Transcript Chapter_034

Pharmacology Math
Chapter 34
Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved.
1
Learning Objectives
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Define, spell, and pronounce the terms listed
in the vocabulary.
Apply critical thinking skills in performing
patient assessment and care.
Demonstrate methods for verifying the
accuracy of calculations.
Differentiate among the terms used in
dosage preparation.
Summarize the important parts of a drug
label.
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2
Learning Objectives
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Describe and perform conversions among the
various systems of measurement.
Calculate the correct dose of a drug using the
standard formula.
Determine accurate pediatric doses of
medication.
Diagram how to reconstitute powdered
injectable medications.
Specify the legal responsibilities of a medical
assistant in calculating drug dosages.
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3
Drug Management
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The medical assistant must be absolutely
certain that the medication prepared and
administered to the patient is exactly what the
physician ordered.
Although drugs often are delivered by the
pharmacy in unit dose packs, the dosage
ordered may differ from the dose on hand.
In this case the medical assistant must be
prepared to calculate the correct dose
accurately.
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4
Dosages
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There is no margin of error in drug
calculations. Even minor mistakes may result
in serious complications.
The MA must take meticulous care in
calculating all drug dosages.
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5
Drug Labels
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Accurately read the drug label to determine if the
physician order and the packaged drug use the
same system of measurement.
Drug name
Brand name – capitalized and typically in bold print;
copyright protected so it is followed by either an ® or ™
symbol.
 Generic name – lowercase letters under the brand name
in smaller print. If a medication is on the market for a
long time the generic name may be the only one listed; if
ordered from the pharmacy and stocked as a generic
drug, then only the generic name will be on the label

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6
Drug Labels
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Dosage strength – under the name of the
drug; how much of the drug is contained in
each of the identified units. This is what you
must compare with the physician’s order to
determine if a calculation will be needed
Route or method of administration
Manufacturer’s name and expiration date
Lot number
National drug code that identifies that
particular drug
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7
Drug Label Figure 34-1
From Brown M, Mulholland JM: Drug calculations: process and problems for clinical practice, ed 7, St Louis, 2004, Mosby.
Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved.
8
Drug Label Figure 34-1
From Brown M, Mulholland JM: Drug calculations: process and problems for clinical practice, ed 7, St Louis, 2004, Mosby.
Copyright © 2011, 2007, 2003, 1999 by Saunders, an imprint of Elsevier Inc. All rights reserved.
9
Label Terms
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Strength: The potency of the drug. Stated as a
percent of drug in the solution (2% epinephrine), as
a solid weight (g, mg, lb, gr), or as a milliequivalent
or unit.
Dose: The size or amount of medication in the drug
unit. Could be in ml, tsp, or a number of tabs. For
example, the label reads “Imitrex, 6 mg/0.5 ml,” which
means there are 6 mg of Imitrex in each 0.5 ml.
Solute: Pure drug dissolved in a liquid to form a
solution.
Solvent (Diluent): The liquid, usually sterile water,
that dissolves the solute.
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10
Mathematics Basics: Fractions
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A fraction is part of a whole
It is a way of dividing a whole unit into parts
The top number in a fraction is the numerator
and the bottom number is the denominator
Proper fraction – numerator is smaller than
the denominator (1/3, ¾, 5/9, 8/23)
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11
Fractions
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Improper fraction – numerator is equal to or
greater than the denominator (5/3, 7/4, 9/3,
27/15)
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Numerator is so large that it is equal to or greater
than 1
To convert improper fractions into whole numbers
divide the numerator by the denominator
Fractions should be reduced to their lowest
terms
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Reduce a fraction by dividing the numerator and
the denominator by the largest number that goes
into each equally
Example: 5/15 – five divides into fifteen three
times which means 5/15 can be reduced to 1/3
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12
Fractions
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Multiplying fractions – multiply the numerators
and denominators of each fraction and
reduce the answer to its lowest terms.
 Example: ⅓ × ¾ = 3/12 = ¼
Dividing fractions – invert the divisor (that is
the second fraction) before you multiply the
numerators and denominators.
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Example: ⅓ ÷ ¾
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⅓ × 4/ 3 = 4/ 9
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13
Mathematics Basics: Decimals
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A decimal is similar to a fraction except it is
expressed in units of tenths (0.1), hundredths
(0.01), and thousandths (0.001)
Convert fractions into decimals to perform
drug calculations

To convert a fraction into a decimal simply divide
the numerator by the denominator
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14
Decimals
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If a decimal is less than a whole number it is
crucial that a zero is placed before the
decimal point so a medication error is
avoided.
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Example: If you are supposed to administer .5 ml
of a medication and the zero is not placed before
the decimal point, you may miss the decimal point
and think that the correct dose is 5 ml.
A zero should never be placed after the
decimal point of a whole number.

Example – 1.0 ml may be misinterpreted as 10 ml.
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15
Mathematics Basics: Percents
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A percent is a number expressed as part
of 100.
Decimals are converted into percentages by
dividing the number by 100 or by simply
moving the decimal point two spaces to
the right.
Example:
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0.25 = 25/100 = 25%
0.03 = 3/100 = 3%
0.005 = 5/1000 = 0.5%
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16
Mathematics Basics: Ratio and
Proportion
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A ratio is an expression of a fraction or division problem.
Shows the relationship of the numerator to the
denominator.
A comparison of two ratios is a proportion.
Example:
4 = 1 or 4:16 = 1:4
16 4
 This is read as 4 divided by 16 equals 1 divided by 4, or 4 is to 16
as 1 is to 4
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Physician’s order may be a ratio different from that of the
medication that is in stock.
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To determine the correct proportion for administration compare
the ordered ratio with the available ratio (what is in stock).
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17
Proportions: Unknown Element
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In calculating dosages, mathematic
proportions are used, but with one element
unknown. We must solve for that unknown,
or x.
Example:
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4=1
16 x
Solve the problem by cross-multiplication
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An equals sign (=) between two fractions means
the equation should be cross-multiplied.
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18
Unknown Element
Cross multiplication example:
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4=1
4x = 16
16 x
To find the value of x divide the number of x
(4x) by itself on both sides of the equation,
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4x ÷ 4 = 1x
16 ÷ 4 = 4
Therefore: x = 4 and 4 = 1
16 4
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19
Methods for Checking Your Answer
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Check your answer by multiplying the means or middle
numbers of the equation and the extremes or the outer
numbers of the equation.
If correct the multiplication of the means and extremes will be
equal.
Example: 3:5 = 6:x
Cross-multiply the equation: 3 = 6
5 x
3x = 30 (divide each side by 3 to determine what 1x is)
x = 10
The equation is: 3:5 = 6:10
To check the accuracy of your equation, multiply the means
or middle numbers (5 × 6 = 30) and the extremes or outer
numbers (3 × 10 = 30). Answers are equal so you have the
correct proportion.
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20
Rounding Calculations
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If you calculate a tablet dose as 1.75 tabs but you only
have whole tablets available, check your calculation for
accuracy, then check the stocked supply of the drug to
make sure no other dosages are available.
If the calculation is correct and there are no other
dosages of the drug available, round your answer to
the nearest amount that matches the dose available.
If the calculation is 0.5 or greater, then round up to the
next whole number. Check with the physician before
administering a rounded dose of medication.
Usually round to the nearest tenth; perhaps round to
the nearest hundredth with pediatric doses.
Can only give a partial dose of a tablet if it is scored.
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21
Three Steps for Correct Dosage
1. Based on the type of system printed on the label,
determine if the physician’s order is in the same
mathematical system of measurement.
 If the systems vary (the order is in teaspoons but
the label states the medication is to be prepared
in milliliters), then accurately convert the order to
match the system on the label.
2. Perform the calculation in equation form, using the
appropriate formula.
3. Check your answer for accuracy, and ask someone
you trust to confirm your calculations.
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22
Accurate Dose
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All three of these steps must be completed
before the medication is dispensed and
administered.
Confirm your calculations with the physician if
you have any doubt about their accuracy.
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23
Systems of Measurement: Table 34-3
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Physician may order medication in a strength
that is different than the one identified on the
drug label.
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Example: orders 2 gr of the drug but the label states
there are 120 mg/tab
Before determining how many tablets to
administer, the MA must first convert the
strength of the physician order to match the
strength of the dose on the label since that is
the medication that is available for
administration.
There are three different systems of
measurement: metric, apothecary, and
household.
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24
Metric System
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Metric system of weights and measures is
used throughout the world as the primary
system for weight (mass), capacity (volume),
and length (area).
Based on units of 10
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Each larger unit of measure is 10 times the previous
unit of measure.
Fractions are written as decimals (1½ liters =
1.5 liters).
Cubic centimeter = milliliter (1 cc holds 1 ml).
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25
Metric Units of Measurement
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Amount or volume of a liquid medication is
expressed in milliliters (ml).
Weight or strength of a solid medication is
expressed in grams (g).
Length is expressed in meters (m)
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One inch is equal to 2½ centimeters (cm)
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26
Conversions to Smaller Units
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Units in the metric system are converted by
moving the decimal point in multiples of 10.
When going from larger to smaller units of
measure, as in converting grams to milligrams,
the answer will be a larger number, so move
the decimal point three places to the right.
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0.35 g = 350 mg
OR multiply 0.35 g × 1000 = 350 mg
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27
Conversions to Larger Units
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If converting smaller units of measurement
to larger ones as in milliliters to liters, the
answer will be a smaller number, so move the
decimal point three places to the left.
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150 ml = 0.15 liter
OR divide 150 ml by 1000 = 0.15 ml
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28
Rules for Metric System Conversions
1. To convert from a smaller unit of measurement to a
larger unit of measurement move the decimal point
three places to the left. Your answer will always be a
smaller number. Example: 62.4 mg = 0.0624 g.
2. To convert from a larger unit of measurement to a
smaller unit of measurement move the decimal point
three places to the right. Your answer will always be
a larger number. Example: 1.7 g = 1700 mg.
3. To prevent dosage errors use a zero before a
decimal point to clarify its presence (0.15 mg) but
never leave a zero after a decimal point (15.0) since
it may not be noticed and an error may result.
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29
Metric System Equivalents

The following equivalents can be used to make
conversions in the metric system.
1 kg = 1000 g
1 g = 1000 mg
1 mg = 0.001 g or 1/1000 g
1 kl = 1000 liters
1 liter = 1000 ml
1 ml = 0.0001 liter or 1/1000 liter
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30
Metric System Conversions
Convert the following problems:
2.5 g
=
_____ mg
0.21 g =
_____ mg
150 mcg =
_____ mg
1.7 g
=
_____ mg
3 mg
=
_____ mcg
0.28 liter =
_____ ml
950 ml =
_____ liter
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31
Apothecary System
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In the apothecary system the basic unit of weight
for a solid medication is the grain (gr) and the
basic unit of volume for a liquid medication is the
minim (M).
As in the metric system, these two units are
related: the grain is based on the weight of a single
grain of wheat, and the minim is the volume of
water that weighs 1 gr.
Either symbols or abbreviations are used; for
example, 11/2 drams might be written Diss or
dr 11/2.
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32
System-to-System Equivalents:
Table 34-3
15 gr = 1 g = 1000 mg
5 gr = 0.3 g = 300 mg
1 quart = 1000 cc
1 fl oz = 30 ml
1 fl dr = 4 ml
15 M = 1 ml
1 M = 0.06 ml
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33
Household Measurements
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This system of measurement is important for the
patient at home who has no knowledge of the
metric or apothecary systems, although it is not
completely accurate; it should never be used in
the medical setting
Basic measure of weight is the pound (lb) and of
volume is the drop (gtt).
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1 gtt = 1 M
60 gtt = 1 tsp
3 tsp = 1 Tbsp (tablespoon)
2 Tbsp = 1 oz
8 oz = 1 cup
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34
Formula Conversion Method
Drug Have × Wanted = Unit wanted in new system
Have
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Drug Have—unit of measurement that is on the label
Wanted—amount or strength ordered by physician
Have—conversion (15 gr = 1 g)
Example physician order: Administer 30 gr of Lasix
Label: 1 g Lasix/tab
You must convert the ordered unit of measurement
(grains) to match the unit of measurement on the
drug label (grams)
1 g (label) × 30 gr (physician order)
= 2 g = 2 tabs
15 gr (conversion factor)

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35
Converting Metric Order to
Household Measurement

Order: 30 ml of an oral antibiotic. What household
unit of measurement is this equal to?
1 tablespoon equals 15 ml; divide the order by the conversion
factor
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30 ml ÷ 15 ml = 2 Tbsp
Or set the problem up as an equation with the
ordered amount on the left side of the equation and
the conversion factor on the right side:
30 ml × 1 Tbsp
15 ml
Cross-multiply, and the ml unit cancels out, so you
have:
30 × 1 Tbsp
= 30 Tbsp = 2 Tbsp
15
15
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36
Conversion Problems
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A patient with risk factors for heart disease is told
to take a baby aspirin equivalent to gr 5 every
morning. How many milligrams is the patient
taking?
A patient scheduled for urinary tract diagnostic
tests needs to drink a minimum of 2 liters of
water over the next 12 hours. How many ounces
should the patient drink?
A pediatric patient is ordered 8 ml of amoxicillin
qid for 10 days. What is the equivalent dose in
household measurements?
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37
Calculating Dosages: Standard
Formula

Available strength = Available amount
Ordered strength
Amount to give
Available strength – strength of the drug that is
written on the medication label
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
Ordered strength – dose ordered by the physician
Available amount – amount of drug that must be
used to deliver the strength identified on the label
If you get confused about where to place the
numbers in the equation, remember that like units of
measurement must be placed on the same side of
the equation.
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38
Standard Formula Example
Order: Administer 250 mg of cefalexin IM
Available: A vial marked 500 mg/ml
 Available strength identified on the label is 500
mg/ml; there are 500 mg of cefalexin in each
milliliter of the medication
 Ordered strength is 250 mg
 Available amount is the amount of the drug that
must be used to deliver the strength identified
on the label; label states "500mg/ml," which
means there are 500 mg of cefalexin in every
milliliter of solution
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39
Example
Available strength = Available amount
Ordered strength
Amount to give
500 mg = 1 ml
250 mg x ml
The milligram units in the numerator and denominator on the left
side of the equation cross each other out. Cross-multiply the
equation.
500x = 250 ml
To determine what x equals you must divide each side of the
equation by 500.
500x = 250 ml
500
500
x = 1/2 ml = 0.5 ml
Solution: Administer 0.5 ml of cephalexin
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40
Alternative Formula: D/H × Q

Regardless of which formula is used, the
answer will be the same
D—desired dose (the physician’s order)
H—what is on hand (the dosage strength
listed on the medication label)
Q—quantity in the unit (identified on the label
as one tablet, 5 ml, etc.)
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41
Sample Problem: D/H × Q

Example: Administer 500 mg of an antibiotic; the
label states 250 mg/2 ml
D × Q = 500 mg (physician order) × 2 ml (label quantity)
H

250 mg (dosage strength on hand)
The milligram quantities cancel out:
500 × 2 ml = 2 × 2 ml = 4 ml
250
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42
Sample Problem: D/H x× Q

Problem: The physician orders 50 mg of
Imitrex and the label states "25 mg/tab."
Dose ordered × Quantity = Amount to give
Dose on hand
Or: D × Q = Amount to give or x
H
50 mg × 1 tab = 2 tabs
25 mg
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43
Sample Problems
 Physician
orders 10 ml of a drug and the
drug label states there are 20 ml/cc.
 Physician orders 4 g of a drug and the
medication label states there are 2 g/tab.
 Physician orders 6 mg of a drug and the
medication label reads there are 12
mg/scored tab.
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44
Pediatric Calculations
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Pediatric doses are different from those in
other age groups because of multiple factors.
Pediatric doses are much more accurate
when based on weight; children can vary
greatly in size and body weight.
Factors used in calculating pediatric doses
are either body surface area or weight.
Must be especially careful in calculating
dosages for children; even a minor
miscalculation may be dangerous.
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45
Clark's Rule
This rule is based on the weight of the child.
 This system is much more accurate, because children
of any age can vary greatly in size and body weight.
Pediatric dose = Child's weight in pounds × Adult dose
150 pounds
(Adult doses are based on average adult weight of
150 lbs)

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46
West's Nomogram

West's nomogram uses a calculation of the
body surface area (BSA) of infants and young
children to determine the pediatric dose.
Pediatric dose = BSA of child in m2 × Adult dose
1.7 m2
(Average adult BSA = 1.7 m2.)
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47
West’s Nomogram
From Behrman RE, Kliegman
R, Jenson HG, editors: Nelson
textbook of pediatrics, ed 16,
Philadelphia, 2000, Saunders.
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48
Dosages Based on Body Weight
1. Carefully weigh the child before beginning to
calculate the dose to make sure you have an
accurate weight.

Convert weight to kilograms by dividing the number of
pounds by 2.2 kg
2. Calculate the total daily dose of the medication.
3. Calculate a single dose of the drug based on
how frequently the medication is ordered
throughout the day.
4. After calculating the amount of a single dose,
compare the ordered amount to the drug label. If
needed, apply the standard formula to calculate
the amount of the medication that should be
administered.
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49
Reconstitution
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Reconstituting powdered injectables requires adding
an amount of solvent (as recommended on the drug
label) to a vial of powdered or crystal medication.
Once the solute and solvent are mixed in the vial, a
solution of medication is formed with a strength
based on equivalents printed on the drug label.
Once the medication is mixed, carefully read the
label to determine how much of the drug must be
withdrawn to equal the physician’s order.
Use the standard conversion formula to determine
the accurate dose for administration.
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50
Legal and Ethical Issues
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Must have complete mastery in calculating
dosages
If there is ever any doubt about the accuracy of a
calculation have the calculation checked
The medical assistant is legally responsible for
his or her own actions
State laws vary; physician may have the authority
to delegate responsibility for giving medications
MA acts as the “agent” of the physician
 MA responsible and accountable for acts performed
and may be subject to penalties

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51