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Pharmacy Calculations

Pharmacy Calculations. Please have a calculator, pencil and paper available to complete this CBL. Supplies needed for this CBL. Menu. Objectives Basic Mathematics Units of Measure Ratios and Proportions Intravenous flow (drip) rate calculations Common Abbreviations.

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Pharmacy Calculations

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  1. Pharmacy Calculations

  2. Please have a calculator, pencil and paper available to complete this CBL. Supplies needed for this CBL

  3. Menu Objectives Basic Mathematics Units of Measure Ratios and Proportions Intravenous flow (drip) rate calculations Common Abbreviations

  4. 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 Objectives

  5. 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. Basic Mathematics

  6. 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) Basic Mathematics cont. (Kinds of Numbers) Numerator Denominator

  7. 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. Basic Mathematics cont. (Kinds of Numbers)

  8. 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 Basic Mathematics cont. (Problem Set #1)

  9. 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 Basic Mathematics cont. (Problem Set #1)

  10. 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 Basic Mathematics cont. (Percentages)

  11. Converting fractions to percentages Write the fraction in decimal form. (3/4=0.75) Write the decimal over one. (0.75/1) Multiply the numerator and denominator by 100. (0.75/1 = 75/100) Because you already know the “divided by a hundred” is the same as percent you can write 75/100 as 75%. Basic Mathematics cont. (Percentages)

  12. 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. Basic Mathematics cont. (Percentages)

  13. 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 Units of Measure (Metric System)

  14. 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 Units of Measure cont. (Metric System)

  15. 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 Units of Measure cont. (Metric System) Example 0.004kg = 4g = 4000mg = 4,000,000mcg

  16. 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) Units of Measure cont. (Other Systems)

  17. 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) Units of Measure cont. (Equivalencies)

  18. Fill in the blanks: 1 liter (L) = ________ml 1000 g = __________kg 1 g = _____________mg 1000 mcg =_________mg 1 TBS = ____________tsp 1 TBS =_____________ml 2 fl oz =_____________ml 70 kg = ______________pounds (lb) Units of Measure cont. (Problem set #2)

  19. Fill in the blanks: 1 liter (L) = 1000 ml 1000 g = 1 kg 1 g = 1000 mg 1000 mcg = 1 mg 1 TBS = 3 tsp 1 TBS = 15 ml 2 fl oz = 60 ml 70 kg = 154 pounds (lb) Units of Measure cont. (Problem set #2)

  20. 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. Ratios and Proportions =

  21. 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 Ratios and Proportions cont.

  22. 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 Concentration and Dilution

  23. 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. Concentration and Dilution cont.

  24. 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. Concentration and Dilution cont.

  25. 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 Concentration and Dilution cont. =

  26. Solving concentration and dilution problems Calculate the number of grams in 100 ml of solution. That is your “known” ratio. Then calculate the number of grams in the volume requested in the problem by setting up a proportion. Check to make sure your units are in the same order. Make sure that the units that are across from each other are the same. Convert your answer to the requested units. Concentration and Dilution cont.

  27. In 100 ml of D5W/0.45% NaCl solution: How many grams of NaCl are there? How many grams of dextrose are there? How many grams of dextrose are in 1 L of a 10% dextrose solution? How many grams of NaCl are in 1 L of 1/2NS? How many mg of neomycin are in 50 ml of a 1% neomycin solution? How many grams of amino acids are in 250 ml of a 10% amino acid solution? Concentration and Dilution cont. (Problem Set #3)

  28. Solutions 1. a. 0.45g b. 5g 2. 100g 3. 4.5 g 4. 500 mg 5. 25 g Concentration and Dilution cont. (Problem Set #3)

  29. An order calls for 5 million units of aqueous penicillin. How many milliliters are needed if the concentration is 500,000 units/ml? How many milliliters are needed fro 15 million units of penicillin if the concentration is 1 million units per milliliter? Pediatric chloramphenicol comes in a 100mg/ml concentration. How many mg are present in 5 ml of solution? How many milliliters of a 250mg/ml chloramphenicol solution are needed for a 4 g dose? Concentration and Dilution cont. (Problem Set #4)

  30. Oxacillin come in a 500mg/1.5ml solution. How many milliliters will be required for a 1.5 g dose? How many grams of ampicillin are in 6 ml of a 500mg/1.5ml solution? How many milliliters contain 3 g of cephalothin if the concentration of the solution is 1g/4.5 ml? How many grams of magnesium sulfate are in 2 ml of a 50% magnesium sulfate solution? How many milliliters of a 50% dextrose solution are needed for a 10 g dextrose dose? How many grams of dextrose are in 50 ml NS solution? Concentration and Dilution cont. (Problem Set #4)

  31. Solutions: 10 ml 15 ml 500 mg 16 ml 4.5 ml 2 g 13.5 ml 1 g 20 ml zero Concentration and Dilution cont. (Problem Set #4)

  32. 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. Intravenous (IV) flow (drip) rate calculations

  33. 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 = Concentration of IV = 100units/ml of heparin 6. IV rate = 10 ml/hr Intravenous (IV) flow (drip) rate calculations cont. Total amount of drug Total volume Dose desired Concentration of IV 25,000 units of heparin 250ml of D5W (1000 units/hr) (100 units/ml)

  34. Practice problem set #5 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)? 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? Intravenous (IV) flow (drip) rate calculations cont.

  35. Practice problem set #5 solutions 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 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 Intravenous (IV) flow (drip) rate calculations cont.

  36. 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 Common Abbreviations

  37. 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 Common Abbreviations cont.

  38. For more information on this topic or to request additional training please contact: Kimberley Hite, MS, PharmD khite2@email.uky.edu 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. Summary

  39. 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. Exit Choose the My Records button to view your transcript. Select Exit to close the Student Interface.

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