1. 1 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Pharmacology Math Chapter 34

2. 2 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Learning Objectives  Define, spell, and pronounce the terms listed in the vocabulary.  Apply critical thinking skills in performing patient assessment and care.  Demonstrate methods for verifying the accuracy of calculations.  Differentiate among the terms used in dosage preparation.  Summarize the important parts of a drug label.

3. 3 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Learning Objectives  Describe and perform conversions among the various systems of measurement.  Calculate the correct dose of a drug using the standard formula.  Determine accurate pediatric doses of medication.  Diagram how to reconstitute powdered injectable medications.  Specify the legal responsibilities of a medical assistant in calculating drug dosages.

4. 4 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Drug Management  The medical assistant must be absolutely certain that the medication prepared and administered to the patient is exactly what the physician ordered.  Although drugs often are delivered by the pharmacy in unit dose packs, the dosage ordered may differ from the dose on hand.  In this case the medical assistant must be prepared to calculate the correct dose accurately.

5. 5 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Dosages  There is no margin of error in drug calculations. Even minor mistakes may result in serious complications.  The MA must take meticulous care in calculating all drug dosages.

6. 6 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Drug Labels  Accurately read the drug label to determine if the physician order and the packaged drug use the same system of measurement.  Drug name  Brand name – capitalized and typically in bold print; copyright protected so it is followed by either an ® or ™ symbol.  Generic name – lowercase letters under the brand name in smaller print. If a medication is on the market for a long time the generic name may be the only one listed; if ordered from the pharmacy and stocked as a generic drug, then only the generic name will be on the label

7. 7 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Drug Labels  Dosage strength – under the name of the drug; how much of the drug is contained in each of the identified units. This is what you must compare with the physician’s order to determine if a calculation will be needed  Route or method of administration  Manufacturer’s name and expiration date  Lot number  National drug code that identifies that particular drug

8. 8 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Drug Label Figure 34-1 From Brown M, Mulholland JM: Drug calculations: process and problems for clinical practice, ed 7, St Louis, 2004, Mosby.

9. 9 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Drug Label Figure 34-1 From Brown M, Mulholland JM: Drug calculations: process and problems for clinical practice, ed 7, St Louis, 2004, Mosby.

10. 10 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Label Terms  Strength: The potency of the drug. Stated as a percent of drug in the solution (2% epinephrine), as a solid weight (g, mg, lb, gr), or as a milliequivalent or unit.  Dose: The size or amount of medication in the drug unit. Could be in ml, tsp, or a number of tabs. For example, the label reads “Imitrex, 6 mg/0.5 ml,” which means there are 6 mg of Imitrex in each 0.5 ml.  Solute: Pure drug dissolved in a liquid to form a solution.  Solvent (Diluent): The liquid, usually sterile water, that dissolves the solute.

11. 11 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Mathematics Basics: Fractions  A fraction is part of a whole  It is a way of dividing a whole unit into parts  The top number in a fraction is the numerator and the bottom number is the denominator  Proper fraction – numerator is smaller than the denominator (1/3, ¾, 5/9, 8/23)

12. 12 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Fractions  Improper fraction – numerator is equal to or greater than the denominator (5/3, 7/4, 9/3, 27/15)  Numerator is so large that it is equal to or greater than 1  To convert improper fractions into whole numbers divide the numerator by the denominator  Fractions should be reduced to their lowest terms  Reduce a fraction by dividing the numerator and the denominator by the largest number that goes into each equally  Example: 5/15 – five divides into fifteen three times which means 5/15 can be reduced to 1/3

13. 13 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Fractions  Multiplying fractions – multiply the numerators and denominators of each fraction and reduce the answer to its lowest terms.  Example: ⅓ × ¾ = 3 / 12 = ¼  Dividing fractions – invert the divisor (that is the second fraction) before you multiply the numerators and denominators.  Example: ⅓ ÷ ¾  ⅓ × 4 / 3 = 4 / 9

14. 14 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Mathematics Basics: Decimals  A decimal is similar to a fraction except it is expressed in units of tenths (0.1), hundredths (0.01), and thousandths (0.001)  Convert fractions into decimals to perform drug calculations  To convert a fraction into a decimal simply divide the numerator by the denominator

15. 15 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Decimals  If a decimal is less than a whole number it is crucial that a zero is placed before the decimal point so a medication error is avoided.  Example: If you are supposed to administer.5 ml of a medication and the zero is not placed before the decimal point, you may miss the decimal point and think that the correct dose is 5 ml.  A zero should never be placed after the decimal point of a whole number.  Example – 1.0 ml may be misinterpreted as 10 ml.

16. 16 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Mathematics Basics: Percents  A percent is a number expressed as part of 100.  Decimals are converted into percentages by dividing the number by 100 or by simply moving the decimal point two spaces to the right.  Example:  0.25 = 25/100 = 25%  0.03 = 3/100 = 3%  0.005 = 5/1000 = 0.5%

17. 17 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Mathematics Basics: Ratio and Proportion  A ratio is an expression of a fraction or division problem.  Shows the relationship of the numerator to the denominator.  A comparison of two ratios is a proportion.  Example:  4 = 1 or 4:16 = 1:4 16 4  This is read as 4 divided by 16 equals 1 divided by 4, or 4 is to 16 as 1 is to 4  Physician’s order may be a ratio different from that of the medication that is in stock.  To determine the correct proportion for administration compare the ordered ratio with the available ratio (what is in stock).

18. 18 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Proportions: Unknown Element  In calculating dosages, mathematic proportions are used, but with one element unknown. We must solve for that unknown, or x.  Example:  4 = 1 16 x  Solve the problem by cross-multiplication  An equals sign (=) between two fractions means the equation should be cross-multiplied.

19. 19 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Unknown Element Cross multiplication example: 4 = 1 4x = 16 16 x  To find the value of x divide the number of x (4x) by itself on both sides of the equation,  4x ÷ 4 = 1x  16 ÷ 4 = 4  Therefore: x = 4 and 4 = 1 16 4

20. 20 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Methods for Checking Your Answer  Check your answer by multiplying the means or middle numbers of the equation and the extremes or the outer numbers of the equation.  If correct the multiplication of the means and extremes will be equal.  Example: 3:5 = 6:x Cross-multiply the equation: 3 = 6 5 x 3x = 30 (divide each side by 3 to determine what 1x is) x = 10  The equation is: 3:5 = 6:10  To check the accuracy of your equation, multiply the means or middle numbers (5 × 6 = 30) and the extremes or outer numbers (3 × 10 = 30). Answers are equal so you have the correct proportion.

21. 21 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Rounding Calculations  If you calculate a tablet dose as 1.75 tabs but you only have whole tablets available, check your calculation for accuracy, then check the stocked supply of the drug to make sure no other dosages are available.  If the calculation is correct and there are no other dosages of the drug available, round your answer to the nearest amount that matches the dose available.  If the calculation is 0.5 or greater, then round up to the next whole number. Check with the physician before administering a rounded dose of medication.  Usually round to the nearest tenth; perhaps round to the nearest hundredth with pediatric doses.  Can only give a partial dose of a tablet if it is scored.

22. 22 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Three Steps for Correct Dosage 1.Based on the type of system printed on the label, determine if the physician’s order is in the same mathematical system of measurement.  If the systems vary (the order is in teaspoons but the label states the medication is to be prepared in milliliters), then accurately convert the order to match the system on the label. 2.Perform the calculation in equation form, using the appropriate formula. 3.Check your answer for accuracy, and ask someone you trust to confirm your calculations.

23. 23 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Accurate Dose  All three of these steps must be completed before the medication is dispensed and administered.  Confirm your calculations with the physician if you have any doubt about their accuracy.

24. 24 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Systems of Measurement: Table 34-3  Physician may order medication in a strength that is different than the one identified on the drug label.  Example: orders 2 gr of the drug but the label states there are 120 mg/tab  Before determining how many tablets to administer, the MA must first convert the strength of the physician order to match the strength of the dose on the label since that is the medication that is available for administration.  There are three different systems of measurement: metric, apothecary, and household.

25. 25 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Metric System  Metric system of weights and measures is used throughout the world as the primary system for weight (mass), capacity (volume), and length (area).  Based on units of 10  Each larger unit of measure is 10 times the previous unit of measure.  Fractions are written as decimals (1½ liters = 1.5 liters).  Cubic centimeter = milliliter (1 cc holds 1 ml).

26. 26 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Metric Units of Measurement  Amount or volume of a liquid medication is expressed in milliliters (ml).  Weight or strength of a solid medication is expressed in grams (g).  Length is expressed in meters (m)  One inch is equal to 2½ centimeters (cm)

27. 27 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Conversions to Smaller Units  Units in the metric system are converted by moving the decimal point in multiples of 10.  When going from larger to smaller units of measure, as in converting grams to milligrams, the answer will be a larger number, so move the decimal point three places to the right.  0.35 g = 350 mg  OR multiply 0.35 g × 1000 = 350 mg

28. 28 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Conversions to Larger Units  If converting smaller units of measurement to larger ones as in milliliters to liters, the answer will be a smaller number, so move the decimal point three places to the left.  150 ml = 0.15 liter  OR divide 150 ml by 1000 = 0.15 ml

29. 29 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Rules for Metric System Conversions 1. To convert from a smaller unit of measurement to a larger unit of measurement move the decimal point three places to the left. Your answer will always be a smaller number. Example: 62.4 mg = 0.0624 g. 2. To convert from a larger unit of measurement to a smaller unit of measurement move the decimal point three places to the right. Your answer will always be a larger number. Example: 1.7 g = 1700 mg. 3. To prevent dosage errors use a zero before a decimal point to clarify its presence (0.15 mg) but never leave a zero after a decimal point (15.0) since it may not be noticed and an error may result.

30. 30 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Metric System Equivalents  The following equivalents can be used to make conversions in the metric system. 1 kg = 1000 g 1 g = 1000 mg 1 mg = 0.001 g or 1/1000 g 1 kl = 1000 liters 1 liter = 1000 ml 1 ml = 0.0001 liter or 1/1000 liter

31. 31 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Metric System Conversions Convert the following problems: 2.5 g=_____ mg 0.21 g=_____ mg 150 mcg=_____ mg 1.7 g=_____ mg 3 mg=_____ mcg 0.28 liter=_____ ml 950 ml=_____ liter

32. 32 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Apothecary System  In the apothecary system the basic unit of weight for a solid medication is the grain (gr) and the basic unit of volume for a liquid medication is the minim (M).  As in the metric system, these two units are related: the grain is based on the weight of a single grain of wheat, and the minim is the volume of water that weighs 1 gr.  Either symbols or abbreviations are used; for example, 11/2 drams might be written Diss or dr 11/2.

33. 33 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. System-to-System Equivalents: Table 34-3 15 gr = 1 g = 1000 mg 5 gr = 0.3 g = 300 mg 1 quart = 1000 cc 1 fl oz = 30 ml 1 fl dr = 4 ml 15 M = 1 ml 1 M = 0.06 ml

34. 34 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Household Measurements  This system of measurement is important for the patient at home who has no knowledge of the metric or apothecary systems, although it is not completely accurate; it should never be used in the medical setting  Basic measure of weight is the pound (lb) and of volume is the drop (gtt).  1 gtt = 1 M  60 gtt = 1 tsp  3 tsp = 1 Tbsp (tablespoon)  2 Tbsp = 1 oz  8 oz = 1 cup

35. 35 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Formula Conversion Method Drug Have × Wanted = Unit wanted in new system Have  Drug Have—unit of measurement that is on the label  Wanted—amount or strength ordered by physician  Have—conversion (15 gr = 1 g)  Example physician order: Administer 30 gr of Lasix Label: 1 g Lasix/tab You must convert the ordered unit of measurement (grains) to match the unit of measurement on the drug label (grams) 1 g (label) × 30 gr (physician order) = 2 g = 2 tabs 15 gr (conversion factor)

36. 36 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Converting Metric Order to Household Measurement  Order: 30 ml of an oral antibiotic. What household unit of measurement is this equal to? 1 tablespoon equals 15 ml; divide the order by the conversion factor 30 ml ÷ 15 ml = 2 Tbsp  Or set the problem up as an equation with the ordered amount on the left side of the equation and the conversion factor on the right side: 30 ml × 1 Tbsp 15 ml  Cross-multiply, and the ml unit cancels out, so you have: 30 × 1 Tbsp= 30 Tbsp = 2 Tbsp 15 15

37. 37 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Conversion Problems  A patient with risk factors for heart disease is told to take a baby aspirin equivalent to gr 5 every morning. How many milligrams is the patient taking?  A patient scheduled for urinary tract diagnostic tests needs to drink a minimum of 2 liters of water over the next 12 hours. How many ounces should the patient drink?  A pediatric patient is ordered 8 ml of amoxicillin qid for 10 days. What is the equivalent dose in household measurements?

38. 38 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Calculating Dosages: Standard Formula Available strength = Available amount Ordered strength Amount to give  Available strength – strength of the drug that is written on the medication label  Ordered strength – dose ordered by the physician  Available amount – amount of drug that must be used to deliver the strength identified on the label  If you get confused about where to place the numbers in the equation, remember that like units of measurement must be placed on the same side of the equation.

39. 39 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Standard Formula Example Order: Administer 250 mg of cefalexin IM Available: A vial marked 500 mg/ml  Available strength identified on the label is 500 mg/ml; there are 500 mg of cefalexin in each milliliter of the medication  Ordered strength is 250 mg  Available amount is the amount of the drug that must be used to deliver the strength identified on the label; label states "500mg/ml," which means there are 500 mg of cefalexin in every milliliter of solution

40. 40 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Example Available strength = Available amount Ordered strength Amount to give 500 mg = 1 ml 250 mg x ml The milligram units in the numerator and denominator on the left side of the equation cross each other out. Cross-multiply the equation. 500x = 250 ml To determine what x equals you must divide each side of the equation by 500. 500x = 250 ml 500 x = 1/2 ml = 0.5 ml Solution: Administer 0.5 ml of cephalexin

41. 41 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Alternative Formula: D/H × Q  Regardless of which formula is used, the answer will be the same D—desired dose (the physician’s order) H—what is on hand (the dosage strength listed on the medication label) Q—quantity in the unit (identified on the label as one tablet, 5 ml, etc.)

42. 42 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Sample Problem: D/H × Q  Example: Administer 500 mg of an antibiotic; the label states 250 mg/2 ml D × Q = 500 mg (physician order) × 2 ml (label quantity) H 250 mg (dosage strength on hand)  The milligram quantities cancel out: 500 × 2 ml = 2 × 2 ml = 4 ml 250

43. 43 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Sample Problem: D/H x× Q  Problem: The physician orders 50 mg of Imitrex and the label states "25 mg/tab." Dose ordered × Quantity = Amount to give Dose on hand Or: D × Q = Amount to give or x H 50 mg × 1 tab = 2 tabs 25 mg

44. 44 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Sample Problems  Physician orders 10 ml of a drug and the drug label states there are 20 ml/cc.  Physician orders 4 g of a drug and the medication label states there are 2 g/tab.  Physician orders 6 mg of a drug and the medication label reads there are 12 mg/scored tab.

45. 45 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Pediatric Calculations  Pediatric doses are different from those in other age groups because of multiple factors.  Pediatric doses are much more accurate when based on weight; children can vary greatly in size and body weight.  Factors used in calculating pediatric doses are either body surface area or weight.  Must be especially careful in calculating dosages for children; even a minor miscalculation may be dangerous.

46. 46 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Clark's Rule  This rule is based on the weight of the child.  This system is much more accurate, because children of any age can vary greatly in size and body weight. Pediatric dose = Child's weight in pounds × Adult dose 150 pounds (Adult doses are based on average adult weight of 150 lbs)

47. 47 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. West's Nomogram  West's nomogram uses a calculation of the body surface area (BSA) of infants and young children to determine the pediatric dose. Pediatric dose = BSA of child in m 2 × Adult dose 1.7 m 2 (Average adult BSA = 1.7 m 2.)

48. 48 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. West’s Nomogram From Behrman RE, Kliegman R, Jenson HG, editors: Nelson textbook of pediatrics, ed 16, Philadelphia, 2000, Saunders.

49. 49 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Dosages Based on Body Weight 1. Carefully weigh the child before beginning to calculate the dose to make sure you have an accurate weight.  Convert weight to kilograms by dividing the number of pounds by 2.2 kg 2. Calculate the total daily dose of the medication. 3. Calculate a single dose of the drug based on how frequently the medication is ordered throughout the day. 4. After calculating the amount of a single dose, compare the ordered amount to the drug label. If needed, apply the standard formula to calculate the amount of the medication that should be administered.

50. 50 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Reconstitution  Reconstituting powdered injectables requires adding an amount of solvent (as recommended on the drug label) to a vial of powdered or crystal medication.  Once the solute and solvent are mixed in the vial, a solution of medication is formed with a strength based on equivalents printed on the drug label.  Once the medication is mixed, carefully read the label to determine how much of the drug must be withdrawn to equal the physician’s order.  Use the standard conversion formula to determine the accurate dose for administration.

51. 51 Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved. Legal and Ethical Issues  Must have complete mastery in calculating dosages  If there is ever any doubt about the accuracy of a calculation have the calculation checked  The medical assistant is legally responsible for his or her own actions  State laws vary; physician may have the authority to delegate responsibility for giving medications  MA acts as the “agent” of the physician  MA responsible and accountable for acts performed and may be subject to penalties