - Too easy to misread and make a mistake.2 or 0.2? 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 Rounding Numbers Lets Try Some Rounding 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. 7.847 to tenths 7.8 0.347 to hundredths 0.35 7.9372 to thousandths 7.937
Page 3 Roman Numerals Used to write prescriptions Used in directions to the patient Used to specify the amounts of ingredients and the quantity being dispensed Roman Numerals Decoded ss = One Half I = One V = Five X = Ten L = Fifty C = One Hundred M = One Thousand III Rules of Roman Numerals 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 Lets give it a try Question 1: VII =? Question 2: CXXXII =? Question 3: 17 =? Type your answers in the Chat Box
Page 4 Question 1: VII = 7 Lets give it a try Question 2: CXXXII = 132 Roman Numerals In Real Life #1 #2 Question 3: 17 = XVII Systems of Measurement There are three systems of measurement Metric Avoirdupois (household system) Apothecary (rarely used) Metric System Conversion Factors Micro One Millionth Milli One Thousandth Centi One Hundredth Deci One Tenth Kilo One Thousand
Page 5 Metric System Conversions 1000mcg = 1mg 1000mg = 1g 1000g = 1kg 1000ml = 1L Metrics are expressed in decimal form, such as 500ml = 0.5L Avoirdupois Conversion Factors 3 tsp = 1 tbsp 2 tbsp = 1 oz 16 oz = 1 pt 2 pt = 1 qt 4 qt = 1 G *16 oz = 1 lb* Conversions Between Systems 1 tsp = 5 ml 1 g = 15.4 gr 1 tbsp = 15 ml 1 gr = 60 mg (64.8mg) 1 oz = 30 ml (29.57 ml) 1 kg = 2.2 lb 1 pt = 480 ml (473 ml) 1 lb = 454 g 1 G = 3840 ml (3784 ml) 1 oz = 30 g Ending Conversion Confusion 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
Page 6 Lets give it a try Convert: 4.1 kg to grams Lets give it a try Convert: 4.1 kg to grams 4.1 kg x 2.2 lb x 454 g = 4,095.08 g 1 kg 1 lb OR approximately 4,100g Convert This 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? Convert This Answers! 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
Page 7 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 Ratios 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 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 Proportion Proportions consist of two equal ratios and is a statement of equality for the two ratios. Example: _3_ = _6_ 5 10
Page 8 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 = 0.25 mg 1 tab X 0.5 mg (X) = (1 tab) (0.25 mg) X = 0.25 0.5 X = 0.5 tablet 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? Proportion & Ratio 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
Page 9 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 Percentages There are three ways to prepare percentages: Percent volume-in-volume (v/v) X milliliters / 100 milliliters 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
Page 10 Percentages Parenteral Calculations 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 deal with the administration of IV fluids 3 Main concepts you will learn Flow rate Drip rate Dose per time Flow Rate 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 Formula: Volume Time = Flow Rate **Always double check what time and volume you are solving for! ml/hour, L/min..etc** Give it a try 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 Volume Time = Flow Rate 1000 ml 5 hours = 200 ml/hr
Page 11 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 1 L 500 ml 3 hours = 167 ml/hr Manipulating the Formula 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 Lets Try Solving for 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
Page 12 Lets Try Solving for Time Say you have an IV running at 138 ml/hr. How long will 1 L last the patient? Again, Convert L to ml. 1 L = 1000 ml Volume Flow Rate = Time Now, Solve for Volume How many ml of solution would be required to run an IV for 8 hours, at a rate of 60 ml/hr? 1000 ml (volume) = 7 Hours 138 ml/hour (flow rate) 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? Remember: Rate x Time = Volume 60ml X 8 hours 1 hr 1 = 480 ml Drip Rate is the number of drops the IV solutions is dripping during a specified time period Function of drops per minute 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
Page 13 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? 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? First, we need to convert liters to milliliters & hours to minutes 4L X 1000ml = 4000 ml 24 hours X 60 min = 1440 min 1 L 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 ITS TIME FOR. THE PHARMACY TECH CHALLENGE!!! How about a friendly competition? This is Troy Polamalu!! His is number 43. What would his number be in Roman Numerals?? Type your answers into the chat box and try to win a PHARMCON KOOZIE!!
Page 14 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 Remember, flow rate is measured in ml/hr. But, just for fun, use your conversion skills and tell us: 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? Convert the numerical expression Decimal Fraction Percent Ratio 0.6???
Page 15 Convert the numerical expression Decimal Fraction Percent Ratio? 7/20?? A child s amoxicillin dose is 20 mg/kg/day in divided doses, every 8 hours A) This could be written as 20 mg/ lb/day.? B) How many grams of amoxicillin would a 44 lb child receive daily? C) How many milligrams per dose? Notes Notes