Index
in Pharmacy CalculationsA
abbreviations
in compounding, 58, 141
Latin, 58–60, 61, 111
metric system, 30
on prescription labels, 58–60, 140–141
abuse of prescription drugs, risk of, 56
accuracy, 4
in measuring doses, 38–39
practice problems, 5, 145
addends, 15
addiction of prescription drugs, risk of, 56
addition
of fractions, 18–19
order of operations in, 21
practice problems, 22–24, 147–149
review of, 15–16
for solving equations, 68–70
for translating word problems into equations, 71
aliquots, 113–114
alligation, 104–107
alligation alternate, 105–107
alligation grid, 106
alligation medial, 104, 105, 106, 107
amino acid solutions, 100
amoxicillin pediatric drops, 81, 82–83
apothecary, 37
apothecary system, 37–38, 140
conversions from, 37–38, 40–42, 140
measuring doses accurately, 38–39
solving problems using, 39–40
Arabic numerals, 8
“as needed” prescription, 60
assets, long- and short-term, 132
average inventory value, 131–132
average wholesale price (AWP), 131
avoirdupois system, 37–38
B
base 10 system, 9–10
body surface area (BSA), 93–94
body weight
body surface area and, 93–94
dosing based on, 91–93
boiling point of water, 48, 49
business math
average wholesale price, 131
depreciation, 132
gross profit, 130
inventory management, 131–132
markup, 130
net profit, 130
practice problems, 133–134, 172–174
profit, 129
revenue, 129
wholesale acquisition cost, 131
C
calculator
to calculate decimal fractions, 21
to calculate quotients, 17
calibrated, defined, 38
calibrated measurement devices, 38–39
carboplatin injection, 81
cefazolin, 31
Celsius, Andres, 49
Celsius system of temperature measurement, 49
centi, 30, 139
centigrade, 48–49
“check-sum” number, 57
commutative operations, 71
compound, defined, 58
compounding
abbreviations used in, 58
alligation to solve problems in, 104–107
of concentrated solutions and dilutions, 102–104
conversion factors in, 40
directions for, 55, 58
errors in (see medication errors)
extemporaneous, 101, 111
formulas (see compounding formulas)
metric measurements in, 30
percent error in, determining, 114
proportion method in, 84
ratios in, 79–80, 84
sterile, 58, 89–90, 102, 119–120
compounding formulas, 111–114
aliquots in, 113–114
Latin abbreviations in, 58
master formula record, 111–112
percent error in, determining, 114
practice problems, 115–116, 168–170
reducing and enlarging, 112–113
concentrated solutions, 102–104
alligation, 104–107
“as is” delivery to patients, 103
dilutions, 102–104
concentrates, 102
concentrations
defined, 100
as ratios, 80–81
controlled substances, 56
Controlled Substances Act, 56
conversion factors, 40–42
conversions
in apothecary system, 37–38, 40–42
cancelling units in, 41
charts for, 38, 41, 140
conversion factors in, 40–42
decimal points in, 31–32
dimensional analysis in, 33
in metric system, 31–33
practice problems, 43–44, 150–151
problems that require, 39, 41–42
proportion equations used in, 84
between systems of measurements, 40–42
time, 48
critical thinking to solve problems
equations in, 67–70
practice problems, 73–74, 158–160
word problems, 70–72
cubic centimeter, 31
D
days’ supply, calculating, 60–61
DEA registration numbers, 56–57
deci, 30, 139
deciliter (dL), 102
decimal fractions
defined, 20–21
denominator of, 20–21
fractions written as, 21
percent values written as, 99–100
place value and, 9–10
decimal points
in metric conversions, 31–32
in place value, 9–10
in rounding numbers, 10
rules for writing, 9–10
decimal system, 9–10
delayed-release, 65
denominator, 17–21
depreciation, 132
dextrose, 104, 107
diabetes management, 95
diethylene glycol, 55
difference, 16
digits
in decimal fractions, 20–21
in rounding numbers, 10
digoxin, 10, 91
dilutions, 102–104
practice problems, 108–109, 165–168
dimensional analysis, 33, 90
directions for use, on labels, 58
discount, 130–131
discount rate, 130–131
dividend, 17
division
of decimals, 9
of fractions, 18
order of operations in, 21
practice problems, 22–24, 147–149
review of, 16–17
for solving equations, 68–70
for translating word problems into equations, 71
writing, 17
division symbol, 17
divisor, 17
dose, defined, 89
dosing. see medication dosing
dosing regimen, defined, 89
dosing spoons, 38–39
dropper, calibrated, 38–39
Drug Enforcement Administration (DEA), 56–57
Durham-Humphrey amendment, 55
E
electrolytes, 102, 121–122, 123
electronic health record or database, 30
epinephrine, 83–84
equal sign, 21, 67–68, 70, 71
equations
defined, 21, 67
to solve problems, 67–70
translating word problems into, 70–72
variables in, 67–70
equivalent weights, 122–123
expenses, 129
expressions, 21, 70–71
extemporaneous compounding, 101, 111
extremes, 84
F
factors, 16–17
cancelling, 18
defined, 16
finding, 16
prime numbers, 17
Fahrenheit, 48–49
Fahrenheit, Daniel, 48
Federal Food, Drug, and Cosmetic Act, 55
flumazenil, 81
Food and Drug Administration, 55
format, of labels, 56–57, 61
formulas. see compounding formulas
fraction bar, 17
fractions. see also decimal fractions
converting to percents, 99–100
defined, 17
denominator in, 17–21
numerator in, 17–21
percent values written as, 99–100
reciprocal of, 18, 69
safe compounding and, 18
simplifying, 18
working with, 17–20
writing as decimals, 21
freezing point of water, 48, 49
frequency of administration, on labels, 56, 58
G
gentamicin, 91–92
graduated cylinder markings, 10
gram (mass/weight), 29, 30
gross profit, 130
H
height. see length/height
heparin, 94
high-risk concentrates, 102
hospital order forms, labeling on, 58, 62
hospital pharmacy practice, 107
household measurements, 38–41, 140
conversions from, 37–38, 40–42, 140
measuring doses accurately, 38–39
problems that require conversions, 41–42
solving problems using, 39–40
weight and volume, 38
hydrocortisone, 101
I
improper fractions, 19–20
infusion. see injection and infusion
infusion flow rates, 123–124
infusion pumps, 124–125
injection and infusion
infusion flow rates, 123–124
infusion pumps, 124–125
IV piggyback bags, 82, 92, 120
medication errors, 119–120
milliequivalents and millimoles, 121–125
practice problems, 126–127, 170–172
reconstituting medications, 120–121
valence and equivalent weights, 122–123
inpatient deaths, due to medication errors, 4
inscription, 58, 139
insignificant digits, 10
insulin doses, measuring and calculating, 94–95
integers, 9, 13
International System of Units (SI). see metric system
international units, 94–95
intravenous (IV) administration. see also injection and infusion
infusion flow rates, 123–124
infusion pumps, 124–125
piggyback bags, 82, 92, 120
intravenous infusion flow rates, 123–124
inventory management, 131–132
inventory value, 131–132
ions, 121–122
irrational numbers, 9
“is” as equal sign, 71
IV administration. see intravenous (IV) administration
K
kilo, 30, 139
L
label for counting. see numbers
labeling
on hospital order forms, 58, 62
on measurement devices, 38
on prescriptions (see prescription labels)
Latin abbreviations on prescription labels, 58–60, 61, 111
leading zero, 9, 10, 13
least common denominator (LCD), 19
length/height, in metric system, 29, 30
license classification, on labels, 56
Linnaeus, Carolus, 49
liter (volume), 29, 30–31
loading dose, 94
long-term assets, 132
lorazepam, 10
M
markup, 130
markup rate, 130
mass. see weight
master formula record, 111–112
mathematics, 8
means, 84
measurements. see also dosing
accuracy of, 4
apothecary system, 37–38
avoirdupois system, 38
converting between systems of, 40–42 (see also conversions)
household, 38–41
metric, 29–33 (see also metric system)
practice problems, 43–44, 150–151
precision in, 4
rounding numbers, 10
temperature, 48–49
time, 47–48
medical terminology, 59–60, 140–141
medication dosing. see also measurements
accuracy in measuring, 38–39, 62
based on body surface area, 93–94
based on body weight, 91–93
errors in (see medication errors)
for insulin, 94–95
international units for measuring, 94–95
patient-specific factors in, 3
practice problems, 96–97, 163–165
problems, common, 89–91
medication errors
acceptable error rate, 113
checking and double-checking calculations to avoid, 120
conversions and, 41, 42
deaths due to, 4
defined, 4
estimating before calculating to avoid, 42
impact of, 4
in insulin doses, 94
in pediatric patients, 92
percent error, determining, 114
place value and, 9
preventing, 8
proportion equations and, 83
ratios and, 80
reasonableness and, checking for, 67
in reconstituting medications, 120
roman numeral conventions and, 8
units of measure and, numbers without, 8
units of measure and, relationship between, 40
“when in doubt, throw it out,” 119
medication forms, 62
medication orders, 56, 58
medicine cup, calibrated, 38–39
meter (length/height), 29, 30
metric system, 29–33
conversions from, 31–33, 140
gram (mass/weight), 29, 30
liter (volume), 29, 30–31
meter (length), 29, 30
practice problems, 34, 150–151
prefixes, meanings, factors, and abbreviations, 30
micro, 30, 139
military time, 47–48
milli, 30, 139
milliequivalent (mEq), 121–125
milligram, 31
atomic weight expressed as, 121
milligrams percent, 102
milliliter, 31
millimole (mmol), 121–125
minimum weighable quantity (MWQ), 113–114
mole (mol), 121–122
molecular formulas, 121
multiplication
of decimals, 9
of fractions, 18
order of operations in, 21
practice problems, 22–24, 147–149
review of, 16–17
for solving equations, 68–70
for translating word problems into equations, 71
N
natural numbers, 9
net profit, 130
nitroprusside, 102
nomograms, 93–94
NovoLog, 95
numbers
defined, 7–8
practice problems, 11–12, 145–147
relationship among, 9
rounding, 10
number systems, 9–10
place value, 9–10
rational and real numbers, 9
numerals, 8–9
converting, 8–9
with decimal points, rules for writing, 9–10
defined, 8
practice problems, 11–12, 145–147
systems of, 8–9
numerator, 17–21
O
order of operations, 21, 71
outpatient
deaths due to medication errors, 4
pharmacies, 38–39, 58
prescriptions, 38, 61, 89–90
over-the-counter (OTC) drugs, 55
P
parentheses, in order of operations, 21
parts per million (PPM), 80, 102
patient information, on labels, 58
pediatric patients, dosing for
based on body surface area, 93
based on body weight, 91–93
percent error, 114
percent strengths, 99–102
defined, 100
labeling, 100
milligrams percent, 102
parts per million, 102
percent volume-in-volume, 102
percent weight-in-volume, 100–101
percent weight-in-weight, 101
practice problems, 108–109, 165–168
strength, defined, 100
percent volume-in-volume (v/v), 102
percent weight-in-volume (w/v), 100–101
percent weight-in-weight (w/w), 101
pharmacies
hospital, 107
retail, 129
place value, 9–10
potassium chloride (KCl), 100, 102, 121, 122–123
precision, 4
prescriber information, on labels, 56–57, 139
prescription
defined, 55
interpreting and transcribing, 58–62
legal requirements of, 56
parts of, 56–58, 139
practice problems, 63–64, 155–158
quantities and days’ supply, calculating, 60–61
prescription labels
abbreviations on, 58–60
concentration on, of liquid or semisolid preparation, 80–81
DEA numbers on, 56–57
directions for use, signa or sig, 58
format, 56–57, 61
frequency of administration on, 56, 58
on hospital order forms, 58, 62
inscription and subscription on, 58
license classification on, 56
measurements in directions on, 38–39
patient information on, 58
percent strengths on, 100
preparing, 61–62
prescriber information on, 56–57
quantities and days’ supply on, 60–61
requirements for, 61–62
route of administration on, 56, 58, 62
translating, 61
on unit-dose packaging, 62
prime factor, 18
prime numbers, 17, 18
product, 16
profit, 129
proportion equations
defined, 81
practice problems, 85–86, 160–162
practice with, 82–84
ratios in, 81–84
to solve for an unknown value, 83
solving, steps in, 81–84
purchase price, 130
Q
quantities, calculating, 60–61
quotient, 17
R
ratio and proportion method, 81–82, 84
rational numbers, 9
ratios
defined, 17, 79
drug concentrations as, 80–81
drug strengths as, 80–81
fractions as, 17
percent values written as, 99–100
practice problems, 85–86, 160–162
practice with, 80
in proportion equations, 81–84
recognizing, 79–81
safe compounding and, 18
solving, steps in, 81–84
writing, 80
ratio strength, 79
real numbers, 9
reasonableness, checking for, 67, 72
reciprocal, 18, 69
reconstituting medications, 120–121
remainder, 17, 20
retail pharmacies, 129
revenue, 129
Roman numerals, 8–9
rounding numbers, 10
route of administration, on labels, 56, 58, 62
Rx symbol, 58
S
saline solutions, 100
selling price, 130
short-term assets, 132
signa, sig, 58, 62, 139
single-dose packages, 62
sliding scale dosing, 95
smart IV pumps, 125
sodium chloride (NaCl), 103–104, 121–122
solute, 100
solution, 100
solvent, 100
sterile compounding, 58. see also injection and infusion
concentrated solutions and dilutions, 102
infusion pumps, 124–125
IV infusion flow rates, 123–124
medication errors, 89–90, 119–120
milliequivalents and millimoles, 121–125
reconstituting medications, 120–121
stock solutions, 102
strengths. see also percent strengths
defined, 100
as ratios, 80–81
subscription, 58, 139
subtraction
of fractions, 18–19
order of operations in, 21
practice problems, 22–24, 147–149
review of, 15–16
for solving equations, 68–70
for translating word problems into equations, 71
sulfonamides, 55
sum, 15, 16
superscription, 139
syringe
calibrated, 38–39
markings, 10
T
temperature, 48–49
conversions, 48, 49
measuring, 48–49
practice problems, 50, 154–155
time measurement, 47–48
practice problems, 50, 154–155
to-be-determined volume, 89–90
tobramycin, 82
topical medications, 58, 62
total, 15, 16
total parenteral nutrition (TPN), 104, 107, 122, 123
trailing zero, 9–10,13
triamcinolone, 106–107
turnover rate, 131–132
U
unit-dose packaging, 62
United States Pharmacopeia-National Formulary (USP-NF), 113
unknowns. see variables
V
valence, 122–123
vancomycin, 10, 83
variables
defined, 67
in equations, 67–70
in measuring drug doses, 94
proportion equations to solve for, 83
in word problems, defining, 70
volume
accuracy in medication dosing, 38–39
in apothecary system, 37–38
converting between systems of measurement, 30–31
in household measurements, 38
in metric system, 29, 30–31
variations in, 38
W
weight, 30
accuracy in medication dosing, 38–39
in apothecary system, 37–38
atomic, of electrolytes, 121
body (see body weight)
converting between systems of measurement, 30, 31–32, 41
equivalent, valence and, 122–123
in household measurements, 38
in metric measurements, 29, 30, 41
milliequivalents and millimoles, 121–125
minimum weighable quantity, 113–114
weight-in-weight (w/w), 101
whole numbers, 9–10
wholesale acquisition cost (WAC), 131
word problems
addition in, 16
subtraction in, 16
translating into equations, 70–72
variables in, defining, 70
Z
zero, place value of, 9
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