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Pharmacy Calculations Curriculum: Pharmacy Target Audience: Pharmacists and Pharmacy Technicians Philip Trapskin, PharmD Rebecca Reagan, RPh Kimberley Hite, MS, PharmD Authors: John Armitstead, MS, RPh, FASHP Service Area: Pharmacy Services Phone: (859) 257-8414 Email: [email protected] Date Developed Or Revised: April, 2005 All materials on this template are Copyright © 2004 University of Kentucky Chandler Medical Center Learning Center unless otherwise noted. All rights reserved. Certain graphic images, text elements and logos are derived from The University of Kentucky and NetLearning and are used by permission. University of Kentucky / NetLearning CBL ‹#› of 39 Supplies needed for this CBL • Please have a calculator, pencil and paper available to complete this CBL. University of Kentucky / NetLearning CBL ‹#› of 39 Menu Objectives Basic Mathematics Units of Measure Ratios and Proportions Intravenous flow (drip) rate calculations Common Abbreviations University of Kentucky / NetLearning CBL ‹#› of 39 Objectives •Review basic mathematics •Review units of measure •Review ratios and proportions •Review concentration and dilution •Review intravenous flow (drip) rate calculations •Provide sample problems and solutions University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics •Numerals – A numeral is a word or a sign, or a group of words or signs that expresses a number. • Arabic (0, 1, 2, 3, 4...) • Roman (I, X, L, D, C, M …) •Numbers – A number is a total quantity or amount that is made of one or more numerals. University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics cont. (Kinds of Numbers) •Whole Numbers (10, 220, 5, 19) •Fractions – Parts of whole numbers (1/4, 2/7, 11/13) Numerator Denominator •Decimal Numbers – Another means of writing fractions (1/2 =0.5, 1&3/4 = 1.75) University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics cont. (Kinds of Numbers) •WARNING: Writing decimals incorrectly can lead to medication errors. – Trailing zeros • Write 5 not 5.0 – Naked decimal points • Write 0.5 not .5 •Periods are sometimes difficult to see leading to a 10 fold error. University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics cont. (Problem Set #1) •Convert the following fractions to decimal numbers: a. 1/2 b. 3/4 c. 1 d. 2/5 e. 1/3 f. 5/8 g. 50/100 h. 12/48 i. 11/2 j. 2 2/3 k. 5 1/4 l. 3 4/5 University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics cont. (Problem Set #1) •Answers for problem set #1: a. 0.5 b. 0.75 c. 1 d. 0.4 e. 0.33 f. 0.625 g. 0.5 h. 0.25 i. 5.5 j. 2.67 k. 5.25 l. 3.8 University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics cont. (Percentages) •Percentage means “by the hundred” or “in a hundred.” Percents (%) are just fractions, but fractions with a set denominator of 100. – Example: “50%” means “50 in a hundred” or “50/100” or “1/2”. •Converting percentages to fractions – Write the number preceding the percent sign over 100 and simplify the resulting fraction – Example: 25%=25/100=1/4 University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics cont. (Percentages) • Converting fractions to percentages 1. Write the fraction in decimal form. (3/4=0.75) 2.Write the decimal over one. (0.75/1) 3.Multiply the numerator and denominator by 100. (0.75/1 = 75/100) 4.Because you already know the “divided by a hundred” is the same as percent you can write 75/100 as 75%. University of Kentucky / NetLearning CBL ‹#› of 39 Basic Mathematics cont. (Percentages) • Concentration expressed as percentage – Percent weight-in-weight (w/w) is the grams of drug in 100 grams of the product. – Percent weight-in-volume (w/v) is the grams of drug in 100ml of the product. – Percent volume-in-volume (v/v) is the milliliters of drug in 100ml of the product. • These will be discussed further later in the CBL. University of Kentucky / NetLearning CBL ‹#› of 39 Units of Measure (Metric System) • The metric system is based on the decimal system, in which everything is measured in multiples or fractions of 10. • Standard measures – Meter; Length – Gram; Weight – Liter; Volume • Prefixes – kilo-; 1000 – milli-; 1/1000 = 0.001 – micro-; 1/1000000 = 0.000001 University of Kentucky / NetLearning CBL ‹#› of 39 Units of Measure cont. (Metric System) • Volume is the amount of space occupied by a three-dimensional object as measured in cubic units (as milliliters or liters) – L = Liter – ml = milliliter – 1 Liter = 1000 milliliters – 3.5L = 3500ml University of Kentucky / NetLearning CBL ‹#› of 39 Units of Measure cont. (Metric System) • Mass is a property of physical objects which measures the amount of matter in an object. kg = kilograms g = gram mg = milligram mcg = microgram ng = nanogram Example 0.004kg = 4g = 4000mg = 4,000,000mcg 1 kilogram = 1000 grams 1 gram = 1000 milligrams 1 milligram = 1000 micrograms 1 microgram = 1000 nanograms University of Kentucky / NetLearning CBL ‹#› of 39 Units of Measure cont. (Other Systems) • Avoirdupois – used in measuring bulk medications (pounds, ounces, grains) • Apothecary – developed after the Avoirdupois system to enable fine weighing of medications (pounds, ounces, drams, scruples, grains, gallons, pints, fluid ounces, fluid drams, minims) • Household – commonly used to measure liquids with home utensils (teaspoons, tablespoons, cups, pints, quarts) University of Kentucky / NetLearning CBL ‹#› of 39 Units of Measure cont. (Equivalencies) • Equivalencies among systems – 1 inch = 2.54 cm – 1 kg = 2.2 pounds (lb) – 1 fluid ounce (fl oz) = 29.57(30) milliliters (ml) – 1 pint (pt) = 473.167 (480) milliliters (ml) – 1 teaspoonful (tsp) = 5 milliliters (ml) – 1 tablespoonful (TBS) = 15 milliliters (ml) – 1 ounce (oz) = 28.35 grams (g) – 1 pound (lb) = 453.59 (454) grams (g) University of Kentucky / NetLearning CBL ‹#› of 39 Units of Measure cont. (Problem set #2) • Fill in the blanks: a.1 liter (L) = ________ml b.1000 g = __________kg c.1 g = _____________mg d.1000 mcg =_________mg e.1 TBS = ____________tsp f. 1 TBS =_____________ml g. 2 fl oz =_____________ml h.70 kg = ______________pounds (lb) University of Kentucky / NetLearning CBL ‹#› of 39 Units of Measure cont. (Problem set #2) • Fill in the blanks: a.1 liter (L) = 1000 ml b.1000 g = 1 kg c.1 g = 1000 mg d.1000 mcg = 1 mg e.1 TBS = 3 tsp f. 1 TBS = 15 ml g. 2 fl oz = 60 ml h.70 kg = 154 pounds (lb) University of Kentucky / NetLearning CBL ‹#› of 39 Ratios and Proportions • A ratio states a relationship between two quantities. – Example: 5 g of dextrose in 100 ml of water (Dextrose 5% in Water often abbreviated as D5W) • A proportion is two equal rations. – Example: 5 g of dextrose in 100 ml of water equals 50 g of dextrose in 1000 ml of water 5g 100ml = 50 g 1000ml – If you know three of the four terms you can calculate the fourth. University of Kentucky / NetLearning CBL ‹#› of 39 Ratios and Proportions cont. • A vial of drug contains 40mg/2ml. How many milliliters (ml) are required to obtain 300mg of drug? 1. 40mg = 300mg 2ml X 2. (40mg)(X)= (2ml)(300mg) 3. X = (2ml)(300mg) (40mg) 4. X=15ml 5. TIP – Make sure your units cancel University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution • Terminology – 5% dextrose in water is the same as D5W. – 0.9% sodium chloride (NaCl) is the same as normal saline (NS). – Half-normal saline is half the strength of normal saline (0.9% NaCl), or 0.45% NaCl. This may also be referred to as 1/2NS University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. • Reminder – Percent weight-in-weight (w/w) is the grams of drug in 100 grams of the product. – Percent weight-in-volume (w/v) is the grams of drug in 100ml of the product. – Percent volume-in-volume (v/v) is the milliliters of drug in 100ml of the product. University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. • Example 1: – 0.9% sodium chloride (w/v) = 0.9 g of sodium chloride in 100 ml of solution. • Example 2: – 5% dextrose in water (w/v) = 5 g of dextrose in 100 ml of solution. • Example 3: – 23.4% sodium chloride (w/v) = 23.4 g of sodium chloride in 100 ml of solution. University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. • Example 4: – How many grams of dextrose are in 1 L of D5W? – Know ratio: D5W means 5g 100ml – Unknown ratio: X 1000ml – Write the proportion and solve for X: X 5g X = 50 g = 1000ml 100ml University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. Solving concentration and dilution problems 1. Calculate the number of grams in 100 ml of solution. That is your “known” ratio. 2. Then calculate the number of grams in the volume requested in the problem by setting up a proportion. 3. Check to make sure your units are in the same order. 4. Make sure that the units that are across from each other are the same. 5. Convert your answer to the requested units. University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. (Problem Set #3) 1. In 100 ml of D5W/0.45% NaCl solution: a.How many grams of NaCl are there? b.How many grams of dextrose are there? 2. How many grams of dextrose are in 1 L of a 10% dextrose solution? 3. How many grams of NaCl are in 1 L of 1/2NS? 4. How many mg of neomycin are in 50 ml of a 1% neomycin solution? 5. How many grams of amino acids are in 250 ml of a 10% amino acid solution? University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. (Problem Set #3) Solutions 1. a. 0.45g b. 5g 2. 100g 3. 4.5 g 4. 500 mg 5. 25 g University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. (Problem Set #4) 1. An order calls for 5 million units of aqueous penicillin. How many milliliters are needed if the concentration is 500,000 units/ml? 2. How many milliliters are needed fro 15 million units of penicillin if the concentration is 1 million units per milliliter? 3. Pediatric chloramphenicol comes in a 100mg/ml concentration. How many mg are present in 5 ml of solution? 4. How many milliliters of a 250mg/ml chloramphenicol solution are needed for a 4 g dose? University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. (Problem Set #4) 5. Oxacillin come in a 500mg/1.5ml solution. How many milliliters will be required for a 1.5 g dose? 6. How many grams of ampicillin are in 6 ml of a 500mg/1.5ml solution? 7. How many milliliters contain 3 g of cephalothin if the concentration of the solution is 1g/4.5 ml? 8. How many grams of magnesium sulfate are in 2 ml of a 50% magnesium sulfate solution? 9. How many milliliters of a 50% dextrose solution are needed for a 10 g dextrose dose? 10. How many grams of dextrose are in 50 ml NS solution? University of Kentucky / NetLearning CBL ‹#› of 39 Concentration and Dilution cont. Solutions: 1. 10 ml 2. 15 ml 3. 500 mg 4. 16 ml 5. 4.5 ml (Problem Set #4) 6. 2 g 7. 13.5 ml 8. 1 g 9. 20 ml 10. zero University of Kentucky / NetLearning CBL ‹#› of 39 Intravenous (IV) flow (drip) rate calculations • Using flow rates you can calculate the volume of fluid or amount of drug a patient will be receiving over a certain period of time. • Calculation of IV flow (drip) rates is necessary to ensure that patients are receiving the amount of medication the physician ordered. • At UKCMC pharmacy technicians perform drip rounds to verify drip rate doses for patient safety, enhance patient care, and minimize drug waste. University of Kentucky / NetLearning CBL ‹#› of 39 Intravenous (IV) flow (drip) rate calculations cont. • Example: – An order is written for 25,000 units of heparin in 250 ml of D5W to infuse at 1000units/hr, what is the correct rate of the infusion (in ml/hr)? 1. Concentration of IV = Total amount of drug Total volume Dose desired 4. IV rate = Concentration of IV 25,000 units of heparin (1000 units/hr) 2. Concentration of IV = 250ml of D5W 5. IV rate = (100 units/ml) 3. Concentration of IV = 100units/ml of heparin 6. IV rate = 10 ml/hr University of Kentucky / NetLearning CBL ‹#› of 39 Intravenous (IV) flow (drip) rate calculations cont. • Practice problem set #5 1. An order is written for 2 g of lidocaine in 250 ml of D5W to infuse at 120mg/hr. What is the correct infusion in (ml/hr)? 2. An order is written for 25,000 units of heparin in 250 ml of D5W to infuse at 17ml/hr. How many units of heparin will the patient receive in 12 hours? University of Kentucky / NetLearning CBL ‹#› of 39 Intravenous (IV) flow (drip) rate calculations cont. • Practice problem set #5 solutions 1. An order is written for 2 g of lidocaine in 250 ml of D5W to infuse at 120mg/hr. What is the correct infusion in (ml/hr)? 15ml/hr 2. An order is written for 25,000 units of heparin in 250 ml of D5W to infuse at 17ml/hr. How many units of heparin will the patient receive in 12 hours? 20,400 units University of Kentucky / NetLearning CBL ‹#› of 39 Common Abbreviations D5W – 5% dextrose in water D10W – 10% dextrose in water NSS or NS – 0.9% sodium chloride (normal saline) 1/2NS – 0.45% sodium chloride (half normal saline) 1/4NS or 0.2NS – 0.225% sodium chloride (quarter normal saline) LR – Lactated Ringer’s D5LR – 5% dextrose in Lactated Ringer’s University of Kentucky / NetLearning CBL ‹#› of 39 Common Abbreviations cont. D5NS – 5% dextrose in 0.9% sodium chloride CL or Cl – Chloride Na – Sodium Mg – Magnesium K – Potassium SO4 or SO4 – Sulfate mEq – milliequivalent mmol - millimole University of Kentucky / NetLearning CBL ‹#› of 39 Summary For more information on this topic or to request additional training please contact: Kimberley Hite, MS, PharmD [email protected] • Please proceed to the test and complete all the questions. • The passing score for this module is 25 correct answers. • Successful completion of this exam is required to demonstrate pharmacy calculations competency. University of Kentucky / NetLearning CBL ‹#› of 39 Exit We hope this Computer Based Learning course has been both informative and helpful. Feel free to review the screens of this course until you are confident about your knowledge of the material presented. Click the Take Test button on the left side of the screen when you are ready to complete the requirements for this course. Choose the My Records button to view your transcript. Select Exit to close the Student Interface. University of Kentucky / NetLearning CBL ‹#› of 39