A

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