Cover
Section I: Review of Math Fundamentals
1. 1 Math Fundamentals: Self‐assessment
2. 2 Review of Key Medical Math Fundamentals: Decimals
  1. 2.1 Relative Values of Decimal Numbers
  2. 2.2 Properly Communicating Decimal Numbers
  3. 2.3 The Rules for the Use of Zero in Decimal Numbers
  4. 2.4 Comparing Decimals – Which Number Is Larger?
  5. 2.5 A Quick Guide to Using Scientific Notation
  6. 2.6 Tips for Adding and Subtracting Decimal Numbers
  7. 2.7 Tips for Multiplying Decimal Numbers
  8. 2.8 Tips for Dividing Decimal Numbers
  9. 2.9 Accurately Rounding Decimal Numbers
  10. 2.10 Chapter 2 Practice Problems
3. 3 Review of Key Math Fundamentals: Fractions
  1. 3.1 Fundamentals of Working with Medical Math Fractions
  2. 3.2 Working with Improper Fractions, Proper Fractions, and Mixed Numbers
  3. 3.3 Equivalent Fractions in Medical Math
  4. 3.4 Simplifying or Reducing Fractions
  5. 3.5 Adding Fractions in Medical Math
  6. 3.6 Subtracting Fractions in Medical Math
  7. 3.7 Multiplying Fractions in Medical Math
  8. 3.8 Dividing Fractions in Medical Math
  9. 3.9 Conversion Between Fractions and Decimals
  10. 3.10 Rounding Fractions in Medical Math
  11. 3.11 Chapter 3 Practice Problems
4. 4 Review of Key Math Fundamentals: Percentages
  1. 4.1 Conversion of Percentages to Fractions
  2. 4.2 Conversion Between Percentages and Decimal Numbers
  3. 4.3 Conversion of Fractions to Percentages
  4. 4.4 Finding Percentages of a Whole
  5. 4.5 Subtracting or Adding the Percentage Fraction of the Whole
  6. 4.6 Determining Percentages Represented by the Fractional Component
  7. 4.7 Chapter 4 Practice Problems
5. 5 Review of Key Math Fundamentals: Finding the Unknown X
  1. 5.1 Analyzing the Problem and Setting up the Equation
  2. 5.2 Addition: Moving Numbers to the Other Side of the Equation
  3. 5.3 Subtraction: Moving Negative Numbers or a Negative Unknown X
  4. 5.4 Finding the Unknown X in Multiplication Problems
  5. 5.5 When the Unknown X is in the Denominator
  6. 5.6 Finding the Unknown X in Division Problems
  7. 5.7 Unknown X Involving Division of Fractions
  8. 5.8 Chapter 5 Practice Problems
Section II: Understanding Units and Labels
1. 6 Measurements Used in Veterinary Medicine
  1. 6.1 Metric Units: The Basics
  2. 6.2 Metric Units of Weight and Mass
  3. 6.3 Metric Units of Volume
  4. 6.4 Metric Units of Length
  5. 6.5 Metric Units of Concentration and Density
  6. 6.6 Nonmetric Units: Household, Apothecary, and Avoirdupois Units
  7. 6.7 Conversion between Quantities of Volume and Mass: Special Cases
  8. 6.8 Converting Between Units: The Proportion and Cancel‐Out Methods
  9. 6.9 Estimating the Answer: Does Your Answer Make Sense?
  10. 6.10 Chapter 6 Practice Problems
2. 7 Understanding Drug Orders and Drug Labels
  1. 7.1 The Dosage Regimen
  2. 7.2 The Dosage Form
  3. 7.3 The Best Practices for Writing Drug Orders
  4. 7.4 Understanding the Drug Label: The Drug Names
  5. 7.5 Understanding the Drug Label: Concentrations and Dosage Forms
  6. 7.6 Understanding the Drug Label: Regulatory Label Information
  7. 7.7 Understanding the Drug Label: Hazards, Storage, and Expiration Dates
  8. 7.8 Chapter 7 Practice Problems
Section III: Dose Calculations
1. 8 Basic Dose Calculations
  1. 8.1 The Basic Steps in Dose Calculation
  2. 8.2 Converting the Animal's Weight into the Units Needed to Calculate the Dose
  3. 8.3 Determining the Dose for the Patient
  4. 8.4 Determining the Amount of Dose Forms Needed per Dose
  5. 8.5 Determining the Number of Dosage Forms Needed to Complete the Dosage Regimen
  6. 8.6 Determining the Cost for Dispensed Medication
  7. 8.7 Using a Syringe with Liquid Dosage Formulations
  8. 8.8 Chapter 8 Practice Problems
2. 9 Intravenous Infusion Calculations
  1. 9.1 Performing IV Infusions and the Use of IV Administration Sets
  2. 9.2 The Basics of Setting IV Fluid Rate Using the Drip Chamber
  3. 9.3 Setting the IV Fluid Rate: Constant Rate Infusions (CRI)
  4. 9.4 Calculating Infusion Rates when Adding Drugs to IV Fluids
  5. 9.5 Calculating Standard IV Fluid Rates
  6. 9.6 Calculating IV Fluid Rate Stop Times
  7. 9.7 Chapter 9 Practice Problems
Section IV: Other Calculations Used in Veterinary Medicine
1. 10 Ratios, Proportions, and Dilutions
  1. 10.1 Ratios and Proportions
  2. 10.2 The Basics of Making a Dilution
  3. 10.3 Making Serial Dilutions
  4. 10.4 Calculating Diluent Needed to Deliver a Specific Dose or Drug Concentration
  5. 10.5 Calculating Dilutions Using the V1 × C1 = V2 × C2 Formula
  6. 10.6 Diluting Percent Solutions
  7. 10.7 Diluting Solutions Expressed as Ratios
  8. 10.8 Making Dilutions with Mixed Types of Concentrations
  9. 10.9 Chapter 10 Practice Problems
2. 11 Additional Calculations Used by Veterinary Professionals
  1. 11.1 Mean, Median, Mode, and Range
  2. 11.2 Converting between Fahrenheit and Celsius
  3. 11.3 Roman Numerals
  4. 11.4 Chapter 11 Practice Problems
Appendix: Answers to Practice Problems
Index
End User License Agreement

List of Tables

Chapter 02
1. Table 2.1 The correct way to read decimal numbers
2. Table 2.2 Examples of numbers converted to scientific notation.
Chapter 03
1. Table 3.1 Examples of improper fractions converted to mixed numbers
2. Table 3.2 Examples of addition of fractions using common denominators
3. Table 3.3 Fractional division is conducted by converting to fractional multiplication operations.
4. Table 3.4 Common fraction to decimal conversions the technician should know.
Chapter 04
1. Table 4.1 Table of conversions between common fractions and the equivalent percentages and decimal numbers
2. Table 4.2 Calculations needed to determine percentage of fractional component of a whole.
Chapter 05
1. Table 5.1 Steps for solving multiplication equations for unknown X
2. Table 5.2 Steps for solving division equations for unknown X
Chapter 06
1. Table 6.1 Commonly used prefixes in the metric system
2. Table 6.2 Rules for writing and speaking in metric units
3. Table 6.3 How to make common metric mass conversions
4. Table 6.4 Conversions commonly used in metric volume calculations
5. Table 6.5 Conversions commonly used in metric linear calculations
6. Table 6.6 Examples of concentrations
7. Table 6.7 Examples of how concentrations might be used to describe the mass of poison or drug per unit of feed
8. Table 6.8 Common conversions between metric and non‐metric units
9. Table 6.9 Common household measurements and their equivalents (US measurements)
10. Table 6.10 Conversion of household measurement of water volume to approximate weight
Chapter 07
1. Table 7.1 Common abbreviations used in veterinary medicine to describe routes of administration
2. Table 7.2 Common abbreviations used in veterinary medicine to describe the dosing interval
3. Table 7.3 Common abbreviations used to describe dosage forms
4. Table 7.4 Example of proprietary names for the veterinary sedative‐analgesic drug xylazine
5. Table 7.5 Examples of proprietary names used to represent other drugs with the same ingredients
6. Table 7.6 Percent solutions with g/100 mL and mg/mL equivalents
Chapter 08
1. Table 8.1 Rounding dose appropriately to nearest half or whole tablet
Chapter 11
1. Table 11.1 Samples of commonly used temperatures in Fahrenheit and Celsius
2. Table 11.2 Examples of Roman numeral representation of numbers containing the digits 4 and 9

List of Illustrations

Chapter 02
1. Figure 2.1 The location of whole numbers and decimal fractions in a decimal number
Chapter 03
1. Figure 3.1 The denominator says into how many parts the whole is divided and the numerator tells how many of the individual parts there are. 1 tablet split into 2 pieces = two ½ pieces
2. Figure 3.2 One half (1/2) of a tablet is a larger piece than one fourth (1/4) of the whole tablet
3. Figure 3.3 Anatomy of a mixed number: a whole number plus a proper fraction
4. Figure 3.4 Two smaller quarter pieces put together equal one half piece
Chapter 06
1. Figure 6.1 1 cubic centimeter (“cc”) is equivalent to 1 mL
2. Figure 6.2 Comparison of 1 m to 1 yard (36 in)
3. Figure 6.3 Comparison of 2.2 pounds to 1 kg
Chapter 07
1. Figure 7.1 A label for the veterinary drug Rimadyl
2. Figure 7.2 Example of USP marking on a drug label
3. Figure 7.3 Drug label for a liquid dosage form
4. Figure 7.4 Drug label for Baytril (enrofloxacin)
5. Figure 7.5 Typical warning label for restricting drug use from animals to be used for human food
6. Figure 7.6 Controlled substance ratings
7. Figure 7.7 Examples of warning labels
8. Figure 7.8
9. Figure 7.9
Chapter 08
1. Figure 8.1 Markings on the barrel of a 3 cc (3 mL) syringe.
2. Figure 8.2 Markings on the barrel of a 6 cc (6 mL) syringe. Note the 0.2 mL increments.
3. Figure 8.3 Markings on the barrel of a 35 cc (35 mL) syringe.
4. Figure 8.4 3 cc syringe filled with 2.7 cc or 2.7 mL of drug.
5. Figure 8.5
6. Figure 8.6
7. Figure 8.7
8. Figure 8.8
9. Figure 8.9
10. Figure 8.10
11. Figure 8.11
Chapter 09
1. Figure 9.1 Intravenous fluid set – complete
2. Figure 9.2 Drip chamber
3. Figure 9.3 Roller clamp
4. Figure 9.4 Slide clamp
5. Figure 9.5 Injection port
Chapter 10
1. Figure 10.1
Chapter 11
1. Figure 11.1 A bell‐shaped curve showing number of dogs exhibiting each percent decrease in heart rate

This edition first published 2019
© 2019 John Wiley & Sons, Inc.

Edition History
Iowa State University Press (1e, 2000); Wiley‐Blackwell (2e, 2009)

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The contents of this work are intended to further general scientific research, understanding, and discussion only and are not intended and should not be relied upon as recommending or promoting scientific method, diagnosis, or treatment by physicians for any particular patient. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of medicines, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each medicine, equipment, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging‐in‐Publication Data

Names: Bill, Robert, author.
Title: Medical mathematics and dosage calculations for veterinary technicians / Robert Bill.
Other titles: Medical mathematics and dosage calculations for veterinary professionals
Description: 3rd edition. | Hoboken, NJ : John Wiley & Sons, Inc., 2019. | Includes index. | Preceded by Medical mathematics and dosage calculations for veterinary professionals / Robert Bill. 2nd ed. 2009. |
Identifiers: LCCN 2018032830 (print) | LCCN 2018033237 (ebook) | ISBN 9781118924136 (Adobe PDF) | ISBN 9781118924143 (ePub) | ISBN 9781118835296 (pbk.)
Subjects: | MESH: Veterinary Drugs–administration & dosage | Drug Dosage Calculations | Mathematics | Handbooks
Classification: LCC SF917 (ebook) | LCC SF917 (print) | NLM SF 919 | DDC 636.089/51–dc23
LC record available at https://lccn.loc.gov/2018032830

Cover Design: Wiley
Cover Images: © DenGuy/E+/Getty Images; © aydinmutlu/E+/Getty Images; © SchulteProductions/E+/Getty Images

1
Math Fundamentals: Self‐assessment

In a medical situation the most beneficial drug can be rendered worthless or dangerous if the veterinarian or veterinary technician does not accurately calculate the dose. As many veterinary professionals can testify, it is not enough to just have a superficial understanding of dosage calculation because superficial knowledge often fails during an emergency situation. The skill of accurately calculating drug dosages or making correct medical math calculations must be deeply ingrained and practiced to be consistently reliable.

Another obligation of professionals is to recognize and accurately identify the limits of their knowledge and to strengthen the weaker areas of their skills or knowledge. To help you define the areas of math and dosage calculation that you need to refresh or review, complete the following self‐assessment exercises. Note that some of the exercises require you to perform the tasks without a calculator. Although a calculator should be used to carry out most dosage calculations, it is also important that the veterinary professional understands how to perform the basic operations manually. They will thereby be able to recognize when an answer to a problem is obviously not accurate (e.g. when the decimal point is misplaced by 1 or 2 places).

For those sections of the self‐assessment that you identify as areas where a review would be useful, work through the chapters and sections of the book to which that section of the self‐assessment exercise refers.

Self‐assessment Exercises

Write each of the following numbers in scientific notation:
1. 23
2. 132
3. 522 178
4. 0.2
5. 0.0452
6. 0.000 067
7. 94.0023
8. 897.010 00
Add or subtract the following decimal numbers, without a calculator:
1. 1.5 + 4 =
2. 9.7 + 1.9 =
3. 6.55 + 7.43 =
4. 0.42 + 0.09 =
5. 0.009 + 4.0 =
6. 7.5 – 2.5 =
7. 9.0 – 3.9 =
8. 23.125 – 1.50 =
9. 0.551 – 0.095 =
10. 0.003 52 – 0.0009 =
11. The veterinarian needs a mixture of the following three drugs to be administered as an anesthetic cocktail: 0.4 mL Drug A, 0.35 mL Drug B, and 1.24 mL of Drug C. What is the final volume of combined drug to be given?
12. Four gerbils are weighed individually. Their masses are 82.0 g, 76.5 g, 92.8 g, and 81.9 g. What is the total weight of all four gerbils?
13. The normal dose for an animal is calculated as 48.7 mg. However, the veterinarian wants to adjust the dose because of changes in the animal's physiology due to the disease being treated. The dose needs to be decreased by 10% (4.87 mg). What is the new dose need for this patient?
14. The veterinarian gives an oral drug order to be added to a bag of IV fluids as follows: “Give twenty‐three point four mL of Drug A and three point one two five mL of Drug B.” What is the total volume (mL) of drugs being added to this bag of IV fluids?
Multiply or divide the following decimal numbers, without a calculator:
1. 2.5 × 5 =
2. 3.0 × 8.35 =
3. 24.75 × 12.35 =
4. 0.02 × 15.5 =
5. 0.003 × 0.0125 =
6. 15 ÷ 2.5 =
7. 2.5 ÷ 1.5 =
8. 35 ÷ 0.5 =
9. 0.25 ÷ 0.125 =
10. 0.010 ÷ 0.0025 =
11. An animal is dispensed 2.5 mg tablets to be given twice daily for six days. What is the total mass of drug that has been dispensed? Give your answer in mg.
12. The veterinarian dispenses 1200 mL of medication to be given equally to 8 calves. How much does each calf get?
13. A laboratory animal colony needs to treat a parasite problem by giving 2.3 mg of a drug to each of the 94 rats in the colony. How many mg of drug is needed to do this?
14. A total of 560 mg of drug needs to be equally divided into two doses per day for a period of one week. How much drug is given in each dose?
15. The veterinarian gives the following drug order: “Dispense one and one‐tenth mL per day for ten days.” What total volume (mL) is to be dispensed?
16. A veterinarian gives the following oral drug order: “42.75 mL of drug needs to be divided into equal doses for these three cats.” How much does each cat get?
Round the following decimal numbers to the nearest 1/100th and the nearest 1/10th, without a calculator:
1. 20.394 =
2. 9.682 =
3. 3.233 =
4. 29.452 =
5. 413.675 =
6. 5.956 =
7. 36.789 22 =
8. 0.255 =
9. 0.093 =
10. 1200.019 22 =
11. The veterinarian gives the following oral drug order: “Give fifteen point seven five mg but round it to the nearest tenth.” How much do you give?
12. The dose calculation for a patient is 37.56 mg. What would the dose be, correctly rounded to a whole number? Is this dose closer to the 40 mg tablet size or the 35 mg tablet size?
Simplify the following fractions to their lowest form (e.g. 6/8 = 3/4), without a calculator:
Add or subtract the following fractions, without a calculator:
Multiply the following fractions, without a calculator:
Divide the following fractions:
Convert the following fractions to decimal numbers (e.g. 1/2 = 0.5):
Convert the following decimal numbers to the common fraction (e.g. 0.5 = 1/2):
1. 0.25 =
2. 0.333 =
3. 0.75 =
4. 0.125 =
5. 1.5 =
6. 2.500 =
Convert the following percentages to commonly used fractions (e.g. 50% = 1/2):
1. 25% =
2. 75% =
3. 33.3% =
4. 10% =
5. 80% =
Convert the following percentages to decimal numbers:
1. 25% =
2. 79% =
3. 100% =
4. 6% =
5. 0.2% =
6. 0.0087% =
Convert the following decimal numbers to percentages:
1. 0.5 =
2. 0.45 =
3. 1.00 =
4. 0.103 =
5. 0.900 23 =
Convert the following fractions to percentages (e.g. 1/2 = 50%):
Answer the following percentage questions:
1. What is 25% of a 200 mg dose?
2. A veterinarian wants to use 50% of 25 mg calculated dose. How much drug (in milligrams) would they be giving?
3. What percentage is 80 pounds of 400 pounds?
4. A veterinary technician has drawn up 15 mg of the total 60 mg drug dose that they need to give an animal. What percentage of the total dose have they drawn up so far?
Solve for the missing X in each of the following:
1. 15 + X = 30 + 45
2. 5 + 10 = 7 + X
3. X + 2.5 = 5.25 + 1.05
4. 40 − X = 65 − 38
5. 6.5 − 2.3 = 7.8 − X
6. X − 14.2 = 53.4 − 41.9
Solve for the missing X in each of the following:
1. 2 × 6 = 3 × X
2. 30 × X = 120 × 2
3. X × 25.5 = 43.2 × 12.25
4. 25 ÷ 5 = 10 ÷ X
5. 300 ÷ X = 12.5 ÷ 8.125
6. X ÷ 25 = 0.5 ÷ 0.75
Solve for the missing X in the following proportions: