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

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

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

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

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

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

gentamicin, 91–92

graduated cylinder markings, 10

gram (mass/weight), 29, 30

gross profit, 130

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

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

kilo, 30, 139

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

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

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

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

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

quantities, calculating, 60–61

quotient, 17

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

R_{x} symbol, 58

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

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

unit-dose packaging, 62

United States Pharmacopeia-National Formulary (USP-NF), 113

unknowns. *see* variables

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

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

zero, place value of, 9