Pharmacy Calculations: Review Sean Tran, PharmD Clinical Pharmacist Self Regional Healthcare stran@selfregional.org October 10, 2013 Disclosures I do not have (nor does any immediate family member have) a vested interest in or affiliation with any corporate organization offering financial support or grant monies for this continuing education activity, or any affiliation with an organization whose philosophy could potentially bias my presentation. Objectives Review fractions and their importance in pharmaceutical calculations Demonstrate ability comparing and expressing ratios in multiple formats Objectives Perform calculations accurately and efficiently Comprehend a variety of mathematical notations Understand and manipulate the commonly used calculation methods Dosing errors Institute of Safe Medication Practices (ISMP), October 2009: Oseltamivir oral suspension shortage contributed to dosing errors Commercially manufactured Tamiflu (Roche) is provided in a 12 mg/ml suspension Pharmacists have begun to compound the product on an emergency basis Compounding directions found in the labeling, however, result in a 15 mg/ml oseltamivir base concentration Gallup Poll 2012 Please tell me how you would rate the honesty and ethical standards of people in these different fields Very high, high, average, low, or very low ISMP Medication Safety Alert. October 15, 2009 Gallup Historical Trends. 2012 1
Honesty/Ethics in Professions Parts of a whole Numerator (part) over Denominator (whole) NOT Gallup Historical Trends. 2012 Example: One whole tablet = 1000 mg One-half tablet = 1 = mg 2 One-fourth tablet = 1 = mg 4 Proper 1, 2, 3. 2 7 5 Improper 5, 8, 11. 2 7 5 Mixed 5 = 2 Comparing 1? 3 5? 3. 8 8 7 7 Comparing 1 1 5 3. 25 10 7 8 as decimals = DIVISION 7 = 7 10 = 10 2
Adding and Subtracting Must get same denominator (common denominator) 1 + 3 = + 3 = = 5 10 10 3-1 = 3 - = 10 5 10 Multiplying Multiply across numerator and denominator 1 x 3 = 5 10 7 x 4 = 10 5 Dividing Multiply by the reciprocal (inverse) 1 3 = 1 x = = 5 10 5 2 3 = 2 x = 5 7 5 Scientific Notation Used to express very large or small values How many times we multiply or divide by 10 to get the actual number Ex: 100,000 = 0.0006 = Ratios and Percents Ratios are fractions and visa versa ½ = 1:2 = 0.5 1/3 = = 0.333 10/3 = = 3.333 The whole is 100%, thus ½ = 1:2 = 0.5 = 1/3 = 1:3 = 0.333 = 10/3 = 10:3 = Percent Strengths 30% means 30 parts in 100 parts 30:100 = 30/100 = 0.3 Solutions Percents represent grams per 100 ml 1% lidocaine contains gram of lidocaine per 100 ml of solution May be expressed as 1:100, 1/100, or 0.01 3
Percent Strengths Solids Percents represent grams per 100 g 0.5% hydrocortisone cream contains gram of hydrocortisone per 100 grams of cream May be expressed as 0.5:100, 0.5/100, or 0.005 Proportions An expression of equality between two ratios Notated by a double colon ( :: ) or an equal sign between two ratios 3:4 = 15:20 3:4 :: 15:20 3 = 15. 4 20 Cross Multiplication a:b = c:d Proportions Three of the four values must be known Numerators must have the same unit of measurement Denominators must have the same unit of measurement Practice makes Perfect! Pharmacy Calculations: Review Sean Tran, PharmD Clinical Pharmacist Self Regional Healthcare stran@selfregional.org October 10, 2013 4
Roman Numerals I = V = X = L = C = D = M = Metric Prefixes 1 kilogram (kg) = 1000 grams 1 hectogram (hg) = 100 grams 1 dekagram (dag) = 10 grams 1 gram (g) = 1 gram 1 decigram (dg) = 0.1 gram 1 centigram (cg) = 0.01 gram 1 milligram (mg) = 0.001 gram 1 microgram (mcg) = 0.000,001 gram 1 nanogram (ng) = 0.000,000,001 gram Standard units 3 teaspoons (tsp) = 1 tablespoon (tbsp) 2 tablespoons (tbsp) = 1 fluid ounce (fl oz) 8 fluid ounce (fl oz) = 1 cup 2 cups = 1 pint (pt) 2 pints (pt) = 1 quart (qt) 4 quarts (qt) = 1 gallon (gal) 1 pound (lb) = 16 ounces (oz) Standard/Metric Conversions 1 teaspoons (tsp) = 5 ml 1 tablespoon (tbsp) = 15 ml 1 fluid ounce (fl oz) = 30 ml 1 cup = 240 ml 1 pint (pt) = 480 ml 1 quart (qt) = 960 ml 1 gallon = 3840 ml ISMP Statement on Metric Units Metric measurements in prescription directions All healthcare professionals Pharmacy computer systems e-prescribing systems Supported by FDA, CDC, and Consumer Healthcare Products Association Standard/Metric Conversions 1 ounce (oz) = 30 g 1 pound (lb) = 454 g 2.2 pound (lb) = 1 kg 1 inch (in) = 2.54 cm F = [(9/5) C] + 32 or F = (1.8 x C) + 32 ISMP Press Release. October 2011 5
DEA Checksum Dr. Alfred Yang, M.D. AY 3456781 How to check that this may be valid? DEA Checksum Always begin with two letters and followed by seven digits First letter usually designates type of authority of the holder A or B for primary-level practitioner M for mid-level practitioner F for foreign country Second letter is the first letter of the prescriber s last name DEA Checksum Add the first, third, and fifth digits Add the second, fourth, and sixth digits DEA Checksum Dr. Alfred Yang, M.D. AY 3456781 Double the sum obtained in Step 2 Add the results of Steps 1 and 3. The last digit of this sum should match the last digit of the DEA number Ratio-Proportion Method Convert 2300 mg to grams Dimensional Analysis Convert 486 mg to grams 6
Dimensional Analysis Convert 4.5 liters to milliliters Weight-based dosing A patient weighs 60 kg and she is to receive a medication of 15 mg/kg. What will her dose be? Concentrations and Dilutions You are instructed to make 1000 ml of a 0.225% w/v solution. You have in stock a concentrate of 23.4%. How much of the concentrate will you use, and how much diluent will be needed? Concentrations and Dilutions Step 1: Determine how many grams there will be in the final product Concentrations and Dilutions Step 2: Determine how much of the concentrated solution is needed to provide the desired number of grams Concentrations and Dilutions Step 3: Determine how much diluent will be mixed with the concentrated solution 7
Practice makes Perfect! Pharmacy Calculations: Review Sean Tran, PharmD Clinical Pharmacist Self Regional Healthcare stran@selfregional.org October 10, 2013 8