Part I: Basic Math Review, 1
Number Systems, 2
Arabic System, 2
Roman System, 2
Conversion of Systems, 2
Fractions, 3
Proper, Improper, and Mixed Fractions, 3
Multiplying Fractions, 4
Dividing Fractions, 4
Decimal Fractions, 4
Decimals, 6
Multiplying Decimals, 6
Dividing Decimals, 7
Ratio and Proportion, 7
Percentage, 8
Post-Math Test, 11
Roman and Arabic Numerals, 11
Fractions, 11
Decimals, 12
Ratio and Proportion, 13
Percentage, 13
Part II: Systems, Conversion, and Methods of Drug Calculation, 17
CHAPTER 1: Systems Used for Drug Administration, 18
Metric System, 19
Apothecary System, 23
Household System, 24
CHAPTER 2: Conversion within the Metric, Apothecary, and Household Systems, 28
Units, Milliequivalents, and Percents, 28
Metric, Apothecary, and Household Equivalents, 29
Conversion in Metric and Household Systems by Liquid Volume, 30
Conversion in Metric and Household Systems by Length, 32
CHAPTER 3: Interpretation of Drug Labels, Drug Orders, Bar Codes, MAR and eMAR, Automation of Medication Dispensing Administration, and Abbreviations, 37
Interpretation of Drug Labels, 38
Military Time versus Traditional (Universal) Time, 42 Drug Differentiation, 43 Drug Orders, 44 xiii Unit-Dose Dispensing System (UDDS), 46
Computer-Based Drug Administration (CBDA), 47
Computerized Prescriber Order System (CPOS), 48
Bar Code Medication Administration, 48
Medication Administration Record (MAR and eMAR), 50
Automation of Medication Dispensing Administration, 50
Abbreviations, 52
The Joint Commission (TJC), 52
Drug Measurements and Drug Forms, 54
Routes of Drug Administration, 54
Times of Administration, 55
CHAPTER 4: Prevention of Medication Errors, 57
Preventing Medication Errors, 57
The Rights in Drug Administration, 59
Right Patient, 59
Right Drug, 59
Right Dose, 59
Right Time, 60
Right Route, 60
Right Documentation, 61
Right to Refuse Medication, 61
CHAPTER 5: Alternative Methods for Drug
Administration, 63
Transdermal Patch, 64
Purpose, 64
Types of Inhalation, 65
Purpose, 65
Types, 65
Nasal Spray and Drops, 66
Purpose, 66
Eye Drops and Ointment, 68
Purpose, 68
Ear Drops, 70
Purpose, 70
Pharyngeal Spray, Mouthwash, and Lozenge, 71
Purpose, 71
Topical Preparations: Lotion, Cream, and Ointment, 71
Purpose, 71
Rectal Suppository, 73
Purpose, 73
Vaginal Suppository, Cream, and Ointment, 74
Purpose, 74
CHAPTER 6: Methods of Calculation, 75
Drug Calculation, 76
Method 1: Basic Formula, 76
Method 2: Ratio and Proportion, 78
Method 3: Fractional Equation, 80
Method 4: Dimensional Analysis, 81
Additional Dimensional Analysis (Factor Labeling), 88 xiv Contents
Contents xv
CHAPTER 7: Methods of Calculation for
Individualized Drug Dosing, 93
Calculation for Individualized Drug Dosing, 94
Body Weight (BW), 94
Body Surface Area (BSA or m2), 95
Ideal Body Weight (IBW), 96
Adjusted Body Weight (ABW), 99
Lean Body Weight (LBW), 99
Part III: Calculations for Oral, Injectable, and Intravenous Drugs, 107
CHAPTER 8: Oral and Enteral Preparations with Clinical Applications, 108
Tablets and Capsules, 109
Pill/Tablet Cutter, 109
Calculation of Tablets and Capsules, 111
Liquids, 113
Calculation of Liquid Medications, 113
Buccal Tablets, 115
Sublingual Tablets, 115
Calculation of Sublingual Medications, 115
Enteral Nutrition and Drug Administration, 131
Enteral Feedings, 131
CHAPTER 9: Injectable Preparations with Clinical Applications, 148
Injectable Preparations, 149
Vials and Ampules, 149
Syringes, 149
Needles, 153
Intradermal Injections, 155
Subcutaneous Injections, 155
Calculations for Subcutaneous Injections, 156
Insulin Injections, 159
Types of Insulin, 160
Mixing Insulins, 165
Insulin Pen Devices, 167
Insulin Pumps, 169
Intramuscular Injections, 170
Drug Solutions for Injection, 171
Reconstitution of Powdered Drugs, 173
Mixing of Injectable Drugs, 174
CHAPTER 10: Intravenous Preparations with Clinical Applications, 198
Intravenous Access Sites, 199
Intermittent Infusion Add-On Devices, 202
Direct Intravenous Injections, 203
Continuous Intravenous Administration, 207
Intravenous Infusion Sets, 207
Calculation of Intravenous Flow Rate, 210
Safety Considerations, 210
Adding Drugs Used for Continuous Intravenous Administration, 211
Types of Solutions, 211
Tonicity of IV Solutions, 211
xvi Contents
Intermittent Intravenous Administration, 215
Secondary Intravenous Sets, 216
Adding Drugs Used for Intermittent Intravenous Administration, 216
ADD-Vantage System, 217
Electronic Intravenous Infusion Pumps, 219
Flow Rates for Infusion Pumps and Secondary Sets, 221
Infusion Pumps, 221
Secondary Sets, 221
Part IV: Calculations for Specialty Areas, 239
CHAPTER 11: Pediatrics, 240
Factors Influencing Pediatric Drug Administration, 241
Oral, 241
Intramuscular, 242
Intravenous, 243
Pediatric Drug Calculations, 244
Dosage per Kilogram Body Weight, 244
Dosage per Body Surface Area, 247
Pediatric Dosage from Adult Dosage, 259
Body Surface Area Formula, 259
Age Rules, 260
CHAPTER 12: Critical Care, 270
Calculating Amount of Drug or Concentration of a Solution, 272
Calculating Units per Milliliter, 272
Calculating Milligrams per Milliliter, 272
Calculating Micrograms per Milliliter, 273
Calculating Infusion Rate for Concentration and Volume per Unit Time, 275
Concentration and Volume per Hour and Minute with a Drug in Units, 276
Concentration and Volume per Hour and Minute with a Drug in Milligrams, 276
Concentration and Volume per Hour and Minute with a Drug in Micrograms, 277
Calculating Infusion Rates of a Drug for Specific Body Weight per Unit Time, 279
Micrograms per Kilogram Body Weight, 280
Basic Fractional Formula, 281
Using Basic Formula to Find Volume per Hour or Drops per Minute, 281
Using Basic Formula to Find Desired Concentration per Minute, 281
Using Basic Formula to Find Concentration of Solution, 281
Titration of Infusion Rate, 283
Determine Titration Factor Using Infusion Pump, 284
Increasing or Decreasing Infusion Rates Using Infusion Pump, 284
Determine Titration Factor Using a Microdrip IV Set, 285
Increasing or Decreasing Infusion Rates Using a Microdrip IV Set, 285
Total Amount of Drug Infused Over Time, 288
CHAPTER 13: Pediatric Critical Care, 304
Factors Influencing Intravenous Administration, 305
Calculating Accuracy of Dilution Parameters, 305
Contents xvii
CHAPTER 14: Labor and Delivery, 313
Factors Influencing Intravenous Fluid and Drug
Management, 314
Titration of Medications with Maintenance
Intravenous Fluids, 314
Administration by Concentration, 314
Administration by Volume, 316
Intravenous Loading Dose, 316
Intravenous Fluid Bolus, 318
CHAPTER 15: Community, 322
Metric to Household Conversion, 323
Preparing a Solution of a Desired Concentration, 325
Changing a Ratio to Fractions and Percentages, 326
Calculating a Solution From a Ratio, 327
Calculating a Solution From a Percentage, 327
Preparing a Weaker Solution From a Stronger Solution, 328
Guidelines for Home Solutions, 329
Hydration Management, 330
Calculate Daily Fluid Intake for an Adult, 330
Standard Formula for Daily Fluid Intake, 330
Calculate Daily Fluid Intake for a Febrile Adult, 331
Body Mass Index (BMI), 331
Calculate Body Mass Index Using Two Formulas, 331
Part V: Post-Test: Oral Preparations, Injectables, Intravenous, and Pediatrics, 339
Oral Preparations, 340
Injectables, 346
Direct IV Administration, 352
Intravenous, 353
Pediatrics, 356
Appendix A: Guidelines for Administration of Medications, 369
General Drug Administration, 370
Oral Medications, 370
Injectable Medications, 371
Intravenous Fluid and Medications, 372
Appendix B: Nomograms, 374
References, 377
Index, 381
PART I
BASIC MATH REVIEW
Objectives • Convert Roman numerals to Arabic numerals.
• Multiply and divide fractions and decimals.
• Solve ratio and proportion problems.
• Change percentages to decimals, fractions, and ratio and proportion.
• Demonstrate an understanding of Roman numerals, fractions, decimals, ratio and proportion, and percentage by passing the math test.
Outline NUMBER SYSTEMS
Arabic System
Roman System
Conversion of Systems
FRACTIONS
Proper, Improper, and Mixed Fractions
Multiplying Fractions
Dividing Fractions
Decimal Fractions
DECIMALS
Multiplying Decimals
Dividing Decimals
RATIO AND PROPORTION
PERCENTAGE
POST-MATH TEST
Roman and Arabic Numerals
Fractions
Decimals
Ratio and Proportion
Percentage 2 PART I Basic Math Review
The basic math review assists nurses in converting Roman and Arabic numerals, multiplying and dividing fractions and decimals, and solving ratio and proportion problems and percentage problems. Nurses need to master basic math skills to solve drug dosage problems for the administration of medication.
A math test, found on pages 11 to 15, follows the basic math review. The test may be taken first, and, if a score of 90% or greater is achieved, the math review, or Part I, can be omitted. If the test score is less than 90%, the student should do the basic math review section. Some students may choose to start with
Part I and then take the test.
Answers to the Practice Problems are at the end of Part I, before the Post-Math Test.
NUMBER SYSTEMS
Two systems of numbers currently used are Arabic and Roman. Both systems are used in drug administration.
Arabic System
The Arabic system is expressed in the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These can be written as whole numbers or with fractions and decimals. This system is commonly used today.
Roman System
Numbers used in the Roman system are designated by selected capital letters, e.g., I, V, X. Roman num-
bers can be changed to Arabic numbers.
Conversion of Systems
Roman Number Arabic Number I 1 V 5 X 10 L 50
C 100
The apothecary system of measurement uses Roman numerals for writing drug dosages. The Roman numerals are written in lowercase letters, e.g., i, v, x, xii. The lowercase letters can be topped by a horizontal line, e.g., i, v, x, xii.
Roman numerals can appear together, such as xv and ix. Reading multiple Roman numerals requires the use of addition and subtraction.
Method A
If the first Roman numeral is greater than the following numeral(s), then ADD.
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