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Calculations are a critical component of pharmacy practice. Pharmacy technicians should have an understanding of how to determine quantities of ingredients accurately. Having a working knowledge of the metric system, as well as familiarity with percentages, proportions, dilutions, and alligations, is crucial. In addition, a working knowledge of Roman numerals, system conversions, and metric and temperature conversions is strongly advised. Tip: When calculating days supply, make sure to convert both the prescribed dose and the total amount of the drug in the container to the same unit. Calculating Days Supply Days supply is the amount of time that the medication will last. Prescriptions do not always last 30 or 90 days and often require simple calculations in order to determine the days supply. An incorrect days supply can result in the patient receiving too much or too little of the medication, as well as insurance claim rejections on future refills. Days supply can be determined by dividing the total number of doses to be dispensed by the number of doses taken per day. Hospital pharmacies supply medications based on units or singular doses. Note that calculations are necessary when quantities are not written on prescriptions. Example 1—Capsules/Tablets A prescription is written for cephalexin 250 mg #30 1 cap PO TID. What is the days supply? Answer Cross multiply and solve for x. The next example is a bit trickier and requires some investigation. In order to calculate the days supply, you will need to know how many “puffs” are in one inhaler. This information can be found by looking at the inhaler package. Example 2—Inhalers A prescription is written for ProAir inhaler 2 puffs QID. A ProAir inhaler has 200 puffs. What is the days supply? Answer: First, determine the number of puffs in 1 day. 2 puffs QID is the same as 2 puffs, four times a day, or 8 puffs a day. Then, move on to calculating the days supply. Cross multiply and solve for x. Example 3 deals with oral liquids. Oral liquids are generally not dispensed in the original container unless the amount to be dispensed is equivalent to the stock bottle amount or if the prescription is written for a complete bottle to be dispensed. Calculations are needed in order to determine the total amount, in mL, to be dispensed. NOTE: In order to determine what size bottle is needed for the volume of medication prescribed, take the total volume in mL (if not already given in oz) and divide it by 30. For example, a 120 mL prescription would be dispensed in a 4 oz bottle. Example 3—Oral Liquids A prescription is written for Dilantin 125 mg/5 mL # 8 oz, 1 tsp PO BID. What is the days supply? Answer: First, convert oz to mL. Cross multiply and solve for x. Now look at the total quantity that is to be taken in 1 day. Finally, determine the days supply. Cross multiply and solve for x. Many times, the prescription will specify an amount of time that the patient should take the medication for. It is best to determine the appropriate days supply based on the amount of drops the patient will use daily. The pharmacy technician should check the amount of mL that is contained in one bottle and select the appropriate size that will maintain the course of therapy as prescribed. In addition, it is customary to assume a conversion factor of 20 drops/mL (typically used for ophthalmic and otic solutions) when determining the total amount of drops per bottle. Some pharmacies may be conservative and use a conversion factor of 15 drops/mL (typically reserved for ophthalmic and otic suspensions). Third-party payers may also require a conversion factor of 16 drops/mL when determining days supply. Check with the pharmacist before proceeding. Example 4—Eye Drops and Ear Drops A prescription is written for Cipro HC Otic suspension, 4 gtts ad BID × 7 days # 10 mL. What is the days supply? Answer: Calculate the actual days supply based on a conversion factor of 20 drops/mL. First, determine the number of drops contained in the bottle. Next, determine the volume of drops that a patient will use per day, and calculate the number of days this prescription will last. The script states: 4 gtts ad BID. This means that the patient will use 4 drops in the right ear twice a day for a total of 8 drops a day. Cross multiply and solve for x. Insulin prescriptions are written in units. Days supply calculations are determined based on 1 mL = 100 units. Insulin may also be referred to as U-100, meaning that each mL contains 100 units. Typical sizing for insulin includes both 10 mL vials (1,000 units) and 3 mL syringes (available as a quantity of 5 syringes for a total quantity of 15 mL or 1,500 units). Example 5—Insulin A prescription is written for Humulin-N U-100 insulin 10 mL vial, 35 U SC QD. What is the days supply? Answer: There are 100 units/mL. First, determine the total number of units in the 10 mL vial of insulin. Cross multiply and solve for x. Then, solve for the total days supply of this prescription. Cross multiply and solve for x. Do not round up because the patient will not have enough to last until the next day. Days supply calculations for ointment/cream prescriptions are not as concrete and require some additional information. It is important to note that ointments/creams vary in size. The days supply depends upon how often the patient will use the medication and how large of an area the patient will use the ointment or cream on. If an amount is not specified, err on the side of caution and use 1 g/dose to calculate days supply. Tip: Labels for inhaler, liquid, and insulin preparations should include a beyond-use date when appropriate. Example 6—Ointments/Creams A prescription is written for hydrocortisone 2.5% cream, 30 g tube, apply once daily to the affected area. What is the days supply? Answer: For this example, we will use 1 g/dose to calculate the days supply. First, determine the total number of doses available in a 30 g tube. Cross multiply and solve for x. Now solve for the total days supply for this prescription. Cross multiply and solve for x. Now practice days supply using the following prescriptions. Prescription 1 Tip: Remember, 1 teaspoonful is equivalent to 5 mL. 1.What is the total quantity of this medication that is to be dispensed to the patient? 2.What is the minimum days supply for this prescription? 3.How many refills are on this prescription? Answers: 1.The total is 120 mL. This can also be interpreted as 4 oz. 2.The minimum days supply is 4 days. Cross multiply and solve for x. 3. There are no refills on this prescription. Prescription 2 1. Translate the sig code into plain English. 2. Is this prescription written for an ear drop or an eye drop? 3. What is the days supply? Answers: 1.Instill 1 drop in each eye every day. 2.This prescription is written for an eye drop. 3.The days supply is 25 days. Cross multiply and solve for x. Calculations for Dispensing Fees, Copays, and Cash Register Calculations Dispensing fees are costs that are associated with filling the prescription. They are determined by a contractual agreement between a third party and the pharmacy. Dispensing fees for prescriptions include the cost of labor, equipment, medications, and rent. Copays are determined by a contractual agreement between a third party and the patient. They are fixed dollar amounts that may reflect a percentage of the medication cost. Cash register calculations require the technician to give the correct change to the patient. In addition, patients who pay cash for their prescriptions are charged a usual and customary price (U&C). These prices reflect the medication’s cost (average wholesale price or AWP) and a professional fee. Some pharmacies also provide discounts to patients without insurance coverage. Example 1 What is the copay for a prescription of prednisone 20 mg # 10 if the copay is 20% of the U&C price of the prescription? The U&C price for prednisone 20 mg #10 is $4.76. Answer:
20% is the same as saying or 0.2. To determine the copay, multiply the percentage by the U&C price. The copay for this prescription is $0.95. Example 2 A third-party contract allows for pharmacy reimbursement of prescription “X” based on the following formula: 80% of AWP + $1.65 dispensing fee. The AWP for prescription “X” is $34.20. Determine the pharmacy reimbursement for prescription “X.” Answer
80% is the same as saying or 0.8. Pharmacy reimbursement can be determined by multiplying the AWP by 0.8 and adding the dispensing fee. The pharmacy reimbursement is $29.01. Example 3 A patient’s prescription costs $75.25, and a patient gives you $80.00. How much change should the patient receive? Answer: There are multiple ways of counting out change, and the currency you provide to the patient can vary based on how you count out change. Here is one method you can use. Start counting out the currency using the smallest denomination of money that will get you to the next coin or bill size. Start with the purchase price of $75.25, and count to the amount given to you ($80.00). 3 quarters (75¢) will make $76.00 4 dollars ($4.00) will make $80.00 Therefore, the patient should receive $4.75 in change. Example 4 A patient qualifies for a pharmacy discount of 5% on her prescription costs. What is the cost that the patient will pay if the retail price of her prescription is $6.15? Answer:
5% is the same as saying or 0.05. To determine the amount the patient will pay, multiply the percentage by the prescription cost. This is the discount that the patient will receive. Subtract this amount from the prescription cost to determine the discounted amount to be paid by the patient. The patient will pay a discounted amount of $5.84. Percentages and Strengths Percentages refer to a quantity out 100. Percentages can be considered to be a fraction. For example, the quantity 75% means 75/100. . Interpreting percentages can be tricky, especially when determining the units involved. Remember the following facts: - Volume/volume percent (v/v%) is measured in mL/100 mL. This is used for liquids. - Weight/weight percent (w/w%) is measured in g/100 g. This is used for ointments and creams. - Weight/volume percent (w/v%) is measured in g/100 mL. This is used for drugs that are dissolved in solutions. When converting a percentage to a fraction, the denominator is always 100. Review the following examples. Tip: Make sure you are using the correct conversion factor and units when you set up proportions. Always double check your answer! Example 1 20 mL of glycerin is dissolved in water to make 80 mL of final solution. What is the percent strength of glycerin? Answer: Calculate the percent strength by dividing the amount of active ingredient by the total weight or volume of the product. Then, multiply the result by 100 and add a percent sign (%). The active ingredient is glycerin, and the final volume is 80 mL. Example 2 A prescription is written for ibuprofen 15% cream. How much ibuprofen powder is needed to prepare 30 grams of the compound? Answer: First, set up your proportion. A proportion is a statement of equality between two ratios. Make sure to put what you want on the left side and what you need on the right side: WANT = NEED. The prescription is written for 15% strength; this is what we want. 15% means . The question also tells us that we need 30 g of the cream. Cross multiply and solve for x. This means that 4.5 g of ibuprofen powder is needed to prepare this prescription. Example 3 The prescription below is written for benzocaine gel 240 g: How much benzocaine and carbopol are needed to prepare this prescription? Answer: To solve this problem, you must determine the amount of each individual ingredient needed to make this preparation. The question does not ask for the amount of alcohol or distilled water needed to formulate this preparation, so only calculate the amount of benzocaine and carbopol. Set up a proportion for each ingredient using 240 g as the total amount of the final preparation. You will need 4.8 g of benzocaine and 4.8 g of carbopol to fill this prescription. Diluting Stock Solutions The concentration of a medication is the amount of drug (e.g., mg, g) given in a specified volume (e.g., mL). Concentrations may be expressed as a percent, fraction, or ratio. Stock solutions are concentrated solutions that are used to prepare less concentrated solutions. These less concentrated solutions (dilutions) are prepared by adding a diluent, such as sterile water.
Remember the following formula when solving these sorts of problems: where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume. Example 1 400 mL of a 40% solution is diluted to 500 mL. What is the percent strength of the resulting solution? Answer: To solve this problem, determine which components are given in the question. This question gives us a final volume of 500 mL with an initial volume of 400 mL. We are also given an initial concentration of 40%. An equation must be set up to determine the final concentration. Divide both sides by 500 mL to solve for x. Make sure to cancel units. The resulting solution will have a percent strength of 32%. This problem can also be solved using the ratio and proportion method. First, calculate the number of grams that are contained in 400 mL of the 40% solution. This tells us that 160 g is diluted in 500 mL. The percent strength can be determined by calculating the number of grams in 100 mL. Alligations Alligations are used to prepare a concentration of solution that is not commercially available. These solutions are made by mixing together two solutions when one solution contains a stronger concentration and the other contains a weaker concentration. The solutions must be expressed in percentages with the desired solution strength lying between the stronger and weaker concentrations. Alligations can be solved using a table that looks similar to a tic-tac-toe board.
Table: Setting Up an Alligation Problem
Example 1 How many mL of a 50% solution and of a 25% solution are needed to prepare 2 liters of a 40% solution? Answer: First, set up a tic-tac-toe layout using the information provided, and solve for the number of parts of each solution. Number of parts in higher % strength solution = (P − L) Number of parts in lower % strength solution = (H − P)
Next, determine the total number of parts by adding them together. Then, set up a proportion using the parts of each concentration. Remember to convert liters to milliliters (1 L = 1,000 mL, so 2 L = 2,000 mL). Check your work by adding the total amounts of each concentration and comparing your answer to the total volume of the preparation, which in this case is 2,000 mL. Infusion Rates and Drip Rates Orders that are written for the rate at which an IV is infused are called infusion rates. These rates are expressed in mL/min, mL/hour, or amount of drug/time. Example 1 What is the rate of infusion in mL/hour of 1,000 mL of drug “X” to be infused over 8 hours? Answer: Using the formula given: This equation can also be manipulated to solve for time. Example 2 The rate of infusion is 125 mL/hr, and the volume of fluid is 500 mL. How long will the IV bag last? Answer Using the formula above: Tip: Drop factors can be found on the IV administration package. IV sets are used to deliver IVs to patients. These sets are calibrated for a specific number of drops per mL. Pharmacy technicians are expected to calculate the rate of infusion in drops per minute. Common drop (gtts) factors are 10 gtts/mL (macro sets), 15 gtts/mL, and 60 gtts/mL (micro sets). Use the following formula to solve for the infusion flow rate: Example 3 What is the infusion rate of a 1 L lactated Ringer’s solution with a flow rate of 125 mL/hr and a drop factor of 15 gtts/mL? Answer Recognize that 1 L = 1,000 mL. Other Calculations/Doses Based on Body Weight, Age, and Body Surface Area Many pediatric, geriatric, oncology, corticosteroid, and antibiotic medications are dosed based on body weight (usually mg/kg). Questions that involve doses based on body weight may require conversions from pounds to kilograms (1 kg = 2.2 lb). Example 1 The prescriber orders a drug to be dosed at 15 mg/kg/day. What is the daily dose for a 132 lb patient? Answer Then, set up a ratio and proportion using the given dosing regimen. Doses based on body weight can be determined using a nomogram, which is a chart that is used to determine body surface area (BSA) based on the patient’s height and weight. Nomograms may be used if the BSA is not given in the question. The BSA is used to calculate doses for patients who are receiving chemotherapeutic agents and is measured in m2. Example 2 A patient has a BSA of 1.54 m2. Calculate the dose of fluorouracil, in mg, for the patient if the doctor has ordered 400 mg/m2 daily. Answer Set up a proportion. One other way to calculate the BSA is to use the Mosteller formula. This formula can be adapted to calculate the BSA based on weight in kilograms and height in centimeters or based on weight in pounds and height in inches. Example 3 A patient weighs 27 lbs and is 30 inches tall. Calculate the patient’s BSA using the Mosteller formula. Answer In the event that the manufacturer’s recommended dose is not available, two alternative methods can be used to determine the pediatric dose. Clark’s rule uses the child’s weight in pounds and assumes an average adult weight of 150 pounds. This formula is valid for patients who weigh less than 150 pounds. Young’s rule, on the other hand, uses the patient’s age (under 12 years old) to determine the recommended dose. You can differentiate between the two formulas by remembering that Young’s rule uses the age; this is even implied in the name (since “Young” implies age, not weight). Clark’s rule: Young’s rule: Example 4 Using Clark’s rule, determine the dose that is required for an 11-year-old child, who weighs 75 pounds, if the average adult dose is 500 mg. Example 5 Using Young’s rule, determine the dose that is required for an 11-year-old child, who weighs 75 pounds, if the average adult dose is 500 mg. Answer Summary - Pharmacy personnel prepare non-sterile compounded medications according to standards of purity in order to maintain product sterility and accuracy. - Proper selection of materials for non-sterile compounding formulations is determined based on the prescription, common practices, and current guidelines. - Non-sterile compounding procedures are based on the standards set by the United States Pharmacopeial Convention (USP <795>). - Beyond-use dates are determined by the manufacturer and are used to identify the medication’s expiration date. - Each medication receives an associated lot number that indicates where and when the medication was processed. This lot number is an important tool that is used to identify a medication that has been affected by a recall. - The National Drug Code (NDC) is a ten-digit sequence of numbers that identifies the labeler, product, and package size of the medication. - Medication returns are identified as dispensable or non-dispensable. They may be eligible for credit, or they will either be returned to stock or returned using a reverse distributor. - Pharmacy technicians should be familiar with common medical terminology, pharmacy abbreviations, Sig codes, and symbols used in pharmacy practice. - Familiarity with pharmacy calculations is a necessary component of pharmacy practice. Morning dose: Evening dose: Therefore, the patient is taking 15 mL/day. Thus:
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