53 Math for Pharmacology Lesson 1:

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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)

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

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

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

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

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)

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

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 = 0.001 (one-thousandth) of a unit Micro = 0.00001 (one ten-thousandth) of a unit

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

FIGURE 53-2 Nomogram chart FIGURE 53-2 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.

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

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

Questions? 69