Download Pharmacy Calculations: Review Disclosures Objectives Objectives

10/7/2013
Pharmacy Calculations: Review
Sean Tran, PharmD
Clinical Pharmacist
Self Regional Healthcare
[email protected]
Disclosures
I do not have (nor does any immediate
family member have) a vested interest in
or affiliation with any corporate
organization offering financial support or
grant monies for this continuing
education activity, or any affiliation
with an organization whose philosophy
could potentially bias my presentation.
October 10, 2013
Objectives
Objectives

Review fractions and their importance in
pharmaceutical calculations

Perform calculations accurately and
efficiently

Demonstrate ability comparing and
expressing ratios in multiple formats

Comprehend a variety of mathematical
notations

Understand and manipulate the
commonly used calculation methods
Dosing errors
Gallup Poll 2012
Institute of Safe Medication Practices (ISMP),
October 2009:

“Please tell me how you would rate the
honesty and ethical standards of people in
these different fields…”

Very high, high, average, low, or very low
◦ Oseltamivir oral suspension shortage contributed
to dosing errors
◦ Commercially manufactured Tamiflu® (Roche) is
provided in a 12 mg/mL suspension
◦ Pharmacists have begun to compound the
product on an emergency basis
◦ Compounding directions found in the labeling,
however, result in a 15 mg/mL oseltamivir base
concentration
ISMP Medication Safety Alert. October 15, 2009
Gallup Historical Trends. 2012
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10/7/2013
Honesty/Ethics in Professions
Fractions

“Parts of a whole”

Numerator (part) over
Denominator (whole)
NOT
Gallup Historical Trends. 2012
Fractions

Fractions
Example:

1 , 2 , 3.
2
7
5
◦ One whole tablet = 1000 mg
◦ One-half tablet
=
◦ One-fourth tablet =
1
2
= ____ mg
1
4
= ____ mg

Fractions
Mixed

◦ 5 =
2

Comparing
1 ? 3
8
8
Improper
5 , 8 , 11 .
2
7
5
Fractions

Proper
5 ? 3.
7
7

Comparing
1
1
25
10
5
7
3.
8
Fractions as decimals = DIVISION
7 = 7 ÷ 10 =
10
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Adding and Subtracting Fractions

Must get same denominator (common
denominator)
1
5
+
3
10
=
3 10
1
5
=
+ 3 =
10
3 10

=
Multiply across numerator and
denominator
1
5
=
Dividing Fractions

Multiplying Fractions
x
3 =
10
7 x
10
4 =
5
Scientific Notation
Multiply by the reciprocal (inverse)
1
5
÷ 3
10
=
1
5
x
=
2
5
÷ 3
7
=
2
5
x
=
Used to express very large or small
values
 “How many times we multiply or divide
by 10 to get the actual number”

=

Ex:
◦ 100,000 = ________
◦ 0.0006 = _______
Ratios and Percents


Percent Strengths
Ratios are fractions and visa versa

◦ ½ = 1:2 = 0.5
◦ 1/3 = ___ = 0.333
◦ 10/3 = ___ = 3.333

The “whole” is “100%”, thus
◦ ½ = 1:2 = 0.5 = ___
◦ 1/3 = 1:3 = 0.333 = ___
◦ 10/3 = 10:3 = ___
30% means 30 parts in 100 parts
◦ 30:100 = 30/100 = 0.3
Solutions
◦ Percents represent “grams per 100 mL”
◦ 1% lidocaine contains ___ gram of lidocaine
per 100 mL of solution
◦ May be expressed as 1:100, 1/100, or 0.01
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Percent Strengths

Solids
Proportions
An expression of equality between two
ratios
 Notated by a double colon ( :: ) or an
equal sign between two ratios

◦ Percents represent “grams per 100 g”
◦ 0.5% hydrocortisone cream contains ___
gram of hydrocortisone per 100 grams of
cream
◦ May be expressed as 0.5:100, 0.5/100, or 0.005
Cross Multiplication
a:b = c:d
Practice makes Perfect!
3:4 = 15:20
3:4 :: 15:20
3 = 15 .
4
20
Proportions

Three of the four values must be known

Numerators must have the same unit of
measurement

Denominators must have the same unit
of measurement
Pharmacy Calculations: Review
Sean Tran, PharmD
Clinical Pharmacist
Self Regional Healthcare
[email protected]
October 10, 2013
4
10/7/2013
Roman Numerals
I
V
X
L
C
D
M
1 kilogram (kg)
1 hectogram (hg)
1 dekagram (dag)
1 gram (g)
1 decigram (dg)
1 centigram (cg)
1 milligram (mg)
1 microgram (mcg)
1 nanogram (ng)
=
=
=
=
=
=
=
Standard units
= 16 ounces (oz)
ISMP Statement on Metric Units

Metric measurements in prescription
directions
◦ All healthcare professionals
◦ Pharmacy computer systems
◦ e-prescribing systems

= 1000 grams
= 100 grams
= 10 grams
= 1 gram
= 0.1 gram
= 0.01 gram
= 0.001 gram
= 0.000,001 gram
= 0.000,000,001 gram
Standard/Metric Conversions
3 teaspoons (tsp) = 1 tablespoon (tbsp)
2 tablespoons (tbsp)
= 1 fluid ounce (fl oz)
8 fluid ounce (fl oz)
= 1 cup
2 cups
= 1 pint (pt)
2 pints (pt)
= 1 quart (qt)
4 quarts (qt)
= 1 gallon (gal)
1 pound (lb)
Metric Prefixes
Supported by FDA, CDC, and Consumer
Healthcare Products Association
1 teaspoons (tsp)
1 tablespoon (tbsp)
1 fluid ounce (fl oz)
1 cup
1 pint (pt)
1 quart (qt)
1 gallon
=
=
=
=
=
=
=
5 mL
15 mL
30 mL
240 mL
480 mL
960 mL
3840 mL
Standard/Metric Conversions
1 ounce (oz)
1 pound (lb)
2.2 pound (lb)
1 inch (in)
=
=
30 g
=
454 g
=
1 kg
2.54 cm
°F = [(9/5) °C] + 32
or
°F = (1.8 x °C) + 32
ISMP Press Release. October 2011
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10/7/2013
DEA Checksum

Dr. Alfred Yang, M.D.

AY 3456781

How to check that this may be valid?
DEA Checksum

Always begin with two letters and followed
by seven digits

First letter usually designates type of
authority of the holder
◦ A or B for primary-level practitioner
◦ M for mid-level practitioner
◦ F for foreign country

DEA Checksum
Second letter is the first letter of the
prescriber’s last name
DEA Checksum

Add the first, third, and fifth digits

Dr. Alfred Yang, M.D.

Add the second, fourth, and sixth digits

AY 3456781

Double the sum obtained in Step 2

Add the results of Steps 1 and 3. The last
digit of this sum should match the last
digit of the DEA number
Ratio-Proportion Method

Convert 2300 mg to grams
Dimensional Analysis

Convert 486 mg to grams
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Dimensional Analysis

Convert 4.5 liters to milliliters
Weight-based dosing
A patient weighs 60 kg and she is to receive a
medication of 15 mg/kg. What will her dose
be?
Concentrations and Dilutions
Concentrations and Dilutions
You are instructed to make 1000 mL of a
0.225% w/v solution. You have in stock a
concentrate of 23.4%. How much of the
concentrate will you use, and how much
diluent will be needed?
Step 1: Determine how many grams there
will be in the final product
Concentrations and Dilutions
Concentrations and Dilutions
Step 2: Determine how much of the
concentrated solution is needed to
provide the desired number of grams
Step 3: Determine how much diluent will
be mixed with the concentrated solution
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10/7/2013
Practice makes Perfect!
Pharmacy Calculations: Review
Sean Tran, PharmD
Clinical Pharmacist
Self Regional Healthcare
[email protected]
October 10, 2013
8