By: Gayle Mayer BSPharm, RPh Director of Pharmacy, Spencer Hospital Adjunct Faculty and Co- Program Coordinator, Pharmacy Technician, Iowa Lakes Community College CPE Information: UAN #: 0107-9999-14-153-H04-T CPE/Hours: 1 contact hours (0.1 CEUs) Target Audience: Pharmacy Technicians Activity Type: Application-based The Collaborative Education Institute is accredited by the Accreditation Council for Pharmacy Education as a provider of continuing pharmacy education. Activity Goal: A sound base of pharmaceutical math skills is essential to the daily functions of any pharmacy department. As technicians move into more responsible roles such as Tech-Check-Tech, the assurance of basic pharmacy math knowledge and the ability to keep up those skills, is critical. This review emphasizes basic pharmacy math and tests the knowledge of technicians to identify questionable doses or quantities which may require the pharmacist s attention. Learning Objectives: Upon completion of this activity, technicians will be able to: 1. Describe examples of common systems of measurement 2. Demonstrate the ability to convert units of measurement 3.Appropriately calculate the days supply from a prescription order 4. Use percentages, ratios, and proportions to make accurate pharmaceutical calculations 5. Solve common pharmacy calculations using mathematical skills reviewed in this activity TECH-CHECK-TECH (TCT) Calculations Review Why are pharmaceutical calculations important? Pharmacy mathematical calculations are a core function of most medication decision making and are an essential competency for any certified pharmacy technician. As an experienced advanced technician, this exercise should reaffirm your core math competencies used in daily dispensing and checking along with math functions that are themselves high alert/easily prone to error. As a Checking Technician you have the opportunity and responsibility to question any dispensing situations and have a pharmacist double check. Technicians may even catch order entry errors! This review emphasizes skills used more often in Tech-Check-Tech (TCT) programs including Core advanced math skills, hospital pharmacy skills and community pharmacy skills. Notes This is NOT an all-encompassing math review, e.g. Certified Pharmacy Technician testing review. Seek out additional practice on your own online, with a friend, coworker or pharmacist. Sometimes a consistent method of problem solving, even if it has an extra step or two, may help but note there are alternate ways of problem solving that we may not review today. You might prefer an alternate method or use an alternate method to check your own work. Certified Technicians should not encounter anything new in this review. Common Measurement Systems Historically, several measurement systems have been used in pharmacy, but we will review only two: Household (not recommended for medical use) and Metric (preferred medical and pharmacy use). The use of different measurement systems can be confusing and result in errors so you must be able to convert within and between systems. It is essential to know which system to use in specific calculations. Household Measures/Overview, usage not recommended This knowledge is important while having discussions with family members or perhaps nursing services as well as taking a medication history. Weight 1 pound 16 ounces Volume 3 teaspoons 1 tablespoon 2 tablespoons 1 ounce 8 ounces 1 cup 2 cups 1 pint 2 pints or 4 cups 1 quart 4 quarts 1 gallon TECH-CHECK-TECH 1
The Use of Over-The-Counter Drugs During Pregnancy Metric System Pharmacy Use It is important to note the main unit of weight is a gram. The main unit of volume (liquid) is a liter and the main unit of length is a meter. Compare all measurements to these basics in the table above. The use of abbreviations is discouraged, but they are often used. Be alert and aware! Prefix Meaning Symbol Kilo- One thousand basic units - 1,000 k BASE ONE BASE UNIT (meter, gram or liter) m, g, l Centi- One hundredth 1/100 or 0.01 of a c basic unit Milli- One thousandth 1/1000 or 0.001 of a m basic unit Micro- One millionth 1/1,000,000 or 0.000001 of a basic unit mc Prefixes Used in Metric System Kilo is a unit prefix in the metric system denoting multiplication by one thousand. It s used in weight measurements. 1 Kilo indicates 1,000 units. 1 kilogram = 1,000 grams 1 gram = 0.001 kilogram Milli is a prefix in the metric system denoting a factor of one thousandth (10-3). It s used in weight or volume measurements. Milli is equal to 1/1,000 (0.001) units. 1 milligram = 0.001 gram 1 gram = 1,000 milligrams 1 milliliter = 0.001 liter 1 liter = 1,000 milliliters Micro is a prefix in the metric system denoting a factor of 10 6 (one millionth) and is used in weight measurements. Micro is equal to 1/1,000,000 (0.000001) units. 1 microgram = 0.001 milligram = 0.000001 grams 1 gram = 1,000 milligram= 1,000,000 microgram Following is one example of the relationship of the prefixes: Kilogram (kg) Gram (g) Milligram (mg) Microgram (mcg) 0.001 kilogram = 1 gram = 1,000 milligram = 1,000,000 mcg Common Metric and Household Conversions Metrix Household Exact 1 ml 14 16 drops 5 ml 1 teaspoonful 30 ml 2 tablespoonfuls, 1 ounce 29.57 ml 1 kilogram 2.2 pounds 30 grams 1 ounce 28.35 grams 454 grams 1 pound 453.59 grams Rounding It is critical to know when and how to use rounding for accuracy. You would not tell a caregiver to give 4.87 ml of amoxicillin oral suspension, you would round up 5 ml. You will not round up in more precise situations, e.g. injections, oncology, pediatrics and intensive care. When doing multiple calculations improper rounding can magnify deviation from desired dose. Measuring for compounding IV solutions and injections You may need to consult with your pharmacist for precise rounding guidance. When rounding, find the place value you want (the rounding digit/number), such as a full milliliter or perhaps a tenth of a milliliter and look at the digit just to the right of it. If that digit is less than 5, do not change the rounding digit, but drop all the digits to the right of it. If that digit is greater than or equal to 5, add one to the rounding digit and drop all digits to the right of it. Example #1: Round 720.7342 to the nearest thousandth Begin by finding the rounding digit - this is the 4. Check the next digit to the right (in the ten thousandths place) - this is a 2. 2 is less than 5, so leave the number 4 and drop the rest to the right. This number is now rounded off. Answer: 720.734 Example #2: Round 22.1378 to the nearest hundredth Find the rounding digit - this is the 3. Examine the digit one place to the right (the thousandths) - this is a 7. The number 7 is greater than 5, so add one to the rounding digit (make the 3 a 4) then drop all digits to the right.this number is also rounded up. Answer: 22.14 Percents The term percent means per 100 or out of 100. Just like a fraction: parts of a whole, this time the whole = 100. The percent symbol (%) can be used to write a fraction with a common denominator of 100. Percents ALWAYS have 100 as the denominator. Examples: 30 out of 100 or 30/100 equals 30% 67 out of 100 or 67/100 equals 67% Percent (% ) Strength: using weight(solids) and volume(liquids) weight/volume (w/v) gram/100 ml volume/volume (v/v) ml/100 ml weight/weight (w/w) gram/100 grams You will do your calculations with decimals. Most often you will label with percents. TECH-CHECK-TECH 2
Fraction, Percents, Decimals Comparison Fraction Per Cent Decimal 10/100 10% 0.1 50/100 50% 0.5 110/100 110% 1.1 To write percents as decimals: move the decimal point two places to the left. 25% 0.25 To write decimals as percents: move the decimal point two places to the right. 0.25 25% Ratios A ratio is used to make comparisons between two numbers. A ratio can be written using a fraction (1/20), using the word to (1 to 20) or with a color: (1:20). 1:20 w/v Weight/ Volume 1 gram in 20 ml of solution 1/20 = 5/100 = 5% = 0.05 as decimal 1:20 v/v 1 ml in 20 ml of 1/20 = 5/100 = 5% = 0.05 as decimal Volume/ Volume solution 1:20 w/w Weight/ Weight 1 gram in 20 grams of compound 1/20 = 5/100 = 5% = 0.05 as decimal Ratio/Fraction/Decimal/Percentage First, you must convert your ratio or fraction to a decimal. Then multiply the decimal by 100 to get the percentage. This review will utilize the symbol * to represent multiplication in all examples. Ratio Fraction Decimal Solve: (multiply times 100 or move 2 spaces to the right) Percentage 2:5 2/5 0.4 0.4 * 100% = 40% 2:3 2/3 0.667 0.667 * 100% = 66.7% 3:8 3/8 0.375 0.375 * 100% = 37.5% 6:10 6/10 0.6 0.6 * 100% = 60% Proportion A proportion is a name given to a statement that two ratios are equal. Each side of the proportion must have the same units of measurement and be in the same position. Proportions may be written these different ways: As two equal fractions: a/b = c/d a = c Using a colon: a:b = c:d b d When two ratios are equal, the products of the means (or middle numbers) equals the products of the extremes (or outside numbers); or multiplying diagonally across when written with stacked fractions. Take the two numbers diagonally from each other and multiply them together (cross multiplying). A = C or A:B = C:D B D OR Multiplying the middle numbers = multiplying the outside numbers A * D equals B * C Now you can solve for one missing number (basic algebra with one unknown): A * D = B * X (X is the missing value) Divide each side by B to solve for the missing number and then you have your answer. Solving proportion to obtain a dose Units must be the same north/above the equal sign and south/below the equal sign. They also must match on both sides of the proportion. If they do not, YOU WILL NOT GET THE CORRECT ANSWER. If the strength of a drug is 250mg/5 ml, what is the volume needed to deliver a 375mg dose? 250mg = 375mg 5 ml X ml (How many ml is X?) 375 times 5 = 1875, then divide 1875 by 250 = 7.5 ml X = 7.5 ml dose **Multiply across (step 1) and divide (step 2) Example 1: You know the dose you need to give, what is the volume to place on the label? Drug Strength Available Elixir Dose (mg) Proportion Solve How many ml? 320 mg 160mg = 320mg 5 ml X ml (320 * 5) divide by 160 1600/160 = 10 10 ml TECH-CHECK-TECH 3
Example 2: A parent tells you the volume they are administering to a child, what is the dose? Drug Strength Available Liquid 75mg/5ml Dose (ml) 3.3ml Proportion Solve How many mg? 75mg = X mg 5 ml 3.3 ml (75 * 3.3) divide by 5 247.5 = 49.5 Alligations Use to make a new strength product out of one or two existing product strengths (which can be higher or even 100% AND can be lower or even 0%) This is the outline of method to solve for a new or desired strength product. See chart on Alligations below. 49.5 mg Make 450 ml of 60% alcohol. You have only 30% and 70% alcohol. 70 30 60 First, you will subtract diagonally to determine parts of each additive: 70 60 = 10 parts 60 30 = 30 parts Then, add the total parts: 10 + 30 = 40 total parts Calculate the decimal values: 30/40 = 0.75 (decimal) 10/40 = 0.25 (decimal) (Check 0.75 + 0.25 = 1) Multiply each decimal by the total quantity you are compounding to get the quantity of each additive: 450 ml * 0.75 = 337.5 ml of the 70% 450 ml * 0.25 = 112.5 ml of the 30% (Check 337.5 + 112.5 = 450ml) You have a 10% ointment and a 1% ointment with the same active ingredient. How will you make a 2% ointment total of 45 grams. 100% 20 0% 20% 80 30 10 9 total parts 1/9 =.111 8/9 =.889 Alligations Chart: Higher Strength Available 1 2 3 4 5 Desired Strength to make Parts of Higher (Desired -Lower) Higher Parts Total Parts = Decimal of Higher Total volume needed x Decimal = volume of higher strength Lower Strength Available Parts of Lower (Higher-Desired) Lower Parts Total Parts = Decimal of Lower Total volume needed x Decimal = volume of lower strength Total Parts= (Higher + Lower) These 2 decimals added should equal 1 These two volumes added should be total volume The higher strength or maybe 100 is always on the top. The lower strength or maybe zero is always on the bottom This is the strength you want to make Subtract going diagonally across to determine the number of parts of each additive. Add up the total parts in column 3 and this equals your denominator. Your numerator is the number in column 3. Divide them to obtain the decimal value for the parts of each ingredient. Multiply the decimal calculated in column 4 by the total volume you need to make. This will equal the volume of each ingredient. Adding these two totals together should equal the total volume you want to make as the final product Pharmacy TECH-CHECK-TECH TEAM Series 4 4
0.11 * 45 gram = 4.95 grams 0.89 * 45 gram = 40.05 grams Or a total of 45 grams Compounding from pure ingredients You need to make 100 grams of a 20% ointment using a drug powder (100% active ingredient) and an ointment base (0% active ingredient.) 100 Total Parts 20/100 or.2 80/100 or.8 10% 1 part 1% 2% 8 parts Multiply final quantity by decimal 0.2 * 100 grams = 20 grams of the 100% drug powder 0.8 * 100 grams = 80 grams of the ointment base Final Product 100 grams of 20% ointment ALTERNATE CALCULATION: Because you have pure 100% active ingredient powder and 0% no active ingredient ointment base, you might use this alternate calculation: 1. How much powder do you need / 20% of the final volume?... so multiply by 0.2 100 grams * 0.2 (decimal of 20%) = 20 grams of the drug powder. 2. You need 100 grams total minus the 20 grams powder you are adding. Therefore 80 grams must be the ointment base. 20 grams (weight) + 80 grams (weight) = 100 grams ointment 20/100 = 0.2 = 20% Caution: If you had merely added 20 grams of powder to 100 grams of ointment, you would have 120 grams total and created a 20 gram/120 gram or 16.66% ointment - a product less potent than desired. Dosing on Body Weight Milligrams per kilogram per day is the most accurate rule. This tells us that for every kg the patient weighs, they are to take a certain amount of drug over 24 hours (per day.) Additionally, you may need to divide the total daily dose into the number of doses per day. Give 10 mg/kg/day, in 3 divided doses. The patient weighs 176 pounds. How much is EACH dose? 176 pounds = 80 kg (1 kg = 2.2 pounds) 80 kg * 10 mg/kg = 800 mg per day Divided into 3 doses is 266.7 mg per dose IV Flow Rate, Infusion Times Accurately determine flow rates to ensure patients receive the correct dose of medication over a specified time. For the pharmacy, this will also impact quantities made, when mixed, concentrations chosen, etc. Maximize the stability of the product and minimize waste. Usually volumes over 250ml are considered large volume and will have dose dependent infusion rates. Smaller volumes are considered IV piggyback. They are infused through the fluid of a large volume IV and run intermittently over a short period of time a certain number of times per day, not continuously IV Orders IV orders may be written as: ml per hour (100 ml per hour, total volume over a total time (1,000 ml over 8 hours) or by dose (60 mg per hour). 1 liter D5W IV over 8 hours is ordered, what is the infusion rate? 1,000ml / 8 hours = 125 ml per hour 40 meq KCl in 1,000 ml to infuse over 8 hours is ordered, how many meq of KCl will infuse per hour? Divide the 40mEq by 8. We see that 5mEq of KCl will infuse per hour. Then divide the 1,000 ml by 8. 125 ml of fluid will infuse per hour. The stock supply is a 25,000 unit heparin/ 500 ml bag. To administer 1,200units/hour, what is the infusion rate? 25,000 units/500 ml = 50 units/ml So how many ml does it take to deliver 1,200 units? 1,200 units/50 units = 24 ml per hour Concentrations & Dilutions The more CONCENTRATED a drug is, the stronger it is and the more DILUTED a drug is, the weaker it is. Concentrations can be defined 3 ways: Volume/Volume (V/V) : the ml of liquid active ingredient added to liquid base or diluent to make a total of 100 ml Weight/Weight (W/W) : the grams of solid active ingredient added to a solid base or diluent to make a total of 100 gm Weight/Volume (W/V) : the number of grams of solid active TECH-CHECK-TECH 5
ingredient added to liquid base or diluent to make 100 ml. These are just another fraction, ratio, or parts of a whole (based on 100). 20% V/V = 20 parts and 80 parts, totaling 100 parts or 20 ml + 80 ml = 100 ml 20% W/W = 20 gm + 80 gm = 100 gm 20% W/V = 20 gm + 80 ml = 100 ml Dilution of Stock Solutions You might use a concentrated stock solution to prepare a more dilute solution. Quantity 1 * Strength 1 = Quantity 2 * Strength 2. Product 1 is what you have, while Product 2 is what you are making. Q1 is the weight or volume of stock solution, S1 is the strength of stock solution, Q2 is the weight or volume of desired solution and S2 is the strength of desired solution. How many grams of a 1% hydrocortisone cream can be made from 240 gm of 2.5 % hydrocortisone cream? Q1 * S1 = Q2 * Q2 240gram * 2.5% = X gram * 1% Change percents to decimals 240 * 0.025 = X * 0.01 Do the first calculation 6 = X * 0.01 Divide each side by 0.01 6/0.01 = X or X = 600 grams So you will add 360 grams of base cream to the 240 grams of 2.5% hydrocortisone cream for a final 600 grams of 1% Cream. Does this make sense? You made 2.5 times as much, and it is 2.5 times less potent. You need 100 ml of 0.45% saline. You only have 0.9% saline available. How do you mix this? Q1 * S1 = Q2 * S2 100 ml * 0.45% = X ml of 0.9% Convert percents to decimals 100 * 0.0045 = X *0.009 Do the first calculation 0.45 = X * 0.009 Divide each side by 0.009 0.45 /0.009 = X 50 ml = X (of the 0.9% saline, add 50 ml of water to final volume of 100 ml) Does this make sense? You cut the strength in ½ so you need ½ the volume of the concentrate, and dilute with water to the final total volume. An order calls for 2% soaking solution. The pharmacy has 50 ml of a 10% solution left. How much 2% can you make from the 50 ml? 50 ml * 10% = X ml * 2% (convert % to decimal) 50 ml * 0.1 = X * 0.02 ( do first math) 5 = X * 0.02 (Divide each side by 0.02) 250 ml = X You will add 200 ml of diluent to the 50ml of 10% solution for final product of 250 ml of 2% soaking solution. Does this make sense? The strength is 5 x less (2% v. 10%).What you can get is 5 x more (50ml v 250ml) Checking Start with an independent double check. Don t just look at other person s calculations and methods. Always start over from scratch. Then double check yourself. You can sse an alternate calculation method or run it twice using your own independent double check. Ask yourself: Does it make sense? Do a quick estimate to determine if your result might be reasonable. Do your best and remember a pharmacist is always there to check your work, if you need help never be afraid to ASK! Your pharmacist is always your resource and support. TECH-CHECK-TECH 6
Question Bank If you are a technician in an inpatient/hospital pharmacy practice, please answer questions 1-10. If you are a technician in an ambulatory/ community/retail pharmacy practice, please answer questions 5-14. Once you have completed the exam, please logon to your CEI portfolio to enter your answers and redeem CPE credit. Once successfully completed, click the Submit button that appears in the column of your portfolio titled CPE Submit. The CPE Statement of Credit can then be accessed on CPE Monitor, www.mycpemonitor.net. 1. 1 gram ceftriaxone vial for injection is reconstituted with 2.5mL of diluent for an approximate concentration of 330mg/ ml. The total volume available is 3mL once reconstituted. A pediatric patient is to receive 50mg/kg/day divided into 4 doses for seven days. The child weighs 77 pounds. What dose (in mg) should the child receive at each administration? a) 140 mg b) 43.75 mg c) 1400 mg d) 437.5 mg 2. Digoxin injection is available in a concentration of 0.3 mg/ ml. How many ml of the injection will provide a dose of 150 micrograms? a) 0.5 ml b) 50 ml c) 5 ml d) 1 ml 3. A D5W-1/2NS 1 liter bag is set to infuse at 100ml/hour. How many hours until the bag is empty? a) 8 hours b) 10 hours c) 6 hours d) 12 hours 4. A 100 ml solution for a patient-controlled anesthesia contains 200 mg of morphine sulfate and 8 mg of droperidol. Calculate the percentage strength of each ingredient in the solution. a) 0.008% droperidol, 0.2% morphine b).08% droperidol, 2% morphine c).028% droperidol and morphine d).8% droperidol, 20% morphine 5. How much water should be added to 300 ml of 85% (v/v) alcohol to prepare 70% (v/v) alcohol? a) 364 ml b) 64 ml c) 70 ml d) 36.4 ml 6. An antibiotic has a dose of 10mg/kg. How many milliliters of a 125mg/ml suspension should be administered to a child weighing 66 lbs? a) 4.8 ml b) 2 ml c) 0.48 ml d) 2.4 ml 7. Which of the following is equivalent to 58 grams? a) 0.058 kg b) 0.0058 kg c) 580 kg d) 5800 kg 8. Which of the following is the correct conversion between systems of measurement? a) 1 pound = 2.2 kilograms b) 1 kilogram = 2.2 pounds c) 1 teaspoonful = 15 ml d) 1 ounce = 60 ml 9. Which of the following is NOT an accurate statement about percentages? a) Percentages are parts per 1,000 b) 120% expressed as a decimal is 1.2 c) 25% of 100 units = 25 units d) 15% = 15/100 = 0.15 10. A young child who weighs 42 pounds has an ear infection and will receive amoxicillin (Amoxil). The dose is 90 mg/kg/day divided every 12 hours. Amoxicillin suspension is available as 400mg/5ml suspension. Rounding to the nearest teaspoon to make measuring easy for the parent, what dose should the child receive at each dose? a) 5 ml b) 10 ml c) 7.5 ml d) 2.5 ml TECH-CHECK-TECH 7
11. A patient drops off a script for: RX: Albuterol 0.083% nebulizer solution Nebulize one vial every 8 hours Dispense 90 vials. Each vial of albuterol holds 3 ml of liquid and each box contains 75ml of albuterol. We cannot split boxes of albuterol. How many boxes should be dispensed if the patient has commercial insurance with a 30 day limit for reimbursement? a) 3 boxes, round down because the pharmacy will not be reimbursed for amounts exceeding the 30 day supply ordered by the physician and covered by the insurance. b) 4 boxes, round up because we want to make the most convenience for the patient. 12. Lantus insulin comes in vials of 10 ml in a concentration of 100units/ml. A patient comes to the pharmacy to fill his Lantus prescription of which the patient injects 8 units every morning and 18 units every night at bedtime. How many units will the patient need for 30 days? a) 1460 units, no b) 780 units, yes c) 780 units, no d) 870 units, yes 13. Mr. Young is getting his warfarin 5 mg prescription refilled. He takes 2.5 mg Monday, Wednesday, Friday, Saturday and 5 mg Tuesday, Thursday, Sunday. How many tablets does he need for a 28-day supply? a) 28 tablets b) 14 tablets c) 21 tablets d) 20 tablets 14. If a patch contains 75 mcg of drug and is packaged in a box of 10, how many boxes will a patient need for one month if they use 1 patch every 72 hours? a) 3 boxes b) 2 boxes c) 1 box d) 2 boxes, but will not finish the second box TECH-CHECK-TECH 8