Essential Math and Calculations for Pharmacy Technicians

Indra K. Reddy, Mansoor A. Khan

• Publisher: Routledge
• Year: 2017
• eBook ISBN: 9781351988629
• Topic: Medicine
• Subtopic: Applied Mathematics

Accurately calculating medication dosages is a critical element in pharmaceutical care that directly affects optimal patient outcomes. Unfortunately, medication dosage errors happen in pharmacies, in hospitals, or even at home or in homecare settings everyday. In extreme cases, even minor dosage errors can have dire consequences. Careful calculations are essential to providing optimal medical and pharmaceutical care.

Essential Math and Calculations for Pharmacy Technicians fills the need for a basic reference that students and professionals can use to help them understand and perform accurate calculations. Organized in a natural progression from the basic to the complex, the book includes:

Roman and Arabic Numerals

Fractions and decimals

Ratios, proportions, and percentages

Systems of measurement including household conversions

Interpretation of medication orders

Isotonicity, pH, buffers, and reconstitutions

Intravenous flow rates

Insulin and Heparin products

Pediatric dosage

Business math

Packed with numerous solved examples and practice problems, the book presents the math in a step-by-step style that allows readers to quickly grasp concepts. The authors explain the fundamentals simply and clearly and include ample practice problems that help readers become proficient. The focus on critical thinking, real-life problem scenarios, and the self-test format make Essential Math and Calculations for Pharmacy Technicians an indispensable learning tool.

1 Working with Roman and Arabic Numerals

Roman Numerals

The Romans were active in trade and commerce, and from the time of learning to write they needed a way to indicate numbers. The system they developed lasted many centuries and is still in use in some areas, including pharmacy. Roman numerals are used with the apothecary’s system of measurement to designate quantities on prescriptions. In the Roman system of counting, letters of the alphabet (both uppercase and lowercase) such as I or i, V or v, and X or x are used to designate numbers.

Examples:

4=IV12=XII19=XIX25=XXV49=XLIX or IL

Rules

In the usage of Roman numerals, the following set of rules applies:

1. Roman numerals have no symbol for zero. This makes computations very difficult.
2. The numbers are written starting from the largest number on the left, and adding smaller numbers to the right. When Roman numeral(s) of lesser value follow one of a greater value, they are added.
   Examples:
   VII = 5 + 1 + 1 = 7
   XVI = 10 + 5 + 1 = 16
   CLX = 100 + 50 + 10 = 160
3. When a Roman numeral of lesser value precedes one of a greater value, it is subtracted from the greater value numeral. However, this rule only works for one small numeral before one larger numeral. For example, IX is 9 but IIX is not 8; it is not a recognized Roman numeral.
   Examples:
   IV = 5 − 1 = 4
   IX = 10 − 1 = 9
   XL = 50 − 10 = 40
4. When a Roman numeral of a lesser value is placed between two greater values, it is first subtracted from the greater numeral placed after it, and then that value is added to the other numeral(s) (i.e., subtraction rule applies first, then the addition rule).
   Examples:
   XXIX = 10 + 10 + (10 − 1) = 29
   XIV = 10 + (5 − 1) = 14
5. There is no place value in this system. For example, the number III is 3 and not 111. Also, when a Roman numeral is repeated, it doubles its value; when a Roman numeral is repeated three times, it triples its value.
   Examples:
   I = 1; II = 2; III = 3
   X = 10; XX = 20; XXX = 30
   Note. Roman numerals may not be repeated more than three times in succession. For example, 4 is written as IV but not as IIII, and 40 is written as XL but not XXXX.
6. When possible, largest value numerals are used. For example, 15 is written as XV but not as VVV.
7. Roman numerals are sometimes combined with the abbreviation for one half, ss. The abbreviation should always be at the end of a Roman numeral. Generally, Roman numerals are written in lowercase when used with ss, such as iss to indicate 1½.

Selected Roman numerals and their Arabic equivalents are shown in Table 1.1.

Arabic Numerals

Arabic numerals are the most common symbols used to represent numbers. Every number can be expressed in Arabic numerals by using 10 basic symbols, alo...

Table of contents

• Cover Page
• Half title
• Title Page
• Copyright Page
• Contents
• Preface
• Chapter 1 Working with Roman and Arabic Numerals
• Chapter 2 Using Fractions and Decimals in Pharmacy Math
• Chapter 3 Using Ratios, Proportions, and Percentages in Dosage Calculations
• Chapter 4 Applying Systems of Measurements
• Chapter 5 Interpreting Medication Orders
• Chapter 6 Identifying Prescription Errors and Omissions
• Chapter 7 Working with Liquid Dosage Forms
• Chapter 8 Working with Solid Dosage Forms
• Chapter 9 Adjusting Isotonicity
• Chapter 10 Working with pH and Buffers
• Chapter 11 Dealing with Reconstitutions
• Chapter 12 Determining Milliequivalent Strengths
• Chapter 13 Dealing with Calories
• Chapter 14 Determining Intravenous Flow Rates
• Chapter 15 Working with Insulin and Heparin Products
• Appendix A Working with Temperature Conversions
• Appendix B Working with Capsule Dosage Forms
• Appendix C Dealing with Pediatric Dosages
• Appendix D Pharmacy Business Math
• Index