Practical Pharmaceutical Calculations

Michael Bonner, David Wright

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781315346861
• Edition: 2
• Topic: Medicine
• Subtopic: Public Health, Administration & Care

Understanding practical pharmaceutical calculations is essential for healthcare professionals. Even simple errors in calculation can have serious - and possibly fatal - consequences. Fully revised and updated, with entirely new chapters and a focus on basic arithmetic, this best-selling practical guide begins by explaining simple units of measurements and expressions of concentration, followed by demonstrations of how straight-forward calculations can be used to estimate individual patient dosages. At the end of each chapter there are self assessment calculations, with fully worked answers - ideal for revision and self-assessment. With the book and free downloads you can always have the guide on hand when you need it most.

1
Fundamentals of arithmetic and algebra

By the end of this chapter, you should be able to:

• develop a concept of magnitude
• perform basic arithmetic operations.

Develop a concept of magnitude: is the answer a credible one?

As you work through this book, one of the skills you should develop is an ability to estimate a credible answer. This is, of course, not only useful in the context of this book but also in everyday life. Consider the following situation:

In a clothes shop you buy five items priced at: £17, £22, £18, £23 and £19. How much do you estimate you will pay?

Is it: £25, £50, £100, £200 or £400?

If you look at the cost of each of the five items you will see that each costs approximately £20, so the total cost should be roughly £20 × 5 = £100. If you can readily estimate the cost, then you can detect if you are ever over- or under-charged. If you can’t readily estimate the cost, you could quickly become poorer!

Let us now consider a more pharmaceutical example:

A patient weighing 61 kilograms needs a drug dosage of 20 milligrams per kilogram of body weight. Estimate how much total drug the patient should receive.

Is it: 200, 400, 600, 800 or 1200 milligrams?

The patient weighs approximately 60 kilograms so requires approximately 20 mg × 60. (If you can’t readily multiply by 60, multiply by 10 and then by 6.) If the patient weighed 10 kilograms he would need 20 mg × 10 = 200 milligrams.

A 60-kilogram patient therefore requires 200 mg × 6 = 1200 milligrams. So, a credible answer is 1200 mg.

A credible estimate is not a wild guess, but rather a sensible answer based on the information presented to you. In this instance the true answer was of course 1260 milligrams, but you are much less likely to cause harm to the patient with a reasonable estimate within 5% of the correct answer than one with an error of 50%, 100% or 900%.

You may think that you are unlikely to give an answer which is incorrect by 900% but a 10-times overdose (or underdose) is just that. Such an error is more likely to occur when a student relies heavily upon a calculator, and then accepts the calculator’s answer without question. Therefore, we urge you to practise the examples throughout this book without the use of a calculator and, when you believe you have answered a question, ask yourself, ‘Is this a credible answer?’

The rest of this chapter is devoted to a brief overview of basic arithmetic and algebra necessary for successful completion of subsequent chapters. If there is any part of this first chapter that you have difficulty with, we suggest you refer to the very useful textbook The Sciences Good Study Guide.¹

Fractions

Fractions express proportions of whole items. For example, you have a disc drive with 400 GB storage capacity and have 100 GB of files stored on it. The fraction of the storage space used on the disc can be written as

$\frac{100}{400}$

The number above the line is known as the numerator, while the number below the line is known as the denominator. In this example you can consider 100 to be the ‘proportion’ of the ‘whole’ 400. If the numerator is larger than the denominator the fraction is called a ‘vulgar fraction’, e.g.

$\frac{18}{4}$

Equivalent fractions

If ...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Contents
• Preface
• About the authors
• 1 Fundamentals of arithmetic and algebra
• 2 Units of measurement
• 3 Understanding concentrations
• 4 Formulae for extemporaneous dispensing
• 5 Dilution, mixing and incorporation
• 6 Dose calculations
• 7 Clinical pharmacokinetics
• 8 Suppository calculations
• Summary test
• Answers to the self-assessment questions
• Answers to the summary test