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PowerPoint® to accompany Math and Dosage Calculations for Medical Careers Second Edition Booth • Whaley Chapter 7 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. CHAPTER 7 METHODS of DOSAGE CALCULATIONS Learning Objectives When you have completed Chapter 7, you will be able to: • Describe how the information on a physician’s order, Medication Administration Record (MAR), or prescription, along with the drug label and package insert, are used to calculate the desired dose. Chapter 7 3 Learning Objectives (con’t) • Convert the dosage ordered to the desired dose, using both fraction proportion, ratio proportion, or dimensional analysis. • Calculate the amount to administer of a drug, using any of the methods of dosage calculation, fraction proportion, ratio proportion, dimensional analysis, or formula. • Recognize common errors that occur during dose calculations. Chapter 7 4 Introduction • This chapter will bring all of the previous information together to calculate the amount of medication to administer to a patient. • You will use: – Basic math – Information from the physician’s order – Drug labels – Method of converting quantities from one unit of measurement to another Chapter 7 5 Dosages and Doses To calculate medication dosages you must know: Desired Dose: • The amount of the drug to be administered at a single time. • Its unit of measurement must be the same as the dosage unit. Chapter 7 6 Dosages and Doses (con’t) Dosage ordered: • The total amount of drug the physician has ordered, along with the frequency. • Its unit of measurement may not be the same as that of the dosage unit. Chapter 7 7 Dosages and Doses (con’t) Dose on hand: • The amount of drug contained within a dosage unit of medication. • If a medication has 250 mg of drug per tablet, the dose on hand is 250 mg. Chapter 7 8 Dosages and Doses Rule 7 - 1 • The unit of measurement for the desired dose must be the same as the unit of measurement of the dose on hand before the amount to administer can be calculated. • This is calculated by converting the dose ordered into the same unit of measurement as the dose on hand; once converted it becomes the desired dose. Chapter 7 9 Calculating the Desired Dose • Before calculating the amount to be administered, you must first determine the desired dose. • The dosage ordered is not always written in the same units that are found on the drug label. • You must convert the dosage ordered into a desired dose having the same units as the dose on hand. Chapter 7 10 Calculating the Desired Dose (con’t) • Three methods to calculate desired dose: – Fraction proportion – Ratio proportion – Dimensional analysis Each gives the same result Use the method that you like Once you identify your favorite method, follow the color coding of that method in the book Chapter 7 11 Fraction Proportion Method Procedure Checklist 3-1 1. Write the conversion factor with the units that you are converting to in the numerator and the units you are converting from in the denominator. 2. Write a fraction with the unknown,”?,” in the numerator and the number that you need to convert in the denominator. Chapter 7 12 Fraction Proportion Method (con’t) 3. Set the two fractions up as a proportion. 4. Cancel units. 5. Cross multiply, then solve for the unknown value. Work out this Example: The dosage ordered is 0.2 mg once a day. The dosage strength is 100 mcg/tablet. Find the desired dose. Desired Dose = 200 mcg Chapter 7 13 Error Alert! • In a fraction proportion, units from the fraction can be canceled only when they are the same portion of the fraction. Units in the denominator of one fraction cannot be canceled with units found in the numerator of the other. Always include the units when performing calculations. Chapter 7 14 Ratio Proportion Method Procedure Checklist 3-2 1. Write the conversion factor as a ratio A : B so that A has the units of the value that you are converting (the dosage ordered) and B has the unit of value of the dose on hand. 2. Write a second C : D so that C is the missing value (desired dose) and D is the number that is being converted (the dosage ordered). Chapter 7 15 Ratio Proportion Method (con’t) 3. Write the proportion in the form A : B :: C : D. Note: When using the ratio proportion method to calculate the desired dose, C indicates the unknown value (desired dose). 4. Cancel units. 5. Solve the proportion by multiplying means and extremes. Chapter 7 16 Ratio Proportion Method (con’t) Example Practice by determining the desired dose. The order reads: ASA gr v PO daily. The drug label indicates 325 mg tablets. Find the desired dose. The desired dose is 325 mg. Chapter 7 17 Error Alert! • In a ratio proportion, units can be canceled only when they are found in the same part of each of the ratios. Always include the units when performing calculations. Chapter 7 18 Dimensional Analysis Procedure Checklist 3-3 1. Determine the units of measure for the answer and place it as the unknown on one side of the equation. 2. On the other side of the equation, write a conversion factor with the units of measure for the answer on top and the units you are converting from on the bottom. Chapter 7 19 Dimensional Analysis (con’t) 3. Multiply the conversion factor by the number that is being converted over one. 4. Cancel units on the right side of the equation. The remaining unit of measure on the right side of the equation should match the unknown unit of measure on the left side of the equation. 5. Solve the equation. Chapter 7 20 Dimensional Analysis (con’t) Example Find the desired dose for the following: Ordered: Levsinex timecaps ER 1500 mcg once daily On hand: Levsinex timecaps 0.375 mg Desired dose = 1.5 mg Chapter 7 21 Error Alert! • In dimensional analysis, units can be canceled only when they are found in both the numerator and the denominator of the fraction. Always include the units when performing calculations. Chapter 7 22 Review and Practice Determine the desired dose. Ordered: Penicillin VK 0.25 g On hand: Penicillin VK 500 mg Desired dose: 250 mg Wonderful ! Chapter 7 23 Calculating the Amount to Administer Once you have determined the desired dose, you still must calculate the amount to administer. Chapter 7 24 Calculating the Amount to Administer (con’t) Rule 7 - 2 To calculate the amount of medication to administer (A), the following information must be known: The desired dose (D) or the amount of drug to be given at a single time - This is the dosage ordered converted to the same units as the dose on hand, if necessary. Chapter 7 25 Calculating the Amount to Administer (con’t) Rule 7 - 2 (con’t) The dosage strength or the dose on hand (H) per the dosage unit (Q) The dose on hand (H) is the amount of drug contained in a dosage unit The dosage unit (Q) is the unit by which you will measure the medication-tablets, capsules, milliliters, teaspoons, etc. (Find this on the medication label) Chapter 7 26 Calculating the Amount to Administer (con’t) Procedure 7-1 Calculating the Amount to Administer by Fraction Proportion: 1. Set up the proportion as follows: dosage unit amount to administer dose on hand desired dose 2. Cancel units QA H D 3. Cross multiply, then solve for the unknown value Chapter 7 27 Calculating the Amount to Administer (con’t) Example: • Ordered: 250 mg IM • Dosage strength available: 0.5 g/mL • Find the amount to administer Amount to administer = 0.5 mL Chapter 7 28 Calculating the Amount to Administer (con’t) Procedure 7-2 Calculating the Amount to Administer by Ratio Proportion: 1. The proportion will be set up as follows: dosage unit : dose on hand :: amount to administer : desired dose Or Q : H :: A : D 2. Cancel units 3. Multiply the means and extremes then solve for the missing value Chapter 7 29 Calculating the Amount to Administer (con’t) Example: The dosage ordered is Famvir 500 mg PO q 8h On hand: Famvir 250 mg tabs Find the amount to administer Amount to administer = 2 tablets Chapter 7 30 Calculating the Amount to Administer (con’t) Procedure 7-3 Calculating the Amount to Administer by Dimensional Analysis: With dimensional analysis you will not need to calculate the desired dose and amount to administer separately. You will place your unknown (amount to administer) on one side of the equation then multiply a series of factors on the right side of the equation. Canceling units will help you determine the equation has been set up correctly. Chapter 7 31 Calculating the Amount to Administer (con’t) Procedure 7-3 Calculating the Amount to Administer by Dimensional Analysis (con’t): 1. Determine the units of measure for the answer and place it as the unknown on one side of the equation. 2. On the right side of the equation, write a conversion factor with the units of measurement for the desired dose on top and the unit of measurement for the dose on hand. Chapter 7 32 Calculating the Amount to Administer (con’t) Procedure 7-3 Calculating the Amount to Administer by Dimensional Analysis (con’t): 3. Multiply the conversion factor by a second factor: the dosage unit over the dose on hand. 4. Multiply by a third factor: dose ordered over the number one. 5. Cancel units on the right side of the equation. The remaining unit of measure on the right side of the equation should match the unknown unit of measure on the left side of the equation. 6. Solve the equation. Chapter 7 33 Calculating the Amount to Administer (con’t) Example: The order reads: Prozac Liquid 40 mg daily On hand: Prozac 20 mg/5 mL Find the amount to administer Amount to administer = 10 mL Chapter 7 34 Calculating the Amount to Administer (con’t) Procedure 7-4 Calculating Amount to Administer Using the Formula Method: 1. Determine the desired dose. Determine the dose on hand (H) and dosage unit (Q) D xQ A H 2. Fill the formula •D for the desired dose •H for the dose on hand •Q for the dosage unit in the formula •A for the unknown or the amount to administer Chapter 7 35 Calculating the Amount to Administer (con’t) Procedure 7-4 Calculating Amount to Administer Using the Formula Method (con’t): 3. Cancel the units 4. Solve for the unknown Chapter 7 36 Calculating the Amount to Administer (con’t) Example: The dosage ordered is 500 mg PO q 8 h On hand: Famvir 250 mg/tabs Find the amount to administer Amount to administer = 2 tablets Chapter 7 37 Apply Your Knowledge The amount of the drug to be administered at a single time is called the: a. dosage ordered b. dosage unit c. desired dose d. dosage strength Answer: c. desired dose Chapter 7 38 Apply Your Knowledge True or False If a medication has 300 mg of drug per tablet, the dose on hand is 300 mg. Answer: True Chapter 7 39 Apply Your Knowledge The MAR reads Glucotrol 10 mg PO qd. The desired dose is ____ mg. Answer: 10 mg Chapter 7 40 Apply Your Knowledge Calculate the amount to administer. • Ordered: Prednisone 10 mg PO qid • On hand: Prednisone 5 mg tablets Answer (Using ratio proportion) 5 mg : 1 tablet : : 10 mg : ? tablet 1 x 10 = 5 x ? ?=2 Amount to administer: 2 tablets Chapter 7 41 Methods of Dosage Calculations Each problem that I solved became a rule, which served afterwards to solve other problems. -- Rene Descartes Chapter 7 THE END 42