1. 53
Math for Pharmacology
Lesson 1:

2. Lesson Objectives
Upon completion of this lesson, students should be able to:
Define and spell the terms to learn for this chapter.
State the differences between the apothecary and metric systems.
Identify metric system prefixes and their values.

3. Lesson Objectives
Upon completion of this lesson, students should be able to:
Convert dosages between the apothecary and metric systems formula.
Identify two methods of calculating drug dosages.

4. Lesson Objectives
Upon completion of this lesson, students should be able to:
Correctly calculate medication dosages using the mathematical conversions.
State four rules for calculating pediatric dosages.

5. Critical Thinking Question
Where in the daily tasks might a medical assistant use math skills? 5

6. Math for Pharmacology Pharmacology Overdose Underdose
Study of medications and drugs, including their forms, intentions for use, and effects
Overdose
Taking too much of a medication
Underdose
When not enough medication is given to achieve the desired effect

7. Mathematics Review Addition and Subtraction Used in drug calculation
Used in everyday tasks within medical office, such as taking inventory and collecting payments

8. Critical Thinking Question
How do people make common addition errors? 8

9. Mathematics Review Multiplication and Division
Used as often as addition and subtraction
Important to have strong knowledge of basic multiplication ("times") tables when working in medical office

10. Mathematics Review Fractions Fraction is a part of a whole number
Numerator (top number)
Denominator (bottom number)
Fraction bar that separates the two

11. Mathematics Review Fractions
Common fractions used in medical field include ½, ⅓, ¼, and ¾
Used often when indicating measurements and dosages
Mixed number made up of both a whole number and a fraction

12. Mathematics Review Decimals
Anything less than the number 1 is often written as a decimal
Fractions can also be written in decimal form
To convert fractions to a decimal, simply divide the numerator by the denominator

13. Mathematics Review Decimal Place Values
When writing and reading decimals, it is necessary to correctly identify decimal point and place value of the number
When speaking or verbalizing decimal values, state decimal placeholder (tenths, hundredths, thousandths) where last digit falls

14. Mathematics Review Equivalents
Equivalents are things that are equal—that have the same value
In mathematics, for example, fraction 3/4 and decimal 0.75 are equivalents
Often, working with a ratio or a decimal is easier than working with equivalent fraction

15. Mathematics Review Leading and Trailing Zero Rules
Important to understand the placement of a zero in a decimal
When writing a decimal number less than 1, you must apply leading zero rule

16. Mathematics Review Leading and Trailing Zero Rules
Trailing zero rule states that it is never appropriate to include a zero after a whole number
These rules used to reduce the number of errors in medicine

17. Mathematical Rules and Guidelines
Adding and Subtracting Fractions
When adding and subtracting fractions, you must have a common denominator
Multiply each fraction by correct multiplier to obtain common denominator
Add the numerators (denominator remains the same)
Reduce final answer to its simplest terms

18. Mathematical Rules and Guidelines
Multiplying Fractions
If numerator of one fraction and denominator of the other fraction have a common divisor, you may cancel out those terms
Multiply all numerators across
Multiply all denominators across
Reduce your answer to its simplest terms

19. Mathematical Rules and Guidelines
Dividing Fractions
Invert the second fraction of the equation, finding its reciprocal
Multiply all numerators across
Multiply all denominators across
Reduce your answer to its simplest terms

20. Mathematical Rules and Guidelines
Convert an Improper Fraction to a Mixed Number
Improper fraction is any fraction with numerator larger than a denominator
Divide the numerator by the denominator

21. Mathematical Rules and Guidelines
Convert an Improper Fraction to a Mixed Number
This becomes the whole number
Remainder (if any) is then placed as new numerator over the denominator to form fractional component of the mixed number
Reduce fractional component to simplest form

22. Mathematical Rules and Guidelines
Convert a Fraction to a Decimal
Divide the numerator by the denominator
Adding and Subtracting Decimals
Always line up the decimals of every number
Add zero (0) placeholders to help keep Numbers aligned

23. Mathematical Rules and Guidelines
Multiplying Decimals
Multiply the numbers as usual
Place zero (0) placeholders as needed
Count total number of decimal spaces to the right of the decimal point for both numbers
Next, place your decimal point this many numbers to left of last number in your answer

24. Mathematical Rules and Guidelines
Dividing Decimals
If your number is not a whole number, move decimal point of divisor the necessary number of spaces to make divisor a whole number
If dividend has a decimal, move it to the right the same number of places as you moved the divisor's decimal point

25. Mathematical Rules and Guidelines
Dividing Decimals
Add zero (0) placeholders as necessary
Divide as usual, and then move decimal directly up in the quotient

26. Mathematical Rules and Guidelines
Convert a Decimal to a Fraction
Simply place the entire number over the value of the decimal placeholder of the last digit of the number
Remember to reduce the final answer to its simplest terms

27. Weights and Measures Two Systems
Apothecary
Metric
Most physicians and medical facilities have moved to metric system
As medical assistant, you must be familiar with both systems
Occasionally, apothecary medication measurements are still used

28. Weights and Measures
Common household measurements, such as teaspoon and tablespoon, still used, although they are not formal medication measurement units

29. Weights and Measures Apothecary System
Considered to be oldest system of measurement
Dry weight measurement was based on the grain (gr)
One grain was equal to the weight of one grain of wheat

30. Weights and Measures Apothecary System
In addition to the grain (gr), other units of dry weight measurement within apothecary system include:
The dram (dr, ℨ)
The ounce (oz, ℥)
The pound (lb)

31. Weights and Measures Apothecary System Fluid Measurements Minims (m)
Fluid dram (fl dr, fl ℨ)
Fluid ounce (fl oz, fl ℥)
Pint (pt)
Quart (qt)
Gallon (gal)

32. Weights and Measures Apothecary System
Common household measurements (ounce, pint, quart, gallon) based on apothecary system
Roman numerals used when numbering in the apothecary system; 3 grains would be gr iii

33. Weights and Measures Apothecary System
Three-fourths of a grain would be gr 3/4
Important to note that the unit of measure in apothecary system is placed before the actual number

34. Weights and Measures Apothecary System
Unit or abbreviation comes before the amount
Example: qt iii, rather than iii qt
Use lowercase Roman numerals to express whole numbers 1 through 10, 15, 20, and 30

35. Weights and Measures Apothecary System
Use Arabic numbers for other quantities.
Example: qt i (one quart), gr 12 (12 grains), gr xx (20 grains)

36. Weights and Measures Apothecary System
Use fractions to designate amounts less than 1
Example: gr 1/2, not 0.5 gr
Symbol ss used to designate the fraction 1/2
Example: pt iiiss (3 1/2 pints)

37. Weights and Measures Metric System
Most commonly used conversion system for dosage calculations
Kilo = 1000 of a unit
Hecto = 100 of a unit
Deka = 10 of a unit
Base unit of 1

38. Weights and Measures Metric System
Most commonly used conversion system for dosage calculations
Deci = 0.1 (one-tenth) of a unit
Centi = 0.01 (one-hundredth) of a unit
Mlli = (one-thousandth) of a unit
Micro = (one ten-thousandth) of a unit

39. Weights and Measures Metric System
Metric conversions are simply accomplished by multiplying or dividing by 1,000
Multiplying by 1,000 would be the same as moving decimal point three places to the right
Dividing by 1,000 would mean that the decimal point moves three places to the left

40. Guidelines for Conversion Within the Metric System
No change is required to change milliliters (mL) into cubic centimeters (cc) because they are equal to each other
To change grams (gm) to milligrams (mg), multiply grams by 1,000 or move the decimal point three places to the RIGHT

41. Guidelines for Conversion Within the Metric System
To change milligrams (mg) to grams (gm), divide milligrams by 1,000 or move the decimal point three places to the LEFT

42. Guidelines for Conversion Within the Metric System
To convert liters (L) to milliliters (mL), multiply liters by 1,000 or move the decimal point three places to the RIGHT
To convert milliliters (mL) to liters (L), divide milliliters by 1,000 or move the decimal point three places to the LEFT

43. Weights and Measures Metric System Dosages
In the metric system, the dosage is written as a decimal number first with the unit of measurement following (2.5 mg)

44. Weights and Measures Metric System Dosages
Commonly used equivalents for apothecary and metric systems are as follows:
Apothecary 1 gr = Metric 65 mg or 0.065g
Apothecary 5 gr = Metric 325 mg or 0.33g

45. Weights and Measures Metric System Dosages
Commonly used equivalents for apothecary and metric systems are as follows:
Apothecary 10 gr = Metric 650 mg or 0.67 g
Apothecary 15 or 16 gr = Metric 1 g
Apothecary 15 or 16 m = Metric 1 mL or cc

46. Weights and Measures Common Household Measures
60 gtts (drops) = 1 teaspoon (tsp)
3 tsp = 1 tablespoon (T)
2 T = 1 oz
4 oz = 1 small juice glass
8 oz = 1 cup or glass

47. Weights and Measures Common Household Measures 16 T or 8 oz = 1 cup
2 cups = 1 pint (pt)
2 pints = 1 quart (qt)
4 quarts = 1 gallon

48. Drug Calculations
Factors involved when calculating correct dose of a drug:
Patient's age
Weight
Current state of health
Other medications patient currently taking

49. Drug Calculations Ratio Method
A ratio establishes a relationship between two quantities
Medical assistant compares amount of drug ordered to amount on hand

50. Drug Calculations Ratio Method
When two ratios are equal, it is a proportion
If you know three of the four numbers for the two ratios in a proportion, you can solve for fourth number by using mathematical principles

51. Drug Calculations Ratio Method
Symbol × is used for the unknown quantity: for example, 10/20 = 1/×
To find unknown quantity, cross-multiply
Multiply top number (numerator) on left side of equal sign (=) by bottom number (denominator) on right side

52. Drug Calculations Ratio Method
Then multiply bottom number (denominator) on left by top number (numerator) on right
Divide result on both sides by number with x

53. Drug Calculations Ratio Method
Another method is to convert 10/20 = 1/x into 10:20::1:x
Multiply extremes (two outer numbers—10 and the x) by each other and the means (two inner numbers—20 and 1) to solve for x, the unknown

54. Drug Calculations Ratio Method
To prove this answer is correct, multiply the extremes and multiply the means
If the answer is correct, they will be equal

55. Drug Calculations Formula Method
Possible to calculate dosages using a very simple formula: D/H x Q
D = desired or ordered dose
H = dose on hand
Q = quantity or unit of the on-hand dose

56. Guidelines for Conversion
To change grains to grams, divide by 15
To change ounces to cubic centimeters (cc) or milliliters (mL), multiply by 30
To change grains to milligrams (mg), multiply by 60

57. Guidelines for Conversion
To change kilograms to pounds, multiply by 2.2
To change cubic centimeters (cc) or milliliters (mL), to ounces, divide by 30

58. Guidelines for Conversion
To change drams to milliliters (mL), multiply by 4
To change cubic centimeters (cc) or milliliters (mL) to minims, multiply by 15 or 16

59. Guidelines for Conversion
To change minims to cubic centimeters (cc) or milliliters (mL), divide by 15 or 16
To convert drams to grams, multiply by 4

60. Calculating Pediatric Dosages
Clark's Rule
Based on weight of the child
Most common calculation of drug dosage for children, especially because the weight of different children at the same age can vary significantly
Pediatric dose = child's weight in pounds/150 pounds x adult dose

61. Calculating Pediatric Dosages
Fried's Law
Applied to children under the age of 1 year
Fried's assumption is that a 12 1/2-year-old child could take an adult dose

62. Calculating Pediatric Dosages
Fried's Law
A fraction of that is taken to figure dosages on a young child
This formula uses 150 months in denominator as the equivalent for 12 1/2 years

63. Calculating Pediatric Dosages
Young's Rule
Used for children who are over 1 year of age
Pediatric dose = child's age in years/child's age in years + 12 × adult dose

64. Calculating Pediatric Dosages
West's Nomogram
Preferred method, particularly for oncology and critical care patients and underweight children
Can be used for both infants and children

65. Calculating Pediatric Dosages
West's Nomogram
Takes into consideration child's body surface area (BSA), which is based on a calculation of child's height and weight and is expressed as m2 (meters squared)

66. FIGURE 53-2 Nomogram chart
FIGURE Nomogram chart. This example shows a line drawn from a child’s height of 100 cm to his weight, 35 lb. The line intersects the BSA at 0.7 M2.

67. Calculating Pediatric Dosages
Body Weight Method
Other method commonly seen in pediatric situations
Uses calculations based on patient's weight in kilograms
Requires converting patient's weight into kilograms
Once child's weight has been converted into kilograms, correct dosage can be calculated

68. Calculating Pediatric Dosages
Body Weight Method
Done by calculating the safe drug dosage in mg/kg (as recommended by reputable drug reference)
Then multiplying that amount by child's weight in kg

69. Questions? 69