Assessment of Mathematical Calculation Skills Needed for Pharmacy Technicians

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Chapter 1

Assessment of Mathematical Calculation Skills Needed for Pharmacy Technicians

Objectives

• Explain why proficiency in basic mathematical skills is essential for pharmacy technicians and other health occupations

• Use medical and pharmaceutical abbreviations

• Assess basic mathematical skills needed to proficiently perform calculations in a pharmaceutical setting

Key Words

Active ingredients

Chemicals in pure, undiluted forms that affect body function

Ambulatory care

Patient care in an outpatient setting; health care provided on an outpatient basis so that those who are treated in a health care facility depart on the same day as treatment

Anatomy

Study of the body structure and body organs

Apothecary system

One of the oldest measurement systems used to calculate drug orders using such measurements as grains and minims

Chemistry

Study of elements, their compounds, and the molecular structure and interactions of matter

Inpatient

Patient who has been admitted to a health care facility such as a hospital for at least a 24-hour or overnight stay

Metric system

Decimal measurement system considered to be the international standard for scientific and industrial measurements, using grams, liters, and meters

Microbiology

Study of microscopic organisms

Pharmacology

Study of drugs, their uses, and their interactions with living systems

Physiology

Study of the processes and functions of the human body

Psychology

Study of behavior and the functions and processes of the mind, as related to the social and physical environment

Round

To express a number to its nearest place value such as tenths, hundredths, thousandths

Pretest

Interpret the following abbreviations.

1. #, lb _____________________

2. ↓_____________________

3. npo _____________________

4. ↑_____________________

5. gtt _____________________

6. qid _____________________

7. q4h _____________________

8. mL _____________________

9. hs _____________________

10. fl _____________________

11. tbsp, T _____________________

12. mcg _____________________

*13. U _____________________

*These abbreviations are found on the TJC Do Not Use List and ISMP’s List of Error-Prone Abbreviations, Symbols, and Dose Designations due to medication safety issues. They should not be used. You are being tested on them here because these abbreviations may still appear in the pharmacy setting.

14. cap(s) _____________________

15. gr _____________________

16. noc _____________________

17. OTC _____________________

18. non rep _____________________

19. bid _____________________

20. qh _____________________

21. q2h _____________________

22. kg _____________________

23. IM _____________________

24. IV _____________________

25. ad lib _____________________

26. _____________________

27. tid _____________________

*28. qod _____________________

29. rep _____________________

30. qs _____________________

31. prn _____________________

32. tab _____________________

33. ung _____________________

34. syr _____________________

35. inj _____________________

36. supp _____________________

37. elix _____________________

38. _____________________

39. _____________________

40. _____________________

41. qam _____________________

42. tsp, t _____________________

43. po _____________________

44. _____________________

45. _____________________

46. qpm _____________________

47. stat _____________________

48. q12h _____________________

49. qd _____________________

50. _____________________

51. TO _____________________

52. q _____________________

53. _____________________

54. _____________________

After completing this exercise, note the abbreviations that you missed and start learning them. You will use these daily in your duties as a pharmacy technician and you must be proficient using these abbreviations.

The Need for a Pharmacy Technician to Have Mathematical Skills

Pharmacology is the study of medications and their uses. It is a science that draws from many disciplines such as anatomy, physiology, chemistry, microbiology, and psychology. Medications are powerful in treating conditions and diseases when prepared and used appropriately. When a drug is not prepared accurately, it may become a potentially deadly chemical. With many conditions and prescriptions, the difference between toxic and curative may only be the careful calculation of the correct dose or dosage of the drug.

All chemicals used as medications, or drugs, are the basis of pharmacology. Different chemical preparation does not contain the same concentration of active ingredients in solid or liquid form. Rather, each drug has its own distinct concentration of active ingredient in a dose. This safe amount of medication has been tested and given acceptable limits by the U.S. Department of Health and Human Services’ Food and Drug Administration (FDA). The FDA is also responsible for the U.S. Pharmacopeia and the National Formulary—manuals that provide the exact ingredients found in medications and the strengths of medications that may be prescribed in the United States. Therefore each prescription has its own dose, and each time a prescription is written the dose must be calculated for that prescription on the basis of the patient’s age, medical condition, weight, and gender.

Pharmacy technicians must calculate the amount of medication necessary to provide each dose. Pharmacy technicians must also ensure that there are sufficient numbers of doses for the desired length of time as prescribed by the physician. Although math is not a basic pharmacology science, it is used daily in preparation of medications whether in an inpatient setting or an ambulatory care setting, such as a pharmacy where the prescription is prepared for the person to take at home. Math is used on a daily basis in all calculations of doses, dosages, and the administration of medications.

This mathematical responsibility that accompanies the preparation of medications is one that must be taken seriously so that dangerous drug levels are not reached. Ethically, you, as a pharmacy technician, must know your level of mathematical skills and must understand the language of the profession by using abbreviations that accompany prescriptions. You must be familiar with acceptable limits—both minimum and maximum—of medications that you are preparing to dispense. Legally, you are responsible for the medications you prepare, although a pharmacist double-checks the medications. Therefore legally, ethically, and morally, you are responsible for your actions, which are heavily dependent on mathematical skills. The course of pharmacology covers the skills required to master acceptable dosages and the expected results of the medication. This text deals with the mathematical skills necessary for the safe administration of the amount of medication prescribed for the patient. The effects of medications on the body are found in another course.

Then why is calculation so important? It does not matter if the correct medication is prescribed or ordered if calculations of medicine to be given for the weight, age, and route of administration are not correct. Calculations are the important steps that you as a pharmacy technician check and recheck for the correct dosage so that patient safety is maintained. To perform pharmaceutical calculations, you must have the math skills covered in this text.

Basic fundamental math skills are necessary in dosage calculation. Fractions, decimals, and whole numbers are used to obtain the correct amount of medication to be given. These skills are used for dosage calculation in the three measurement systems—household measures such as drops, teaspoons, and tablespoons, which are used almost daily because these measurements are easily understood in the United States; metric system measures such as grams, liters, and meters, which are used throughout the world for common measures; and the apothecary system such as grains, drams, and ounces, which has been the basis of pharmacology since Greek and Roman times but is now used less often. You must understand all systems of measurement and be able to convert among these systems to prepare prescriptions for administration.

Special mathematical conversions that are not directly related to medication dosage are also necessary. The conversion between 24-hour time and military time is a necessary skill, because military time is often used in an inpatient setting for medication administration. The standard 24-hour time is used in most ambulatory care situations, so the ability to give the correct time in either place is necessary. Conversions between Fahrenheit and Celsius temperatures and the use of Arabic versus Roman numerals are also important in prescription reading. Clearly, many factors are necessary to be sure the math for pharmacology is accurate and used correctly.

Interpreting the Abbreviations Used in Medical Language

Pharmacology also has a language of its own, including shorthand, that allows physicians and other health professionals to avoid writing an entire order. Interpretation of this shorthand is a necessary component for properly dispensing prescriptions and educating patients as they take medications at home. Abbreviations are used to refer to the route or method of administration, the frequency with which a drug is to be given, and to general terms such as those found in measurement systems or those related to food and sleep. These abbreviations as well as their interpretation need to be memorized. Chapter 6 discusses using abbreviations to interpret drug orders, but learning abbreviations should start now to ensure success in interpreting orders and prescriptions later.

Routes of Administration

Parenteral

IM—intramuscularly

SC, SQ, Subq—subcutaneously

IV—intravenously

ID—intradermally

By Mouth

PO, po—by mouth (per os in Latin)

SL, subling—sublingually

For ease of learning

“q” means every

“id” means the number of times in a day (in die)

“c” means cibus, or food, in Latin

Forms of Administration

What Are Your Basic Math Skills?

You use basic math skills daily to perform calculations in the pharmaceutical world. Many of the skills required for calculating doses and dosages are simply the basic arithmetic of daily living taught in elementary school. However, they may become the source of frustration when described as “math” or when these skills have not been used for an extended time.

Understanding whole numbers, fractions, decimals, percentages, Roman numerals, ratio and proportion, and basic problem solving is essential to perform calculations. Basic insertion of numbers into formulas and then solving for an unknown are other skills that you will use daily. These skills are necessary for safe and accurate calculation of medication doses and dosages for the patients.

During practice exercises throughout the text, you may use a calculator if your instructor permits, but remember that a calculator may not always be available in pharmacy situations. Practicing the math skills that you may not have used for years will sharpen your thinking skills to perform calculations with confidence. Using math skills without a calculator is a way to increase your analytical skills—skills that enable you to solve equations and take components of a whole to form relationships among its parts. Analysis of pharmacological problems is an important step in ensuring accurate calculations with each medication order. If your answers seem incorrect, always check your answers. Calculations are analytical skills that will increase with use.

Prerequisite skills of adding, subtracting, multiplying, and dividing whole numbers are essential before you can begin drug calculations. You must also be able to work with decimals, fractions, ratios/proportions, and percentages. Following is a self-test to be used as a tool to help you determine your math skill strengths and weaknesses. It is also an indicator of your readiness to proceed through the text. Proficiency in these basic math concepts is gauged by attaining a grade of 90% or better. In Chapter 2 you may skip basic skills in which you are proficient, but do not skip any part that gives you difficulty on this test. Having proficiency in basic math skills is of utmost importance.

General rules for taking the self-test are as follows:

• Allow yourself at least 1 hour to take the test. Each question is worth 2 points. Thus you may miss 5 questions and achieve 90%. If all the questions you miss are similar, please take time to use the materials in Chapter 2 for review of this material. In this scenario, you may pass the test yet not understand a basic math principle.

Self-Test of Proficiency in Basic Math Skills

Directions

1. Figure all decimals to three places but round answers to two places, so 1.454 would become 1.45 and 7.5685 would become 7.57.

2. Always express fractions in their lowest possible terms; for example, 4/8 should be expressed as 1/2.

3. Complete ratio and proportion problems to the lowest terms (e.g., 5 : 10 should be reduced to 1 : 2).

4. Do your work on paper, without a calculator, and keep your paperwork attached so that, if you made an error you can return to the paper and find the mistake.

Basic Math Skills Proficiency Self-Test

1. Express the following sum in Arabic numerals: XXV + LX =	_____________________
2. 156.90 + 368 =	_____________________
3. 4.65 – 3.056 =	_____________________
4. 3.50 × 43.5 =	_____________________
5. $12.56 + $152.47 + $4.98 + $68.08 =	_____________________
6. $52.43 × 0.25 =	_____________________
7. 0.7 ÷ 0.0035 =	_____________________
8. 78 + 0.186 =	_____________________
9. +=	_____________________
10. 25 − 13 = (express in Roman numerals)	_____________________
11. $15.43 × 25 =	_____________________
12. 5025 − 4995 = (express in Roman numerals)	_____________________
13. 1932 ÷ 102 =	_____________________
14. + ++ =	_____________________
15. =	_____________________
16. × 150 =	_____________________
17. 0.6% of 36 =	_____________________
18. Express 0.4 as a fraction.	_____________________
19. Express 0.006 as a %.	_____________________
20. of 20 =	_____________________
21. + =	_____________________
22. − =	_____________________
23. ÷ =	_____________________
24. Which fraction has the greatest value? 1/150, 1/200, 1/500	_____________________
25. Which decimal has the least value? 0.012, 0.12, 0.0125	_____________________
26. Change 3/4 to a percentage.	_____________________
27. Change to a decimal.	_____________________
28. × 60 =	_____________________
29. =	_____________________
30. Which has the greatest value? 3.75, ,	_____________________
31. If a medication container holds 20 tablets, how many containers would you need for 120 tablets?	_____________________
32. A prescription is written for 150 tablets. How many containers containing 50 tablets will it take to fill the prescription?	_____________________
33. A prescription is written for a solution to contain 10% of an active ingredient. How many milliliters of active ingredient would be necessary in a 100-mL solution?	_____________________
34. If 1 inch contains 2.54 cm, how many centimeters are in 10 inches?	_____________________
35. Express 70 : 350 in its lowest terms.	_____________________
36. Solve for x. x = 120	_____________________
37. Solve for x. × 350 = x	_____________________
38. 7 × −5 =	_____________________
39. l g = 1000 mg. How many milligrams are in 5.5 g?	_____________________
40. If one kg equals 2.2 lb, how many kg are in 88#?	_____________________
41. 906.2 × 1.34 =	_____________________
42. If one kg equals 2.2 lb, how many pounds are in 11 kg?	_____________________
43. Express 4% as a ratio in its lowest term.	_____________________
44. =	_____________________
45. A stock bottle of medicine contains 500 tablets. How many prescriptions of 25 tablets can be filled with that bottle of medication?	_____________________
46. Subtract the following and express in Roman numerals. XIX − XIV =	_____________________
47. 3.6 ÷ 0.0005 =	_____________________
48. $4.28 + $5.65 + $0.78 + $15.39 =	_____________________
49. 195.46 − 35.86 =	_____________________
50. =	_____________________

After grading this test, look at the problems you missed. If you did not score 90% or higher, continue working on basic skills in Chapter 2. If you missed a group of problems that are related and you scored 90% or higher, review your areas of weakness. Be sure your basic mathematical skills are adequate for learning the more advanced skills that are used in pharmaceutical calculation. Self-confidence in your math skills will make learning less frustrating and calculating math fun. Be fair with yourself and spend the time necessary for basic mathematical skills.