University of Kentucky / NetLearning CBL 1 of 39 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. Pharmacy Calculations Authors: Philip Trapskin, PharmD Rebecca Reagan, RPh Kimberley Hite, MS, PharmD John Armitstead, MS, RPh, FASHP Service Area: Pharmacy Services Phone: (859) Date Developed Or Revised: April, 2005 Curriculum:Pharmacy Target Audience:Pharmacists and Pharmacy Technicians

University of Kentucky / NetLearning CBL 2 of 39 Supplies needed for this CBL Please have a calculator, pencil and paper available to complete this CBL.

University of Kentucky / NetLearning CBL 3 of 39 Objectives Basic Mathematics Units of Measure Ratios and Proportions Intravenous flow (drip) rate calculations Common Abbreviations Menu

University of Kentucky / NetLearning CBL 4 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 5 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 6 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) Decimal Numbers –Another means of writing fractions (1/2 =0.5, 1&3/4 = 1.75) Numerator Denominator

University of Kentucky / NetLearning CBL 7 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 8 of 39 Basic Mathematics cont. (Problem Set #1) Convert the following fractions to decimal numbers: a. 1/2b. 3/4c. 1d. 2/5 e. 1/3f. 5/8g. 50/100h. 12/48 i. 11/2j. 2 2/3k. 5 1/4l. 3 4/5

University of Kentucky / NetLearning CBL 9 of 39 Basic Mathematics cont. (Problem Set #1) Answers for problem set #1: a. 0.5b. 0.75c. 1d. 0.4 e. 0.33f g. 0.5h i. 5.5j. 2.67k. 5.25l. 3.8

University of Kentucky / NetLearning CBL 10 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 11 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 12 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 13 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 = –micro-; 1/ =

University of Kentucky / NetLearning CBL 14 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 15 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 1 kilogram = 1000 grams 1 gram = 1000 milligrams 1 milligram = 1000 micrograms 1 microgram = 1000 nanograms Example 0.004kg = 4g = 4000mg = 4,000,000mcg

University of Kentucky / NetLearning CBL 16 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 17 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) = (480) milliliters (ml) –1 teaspoonful (tsp) = 5 milliliters (ml) –1 tablespoonful (TBS) = 15 milliliters (ml) –1 ounce (oz) = grams (g) –1 pound (lb) = (454) grams (g)

University of Kentucky / NetLearning CBL 18 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 19 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 20 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 5 g 50 g 100ml 1000ml –If you know three of the four terms you can calculate the fourth. =

University of Kentucky / NetLearning CBL 21 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 2. (40mg)(X)= (2ml)(300mg) 2ml X 3. X = (2ml)(300mg)4. X=15ml (40mg) 5. TIP – Make sure your units cancel

University of Kentucky / NetLearning CBL 22 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 23 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 24 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 25 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 5gX = 50 g 1000ml100ml =

University of Kentucky / NetLearning CBL 26 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 27 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 28 of 39 Concentration and Dilution cont. (Problem Set #3) Solutions 1. a. 0.45g b. 5g g g mg g

University of Kentucky / NetLearning CBL 29 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 30 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 31 of 39 Concentration and Dilution cont. (Problem Set #4) Solutions: ml ml mg ml ml 6. 2 g ml 8. 1 g ml 10. zero

University of Kentucky / NetLearning CBL 32 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 33 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 = 4. IV rate = 2. Concentration of IV = 5. IV rate = 3.Concentration of IV = 100units/ml of heparin 6. IV rate = 10 ml/hr ( 1000 units/hr) (100 units/ml) Dose desired Concentration of IV Total amount of drug Total volume 25,000 units of heparin 250ml of D5W

University of Kentucky / NetLearning CBL 34 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 35 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 36 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 37 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 SO 4 – Sulfate mEq – milliequivalent mmol - millimole

University of Kentucky / NetLearning CBL 38 of 39 Summary For more information on this topic or to request additional training please contact: Kimberley Hite, MS, PharmD 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.

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