ss
I
V
X
L
C
D
M
_
V
Roman Numerals
Rules for Roman
Numerals
5000
1. Write larger on left and decrease as
you go to the right. The Arabic
equivalent is the sum of the symbols.
2. Do not use a symbol >3 times.
3. If you need 4 symbols (4 or 9), then you
must use subtraction; place smaller
value symbol to the left of a larger value.
4. You are limited in subtraction by which
symbols are allowed. Only a symbol
1/100 or less is allowed.
5. Use the largest symbol.
___
____ ___ ____ . ___ ____ ___ ____
1000s 100s
Fractions and
Decimals
½
1
5
10
50
100
500
1000
10s
1s
10ths |
1000ths |
100ths
10000ths
6.1 = “six and one tenth”
208.31 = “two hundred eight and thirtyone hundredths”
.215 = incorrect form – leading zero
required
0.215 = Correct form: “two hundred
fifteen thousandths”
Decimals
Addition
Line up the decimals and
add.
Decimals
Subtraction
Line up the decimals and
subtract (include zeros to
the right of the decimal for
whole numbers).
Decimals
Multiplication
Do not need to line up
decimals.
Multiply values out.
Count total places behind
the decimal.
Move from right to left that
number of places
Decimals
Division
Fractions
a ÷ b a/b a divided by b
Move the decimal to the
right as many times as
needed to make the
denominator a whole
number. Move the decimal
an equal number of times
to the right for the
numerator.
Changing mixed to Improper and
Vice Versa:
ex: 2 1/3 = 7/3
(2*3) + 1 = 6 + 1 = 7
3
3
3
Changing Improper (“Dolly Partons”
=> top-heavy) to Mixed:
ex 13/7 = 1 6/7 = 1.86
ex 22/3 = 7 1/3 = 7.33333333
Fractions
Addition &
Subtraction
(Algebra Way)
1. Write both in fractional
form (a/b form).
2. Rah Rah Kick (cross
multiply top and multiply
bottom):
a + c = ad + bc
b
d
bd
Fractions
Addition &
Subtraction
Old School
1. Find the common
denominator.
2. Write equivalent
fractions.
3. Add or subtract.
Ex: 2 ¼ =
2 5/20
3 2/5 + 3 8/20
5 13/20
Fractions
Multiplication
1. Write all in a/b form:
2 3/5 = 13/5; 6 = 6/1
2. Simplify. Reduce any
numerator with any
denominator if there is a
common factor.
3. Multiply straight across.
4. Simplify.
Fractions
Division
Change to multiplication
by using “flip” of the the
fraction to the right of the
division sign
(denominator).
[Flip = reciprocal]
Terminating and Non-terminating
Repeating and Non-repeating
Decimal
Approximations
Terminating: 5/4 = 1.25
_
Repeating: 5/3 = 1.66666666 or 1.6
Do not truncate repeating decimals
in the middle of a problem, as this
may skew your results.
Ex: 3000 * 1/3 = 1000
3000 * 0.3 = 900
3000 * 0.3333333 = 999.9999
Most rounding is to the hundredths place: 0. _ _
Look at digit in 1000ths place: 0. _ _ _
Rounding
Word Problems
If that digit is 0 – 4, just use what you have.
If that digit is 6 – 9, add 1 to the 100ths place.
If that digit is 5,
if there are multiple digits to the right (51-59),
increase the 100ths, but if the digit is 5 and
there is no digit after it,
if the digit in the 100ths place is even, leave
it alone;
if the digit in the 100ths place is odd, add 1 to
the 100ths place.
1. Read the problem.
2. Focus on the important phrases
and facts. You may find extraneous
information in any problem. Filter it
out.
3. Organize facts: a) as ratios or
b) as not ratios.
4. Use appropriate labels.
Ratios are fractions.
Ratios
A ratio compares two
quantities:
fraction form: a/b
ratio form: a: b
You must reduce final
answers: 6:8 => 3:4
In pharmacy, a:b always means
a grams
g
b milliliters ml
Pharmacy Ratios
What is a 1:3 solution? 1 g
3 ml
(this is a reduction, not necessarily 3
ml of solution)
Proportions declare that two ratios
are equal. a/b = c/d
a:b = c:d – Matching labels are
required.
Nancy
Massengale's
Rules for Pharm
Tech Math
1. Must use labels.
Weight: g (grams), gr (Apothecary unit
grains), mg (milligrams)
Volume: ml (milliliters), L (liters), tsp
(teaspoons)
2. Label position must match. Most
ratios will be g/ml or mg/ml.
3. To solve: a. cross multiply.
b. divide both sides by the quantity
with the x (cancel labels as you go).
c. Make sure the answer makes
sense.
Volume base is liters (L).
1 L = 1000 ml.
Usually use milliliters.
Metric Units
Volume
To change between ml and L:
L to ml: move decimals 3
places to the right.
ml to L: move decimals 3
places to the left.
Weight: grams (g) 1 g = 1000 mg
milligrams (mg).
Metric Units
Weight
Volumes,
Weights, and
Concentrations
To change between mg and g:
g to mg: move decimal 3 places to
the right.
mg to g: move decimal 3 places to
the left.
Volume: liquid measure: ml, tsp,
quarts, etc.
Weight: dry measure (amount of
drug): g, mg, gr, etc.
Concentrations: amount of drug
over volume (always a fraction):
amount of drug
volume
A:B is a concentration of weight
over volume.
% Concentration
% Concentration is just a
very specific
concentration: the amount
of drugs in grams over 100
ml. The denominator is
always 100 ml.
For the purposes of this class,
=>
indicates reduction.
What is the percent concentration of the
following?
1:10
Common Percent
Concentrations
1 =
10
x
100
1:100
1
=
100
Common
Substitution
1%
x
100
1:1000
1 =
1000
10%
x = 100
10
x
100
x = 100
100
0.1%
x = 100
1000
What is the common substitution?
1g
1000 ml
= 1000 mg
1000 ml
= mg
ml
amount of drug
volume
Concentrations: Look for form requested.
Concentrations
Mg always
ml reduced
g
g
or %
ml 100 ml
in colon form a:b ; in fraction form
ex 30 g of D1 are dissolved in 40 ml. What
is the concentration? 30 g/ 40 ml 3:4
Find the amount of active drug – looking for
weight of active drug. Method: ratio and
proportion.
Finding Weight
Word Problems
Steps
1. Write a ratio which represents the
concentration.
x
2. Write the other ratio as volume.
3. Solve.
ex: You have 40 ml of a 15% solution. How
many grams of active drug?
x g = 15 g x g = 40 ml * 15 g = 6 g
40 ml
100ml
100 ml
Finding Volume
Word Problems
Steps
1. Write a ratio for the concentration.
2. Write the other ratio as weight
x
.
3. Solve.
Ex: You have 14 grams of D1. You want
a 5 g/12 ml concentration. How much
sterile water do you use?
14 g = 5 g
x ml = 14 * 12 ml = 33.6 ml
x ml
12 ml
5g
Metric System
Prefixes
Most Common
Metric System
Units, Symbols, &
Conversion
Factors
Metric System
Conversion
Process
Prefix
kilo
deca
centi
milli
micro
Volume
kiloliter
kl
liter
L
milliliter ml
cubic
cc
centimeter
Meaning
1000 * > base
10
* > base
100 * < base
1000 * < base
100000 * < base
1000 liters = 1 kl
liter is base unit
1000 ml = 1L
1 cc = 1 ml
Weight
kilogram kg
gram
g
milligram mg
microgram mcg (µg)
1000g = 1 kg
gram is base unit
1000 mg = 1 g
1000 mcg = 1mg
Conversions within the metric
system are done by moving the
decimal point. Each step down the
list* moves the decimal 3 places to
the right because you are going
from a larger unit to a smaller unit.
Each step up the list moves the
decimal 3 places to the left because
you are going from a smaller unit to
a larger unit.
*Please see the card titled “Most Common Metric
System Units, Symbols, & Conversion Factors.”
Abbreviations
When
Cc with meals
qwk once a week
Ac before meals
prn as needed
Pc after meals
ut dict as directed
Hs before sleep
act around the clock
qd once a day
qh every hour
bid twice a day
c with
tid 3 times a day
s without
qid 4 times a day
q4h every 4 hours
qod every other day
Abbreviations
Where
po by mouth
od right eye
os left eye
ou both eyes
ad right ear
as left ear
au both ears
IM intramuscular
IV into the vein
SC under the skin
Abbreviations
How Much
cc cubic centimeter
fl fluid
g gram
gr grain
gtt drop (from Latin guttae)
mg milligrams
mcg micrograms
aa of each
tsp teaspoon
Tbs tablespoon
ID into the skin
IA into the artery
IT intrathecal
IC intracardiac
SL under the tongue
rect rectally
Abbreviations
Drug Form
tab tablet
cap capsule
pul pulvule
syr syrup
susp suspension
el elixir
ext extract
tinct tincture
ung ointment (unguent)
Household – often used in
orders to the patient.
3 basic Systems
of Measurement
Volume (liquid): tsp, Tbs, qt, gal, pint
Weight (solid): oz, lb
Metric – if used in patient orders, give
calibrated equipment.
Volume (liquid): liters
Weight (solid): grams
Apothecary – use Roman Numerals for
quantity for most of these.
Volume (liquid): drams, scruples
Weight (solid): grains, scruples
Extra Measures include International Units
and milliEquivalents.
milli centi deci base deca hecto kilo
1
1
1
1
10
100 1000
1000 100 10
Metric to Metric
Conversions
kilo
base
milli
micro
kilogram
gram
milligram
microgram
kiloliter
liter
milliliter (ml or cc*)
microliter
*cc = cubic centimeter
Non Metric to
Metric
Conversions
1. List the conversions (can be
an actual list or ratios).
2. Set up the proportions.
Ex 130 mg = ______ gr
130 mg
x gr
= 65 mg
1 gr
x gr = 130 mg * 1 gr
65 mg
x = 2 gr
Centigrade (Celsius) to
Fahrenheit:
Temperature
Conversions
F = (C * 1.8) + 32
Fahrenheit to Centigrade
(Celsius):
C = (F – 32) * 5/9
Conversions
Metric to Metric
Volume
kiloliter kl
liter
L
milliliter ml
cubic
cc
centimeter
1000 liters = 1 kl
liter is base unit
1000 ml = 1 L
1 cc = 1 ml
Conversions
Metric to Metric
Weight
Conversion
Factors
Volume
Conversion
Factors
Weight
kilogram kg 1000 g = 1 kg
gram
g gram is base unit
milligram mg 1000 mg = 1 g
microgram 1000 mcg = 1 mg
mcg or µg
1
1
1
1
1
1
1
1
gtt (drop)
= 1 minim = 0.06 ml
teaspoon (tsp) = 5 ml
Tablespoon (Tbs) = 15 ml
fluid dram (fl dr) = 4 ml = 3 sc = 60 min
fluid ounce (fl oz) = 30 ml = 8 drams
pint = 16 fl oz
quart = 2 pints = 1 L = 960 ml
gallon = 4 quarts
1
1
1
1
1
1
1
1
oz = 30 grams = 8 drams
g
= 15.4 gr
gr (gr I) = 65 mg
sc (sc I) = gr xx = 1300 mg
dram = sc iii
pound (lb) = 454 g = 16 oz (household)
pound = 12 oz (Apothecary & troy)
kg = 2.2 lbs
Solid Dose Forms
1. Make sure that the units of the order and
the stock match. (Do the easiest
conversion, i.e., to what's in stock.)
2. Make sure that the answer is within a
range of measurement.
3. Unit dose – should be the weight of the
drug taken in a 24-hour period.
If too many tablets, “See pharm.” If tablets
are not scored or capsules or other form
that cannot be scored and your answer is
not a whole number, “See pharm.”
Solid Dose Forms
Method 1 (Ratio)
1. Write ratio of order: order
dose
2. write the stock ratio:
weight of stock weight of stock
tab
cap
3. Set them equal.
4. Solve for “dose” (x).
1. order
stock
Solid Dose Forms
Method 2
(Order/Stock)
(tab, cap)
ex. Order: 60 mg (tab)
Stock: 20 mg
60 mg (tab) => 3 tab
20 mg
Alligation
Mixing 2
Solutions of the
Same Drug
Liquid Doses
Syrup
Liquid Doses
Elixir
Desired % must be between larger
% in stock and smaller % in stock.
If you add water, H2O is a 0%
solution.
Syrup
homogenous
contains drug
sugar (60% - 85%)
antimicrobial preservative
flavoring
Elixir
homogenous
hydro-alcoholic (both water
& alcohol)
used with emetics* or
potent drugs
*emetic – may induce nausea
Suspension: two-phase system
Liquid Doses
Suspension
Situations
Involving Liquid
Doses
Liquid Doses
Enlarging or
Reducing
Quantities
1. very finely divided particles in
solution → insoluble or poorly soluble
2. usually stored as a dried powder that
needs to be reconstituted or
rehydrated.
Vehicles commonly used – sterile water
NS = normal saline (0.9%)
½ NS = 0.45%
D5W = dextrose in a 5% solution
G5W = glucose in a 5% solution
1. Enlarging or reducing
quantities (% remains the
same)
2. Dilutions or Concentrations
3. Alligation & Alligation
Medial
4. Filling Prescriptions
No change in % concentration
As the volume increases, the
amount of drug increases.
As the volume decreases, the
amount of drug decreases.
1. Find given.
2. Write proportion.
3. Solve.
amt drug
ml
Liquid Dose
Dilutions &
Concentrations
(indirect proportion)
1. Find the amount of drug.
given %
xg
100 ml
vol orig. solution
2. Find the new volume.
a) If given, use it.
b) If “evaporated to” → Concentration
after “to” is new volume.
c) If “evaporated by”, the amount
referenced is removed and the new
volume is the remainder.
3. Set up a proportion and solve it.
Assume 100 ml if given %.
Liquid Doses
Alligation
Desired % must be between larger % in stock
and smaller % in stock. If you add water, H2O is
a 0% solution.
L% or S% * Multiplication Factor = Associated
Volume
(D% - S%) + (L% - D%) * Multiplication Factor =
Total Volume
Combine 3 or more solutions of the
same drug.
Liquid Doses
Alligation Medial
1. Find the amount of drug in each
and find the sum.
2. Find the new volume (either the
sum of the old volumes or it is
given).
3. Solve. x g
= sum of drug (g)
100 ml
new volume (ml)
Liquid Doses
Prescriptions
Dose is in ml.
Same process as tablets and
capsules.
If stock is in mg/ml, can use either
ratio or order/stock method.
If stock is in mg/# ml, then use only
ratio method.
Label expressed as mg/kg; no set
conversion, depends on manufacturer.
Pediatric Doses
(computation of Adult Dose
by Body Weight)
Ex: an adult weighs 75 kg –
recommended adult dose (RAD) is 10
mg/kg.
x mg = 10 mg x = 75 kg * 10 mg = 750 mg
75 kg
1 kg
1 kg
If drug does not mention pediatric dose,
check with pharmacist to be sure it can be
used with kids.
Pediatric Doses
(Standard
formula)
IF NO OTHER METHOD IS
GIVEN:
Child dose = Adult dose ÷ 1.7
If pediatric medication, follow
label instructions for child
dose.
Body Surface Area (BSA): See
nomogram example at the end of
this document.
Pediatric Doses:
Body Surface
Area (BSA)
Potential Exam Question: What
graph is used to determine the
BSA?
Answer: Nomogram.
BSA always given as m2. Most
doses are usually mg/m2 .
Pediatric Doses
Young's Rule
Pediatric Doses
Clark's Rule
Young's Rule: For children 1 –
12 years of age:
Child dose = age of child * adult dose
age + 12
Clark's Rule
Child dose =
weight of child * adult dose
weight + 150
Pediatric Doses
Drilling's Rule
Pediatric Doses
Fried's Rule
Pediatric Doses
Webster's Rule
Drilling's Rule
Child dose = age * adult dose
12
Fried's Rule: Age in months for
infants < 2 years old
Child dose =
age in months * adult dose
150
Webster's Rule
Child dose =
age in years + 1 * adult dose
age in years + 7
Used by very old and very young – those
who cannot swallow pills.
Dispensing Liquid
Medications
Dosed by teaspoons, tablespoons, fluid
ounces, or milliliters. Include dosing cup
or syringe for fl oz or ml.
DO NOT shake medicine vigorously –
gently rotate to avoid bubbles.
Some can be crushed and added to apple
sauce, tuna, or ice cream.
Do not break coated capsule or timerelease capsules.
The Safe Dose is what is allowed for a
24-hour period.
SAFE DOSE
Recommended
Daily Dose (RDD)
If there is no recommended dose for
children, check with pharmacist to make
sure it is safe for a child.
Ex: 1 Safe dose range “0.2 mg to 0.8 mg”
– POTENT DRUG
2 “150 mg – 250 mg” freer – need to see
pharm
3 Given as signal value – “safe dose is
300 mg”; <300 okay.
Our body needs salt to operate our muscles.
MilliEquivalents are the number of positively
charged ions per liter of salt solution.
milliEquivalents
(mEq)
Concentrations are expressed in equivalents per
liter (Eq/L) or milliEquivalents per liter (mEq/L).
1 Eq = molecular weight of the salt (g)
ionic charge (valence)
1 Eq = 1000 mEq
1 mEq = Eq in mg
1 Eq = 1000 mEq
Converting Eq to
mEq
Ex:
1Eq = 74 g
1 mEq = 74 mg
Change g to mg – DO NOT
move decimal.
Some Common
Elements with
milliEquivalents
Element
Atomic Weight Valence
Sodium Na+
23
1
+
Potassium K
39
1
++
Magnesium Mg
24
2
+++
Aluminum Al
27
3
Chloride Cl35.5 (or 35)
1
++
Calcium Ca
40
2
1 Eq = Atomic Weight/Valence g
1 mEq = Atomic Weight/Valence mg
Atomic Weight
and Valence
ex: Find the mEq of a calcium ion.
40 = Atomic Weight
2
Valence
1 mEq = 20 mg
mEq Word
Problems
Easy: Simple
Order Problem
mEq Word
Problems
Hard: Step 1 2 3
Ex: Potassium chloride is available
in a concentration of 40 mEq in 30
ml. A patient is to receive 20 mEq
of KCl. What do you administer?
40 mEq = 20 mEq x = 30 ml * 20 mEq
30 ml
x ml
40 mEq
x = 15 ml or 1 Tbs
1 Find the amount of drug.
a) could be given
b) set up a proportion – to find
concentration or to find volume; x will
always equal the amount of drug.
2 Find the mEq => mg (based on atomic
weight and valence: 1mEq = x mg)
3 Use a proportion: 1 mEq = mEq
__ mg
mg
1 mEq = x mEq OR 1 mEq = # mEq
# mg
__ g
__ mg
x mg
Ex: What is the number of mEq in 5 ml of
a 2% solution of CaCl2?
3-Step mEq Word
Problem Example
1 2g
=xg
100 ml 5 ml
x g = 2 g * 5 ml
100 ml
2 40 3 1 mEq = x mEq
35.5 55.5 mg 100 mg
35.5
110 / 2 = 55.5 mg
x = 1 mEq * 100 mg
55.5 mg
x = 1.82 mEq
Two types of measuring
equipment:
Reconstitution
1 Liquids
2 Solids
Use the most accurate device.
Syringe => <10 ml
Graduated cylinder => >10 ml
Measuring Liquids
Liquids
Glass vs Plastic
Want to measure a solution in the
least number of containers you can.
Temperature does affect accuracy:
*Warm liquids expand, meaning less
drug delivered.
*Cool liquids contract, meaning
more drug delivered.
A glass cylinder is harder to read
than plastic.
Plastic: read on the line.
Glass: read on the bottom of
the meniscus.
Meniscus – found on glass – little tiny
refraction of light.
To calibrate a cylinder, weigh it with 1 ml
of H2O. 1 ml of H2O should weigh 1 gram
at 25o C (@ 77o F).
3 ml or 3 cc syringe
Use Top of plunger for
reading
Syringe
IV = intravenous
IM = intramuscular
Syringes may contain minims
(minim or m).
Increments are often in 0.1 ml or
100 mcl (equal).
Types of Syringes
Other syringes
Tuberculine or TB syringe: 1 ml syringe
Measured in 0.01 ml or 10 mcl
Used for allergy testing; sometimes for
pediatric doses. Much smaller syringe
with much smaller needle.
Insulin Syringe – calibrate for
IU or U (units)
Insulin Syringe
specific to the concentration of normal
insulin
100 U = 1 ml volume (comes with 30-gauge
100 U ᵙ 1 ml volume needle attached)
Needles: 30-gauge is for insulin
25-30 gauge fine needle: allergy testing
pediatrics, subcutaneous injections
16-18 gauge large-bore needle for IV or
IM
Other Liquids
Tools
Other Liquids Tools
Calibrated Dropper
Calibrated Spoon
Oral Syringe
Dosage Cup – Dosage Cups are
hard to read
Accurate to 4 ml or 1 dram
30 ml 1 fl oz drams
ml
fl
Solids
Double Pan
Balance
Can be used for 1 gram or more
Put material to be weighted on one pan and a
counterbalance on the other.
Use padded forceps to pick up weights – oils
from fingers could accumulate, leading to
inaccurate readings.
Use paper called glassine – low static
electricity, low adherence.
Prescription Balance can be used for
from 5 to 6 mg to 120 grams.
Prescription
Balance
Temperature is important because of air
currents in the room. Should not work directly
beneath a vent.
Torsion balance is very rare.
Torsion Balance
Parenteral: bypasses the digestive
tract; anything injected.
Ways of
Administering
Drugs
IV intravenous
IA intra-arterial
IM intramuscular IT intrathecal
SC subcutaneous IC intracardiac
IV bolus – all at once
IV drip – over a period of time
Calculations: concentrations, ratio, %,
weight/volume, :
From Manufacturer label
Bolus injection: most < 3 ccs
Order: 25 mg
Stock: Contains 100 mg of active
drug once you add 5 ml
Bolus
Calculations
Example
25 mg = 100 mg x = 25 * 5 ml
x
5 ml
100 mg
x = 1.25 ml
5 ml – 1.25 ml = 3.75 ml remainder
to be stored
Rehydration & Reconstitution
Rehydration &
Reconstitution
Many drugs are unstable with water – mixed
right before use.
Usually supplied with saline solution (0.9%).
Rehydration – use water only.
Reconstitution – may use water or NS (0.9%), ½
NS (0.45%), or ¼ NS (0.225%).
D5W: 5% dextrose.
Ringer's Solution: lot of salts, NaCl, KCl, CaCl
Lactated Ringer's: Ringer's Solution plus
sodium lactate.
Admixture
Reconstituted
Liquids
Admixture: Drug or other
therapeutic substance
added to an IV.
Reconstituted Liquids can
be used in large amounts
in an IV or with an
admixture.
5 Different Math
Problems for
Rehydration &
Reconstitution
Single Strength
Solution
Calculations
1 Reconstitution &
Rehydration
2 Concentration of Drug in IV
3 Flow Rate, Drop Factor, and
Drop Rate
4 Correcting Mistakes
5 Dose Per Time
1 Find the directions and read the
label.
2 Use sterile syringe and aseptic
techniques.
3 Weight of the powder in the vial IS
NOT the weight of the active drug.
Minimize air bubbles by adding water slowly.
Rotate gently – DO NOT VIOLENTLY SHAKE.
Withdraw what you need, label the remainder
with date, concentration of drug, amount of
drug, storage information, and your name or
initials.
Ex: Order: 200 mg of drug; IM; directions on
label of vial containing 1 g of powder indicate
that adding 7.2 ml will yield a concentration of
125 mg/ml.
Stock: 125 mg/ml
Single Strength
Solution Example
What do you do?
200 mg = 125 mg x = 200 mg * 1 ml x = 1.6 ml
x ml
1 ml
125 mg
7.2 ml – 1.6 ml = 5.6 ml
Administer 1.6 ml of reconstituted drug.
Label remainder as 5.6 ml of 125 mg/ml solution,
stored as given on label. 10/16/09 BF
Multiple Strength
Solutions
(usually with multiple strength
directions)
A bottle of penicillin may contain a
dilution table:
23 ml provides 200000 U/ml
18 ml provides 250000 U/ml
8 ml provides 500000 U/ml
3 ml provides 1000000 U/ml
1 See order.
2 Order/Stock for each line.
3 Evaluate answers for best choice.
Criteria: <3 ml, as few decimals as possible.
Multiple Strength
Solution
Example*
*See Multiple Strength Solutions card for dilution
table for this example
Ex: Order: 500000 U*
500000 U = 2.5 ml 500000 U = 2 ml
200000 U
250000 U
500000 U = 1 ml
500000 U
500000 U = 0.5 ml
1000000 U
8 ml => 8 ml – 1 ml = 7 ml
Add 8 ml to vial – use 1 ml to fill order.
Label 7 ml of 500000 U/ml on 10/16/09,
per label storage instructions. BF
*All 4 dilutions could work.
IV drip – dispenses liquid over a period of
time: 30 minutes to 24 hours.
Flow rate – fluid flows at a certain rate.
Intravenous Flow
Rates
In mathematics, rate is over time.
Volume
Time
Set by a device called an infusion set.
Can be set, altered, and monitored by a
computer, tech, or nurse.
Calibrated to deliver a certain number of
drops (gtt) per ml.
Common Infusion
Sets
Isotonic
#10
#15
#20
#60
infusion
infusion
infusion
infusion
set:
set:
set:
set:
10
15
20
60
gtt/ml => macro drip
gtt/ml
gtt/ml
gtt/ml => micro drip
If salt concentration in the
blood is too high, water is
drawn from the cells and they
smush up, which is not good.
If salt concentration is too low,
it will drive water into the cells
and they might rupture, which
is also not good.
Flow rate is volume over time.
L
L
ml ml gtt gtt = Drop
hour min hour min hour min rate
Flow Rate is
Volume
Time
A flow rate done with gtt/min is a drop
rate. All drop rates are flow rates; not all
flow rates are drop rates. Flow rate is to
“dog” as drop rate is to “Labrador
retriever.”
Flow Rate * Drop Factor = Drop rate
ex: ml x gtt = gtt
min
ml
min
ALWAYS MAKE SURE LABELS CANCEL.
Flow Rate
Word Problems
FR = Flow Rate
DF = Drop Factor
DR = Drop Rate
Flow Rate
Word Problem
Example
1 Read the problem.
2 Find the volume.
3 Find time.
4 Reduce flow rate: ex: 2 L/4 hours = 1 L/2
hours = 1000 ml/120 min = 8.33 ml/min =
Flow Rate.
5 Find the drop factor. Usually given in
problem – infusion set, microdrip,
macrodrip.
6 Plug into formula: FR * DF = DR
Round answer (often to the next highest
whole number).
100000 U of penicillin (D1) is added to
a 1 L bag of NS and infused over 5
hours. The Drop Factor is 10 gtt/ml.
Find the Flow Rate in gtt/min.
1000 ml => 3.3 ml * 10 gtt = 33.33 gtt
300 min
min
ml
min
34 gtt
min
A drug or other therapeutic substance
added to a large-volume IV. WE DO
NOT IGNORE THE ADDED VOLUME.
Admixtures
IV piggyback: A separate IV that goes
through the main IV.
*May interrupt main IV. (Depending on
*May blend into IV.
Doctor's orders)
Operates via the law of gravity.
IV Diagram
IV Admixture
IV Calculations
Usually expressed as mg/ml – could be as
high as 100 ml. Amount added to IV is
often very small.
Give the answer in the form requested.
Results may differ slightly from State
Test.
1 Compute what is needed to fill the
order.
2 Reconstitute or rehydrate stock (prefer
<3 ml, but may be more).
3 Find the amount of drug (g, mg, gr, U,
mEq).
4 Add the volume of the vial to the
volume of the IV to derive new volume.
5 Find the concentration:
amount of drug * x g
new volume
100 ml
(IV conc. differs from vial conc.).
Add 10 ml of a 5% solution to a 1 L bag.
Find the concentration of the IV in mg/ml.
IV Calculation
Example
xg = 5g
10 ml 100 ml
x = 500 mg
10 ml + 1000 ml = 1010 ml
500 mg = 0.495 mg
1010 ml
ml
If you add too little drug, simply add the
difference.
Correcting
Mistakes Example
Mistakes happen.
Inform the pharmacist.
You may be able to recover.
Dose Per Time
(could be called Dose Rate)
Ex: If you add too much drug:
Stock: Label: “Add 8 ml of D5W to get 250
mg/ml.” You add 10 ml by mistake. Tell
pharmacist.
250 mg = x mg x = 2000 mg
1 ml
8 ml
2000 mg = x g
10 ml
100 ml
x = 200 mg/ml
x = 20%
Dose per time is the amount of
drug a patients gets over time
in an IV.
amount mg
g
gr
U
time
min hour hour min
mEq
min
Dose Per Time
Calculation
Method 1
Dose Per Time
Method 1
Dose Per Time
Method 1
Example
Method 1 always works.
Concentration * Flow = Dose
Rate Time
mg * ml = mg
ml
min
min
1 Find concentration
Order: amount of drug.
New Volume: IV + Admixture
2 Find Flow Rate: volume/time.
The volume is typically the same as
the new volume. Time is the time
the IV runs. To find FR, try FR * DF
= DR if you are given gtt.
3 Labels: make sure the problem is
set up to cancel. Find labels of
given and unknown.
A L bag contains 1.5 g of D1 to be infused
at a rate of 100 ml/hour. What is the
hourly dose? Find the dose per time in
ml/hour. FR = 100 ml/hour. Amount of
drug = 1.5 g
1000 ml = 100 ml 1.5 g => 1500 mg
x hour
1 hr
1000 ml
1000 ml
=> 1.5 mg/ml
Concentration * Flow Rate = Dose/Time
1.5 mg/ml * 100 ml/hr = 150 mg/hr
Dose Per Time
Method 2
(shortens time for strong math students)
Dose Per Time
Method 2
Example
1 Find the amount of drug.
Ex: 30 ml of 2 mg/ml solution
x mg = 2 mg = 60 mg
30 ml 1 ml
2 Find time. Volume = vol of IV
Time
x time
3 Put amount . Simplify.
Time
A 1 L bag contains 1.5 g of D1 to be
infused at a rate of 100 ml/hr. What is
the hourly dose? Find the dose per time
in ml/hr.
1 1.5 g = amount of drug
2 100 ml/hr = 1000 ml / x hours = 10 hours
3 1.5 g = 1500 mg = 150 mg
10 hrs
10 hrs
hr
Insulin injections are for diabetic
patients.
Units of activity U-10 = 10 U
ml
1 ml
Insulin
Insulin for Type 1 Diabetes
Standard Dose: 100 U/ml
3
1
2
3
Typical Syringes
3/10: measures up to 30 U
½: measures up to 50 U
1 cc or 1 ml: measures up to 100 U
When using insulin, attempt to avoid IV
injection – absorption can occur in the
container or in the plastic tubing.
Insulin Syringe
Insulin syringe:
1 Order is given in Us or IUs and an
insulin syringe is available.
2 Order is given in units and you need to
derive the volume administered in ml.
Ex: A doctor orders 300 U of U-100.
100 U = 300 U x = 3 ml
1 ml
x ml
Most orders are in U/kg.
Insulin
Units by Weight
1 Find the weight in kilograms.
2 Find the order.
3 Find the stock volume needed to fill the
order.
Ex: Find the total daily insulin in U if the
order is 1.5 U/kg and the patient weighs
160 lbs and uses U-100.
1 kg = x kg
1.5 U = x U = 109.09 U
2.2 lbs
160 lbs 1 kg 72.73 kg
x = 72.73 kg 109.09 U = 100 U x = 1.09 ml
x ml
1 ml
Type 2: mg %: Blood glucose is
given as mg %, using actual reading
& desired reading.
Insulin for
Type 2 Diabetes
1 Find the difference between the
two (actual & desired) for every or
each reading (usually morning &
evening).
2 Use the given ratio for
adjustment.
3 Solve proportions.
Mg % Example
Order is for 0.4 ml for every 30 mg % or
blood glucose over 170 mg % for each
morning and evening reading. Actual
readings: 300 mg % and 350 mg %. What
volume is dispensed?
300 350 0.4 ml = x ml
0.4 ml = x ml
-170 -170 30 mg% 130 mg% 30 mg% 180 mg%
130 180 x = 1.73 ml
x = 2.4 ml
1.73 ml
+2.40 ml
4.13 ml
Standard Dose: 100 U = 1 ml
Tuberculine
Syringe
(Not Recommended)
ex: Order is for 70 U of U-40
insulin.
40 U = 70 U
1 ml
x ml
x = 70 U * 1 ml
40 U
x = 1.75 ml
Heparin is a very dangerous drug. It is
measured in units. It is used for thinning
blood. It is available in ½ to 1 ml ampules,
measured in U/hour.
Adult dose is 20000 U to 40000 U/day.
Heparin
Red-label drug
used for thinning blood
Dilute with NS, D5W, or Ringer's lactate.
Stored at room temperature. Heparin
usually has a different density than its
admixtures. Mix thoroughly – rotate bag 6
or 7 times. It is a red-label drug – can
cause death. Be careful. Usually
restricted to hospital use.
1 Watch for any symptoms
of bleeding.
Heparin
Cautions for Patient
2 Strict adherence to
dosage schedule.
3 No aspirin.
Heparin orders often per kg.
Heparin
Word Problems
Find ml.
A dose of 90 U/kg is ordered. How many ml
containing 5000 Hep U/ml for a 180-lb
patient?
x kg = 1 kg x = 81.81 kg
180 lb
2.2 lb
81.81 kg = 1 kg x = 7363.6362 U
xU
90 U
7363.6362 U = 5000 U x =1.4727272 ml
x ml
1 ml
An IV of 1000 ml contains 60000 U
of heparin. 60 U/ml has been
ordered to infuse at 20 ml/hour.
Heparin
Word Problems
Find U.
20 ml = x ml x = 480 ml
hr
24 hr
x U = 60000 U
480 ml
1000 ml
x = 60000 U * 480 ml
1000 ml
x = 28800 U
A patient gets IV drip of Sodium Heparin:
50000 U/1000 ml ½ NS.
Heparin
Word Problems
Dose/Time & Drop Rate
a) How many ml/hour to get 20000
U/hour?
2000 U = 50 U x = 40 ml
x ml
1 ml
b) With a macrodrip, find the drop rate.
40 ml/hour => 0.666 ml/min
0.666 ml/min * 10 gtt/ml = 6.67 gtt/min
=> 7 gtt/min
Pediatric Dose must be intermittent – does not
flow constantly. Range: 60 – 80 U/kg every 4
hours (6 times per day). Answer is a range with
upper and lower values.
Heparin
Pediatric Dose
x kg = 1 kg x = 33 kg
66 lb
2.2 lb
Bulk
Compounding
Ex: For a 66-lb child, calculate the range in ml of
a heparin injection containing 5000 U/ml to be
administered daily.
lower
upper
60 U = x U
80 U = x U
1 kg 30 kg
1 kg
30 kg
x = 1800 U
x = 2400 U
*6 = 10800 U
*6 = 14400 U
10800 U = 5000 U
14400 U = 5000 U
x ml
1 ml
x ml
1 ml
x = 2.16 ml
x = 2.88 ml
Unit Dose
Unit Dose
Bulk compounding is a
process which allows you
to make a batch by
following a formula or
procedure.
Bulk
Compounding
Reducing &
Enlarging Formula
1 Conversion New Mix Wt
Factor:
Formula Wt
2 Multiply each step by the
conversion factor.
Procedure for 500 g of Antibiotic
Reducing &
Enlarging Formula
Example
Ointment:
Neomycin 2.5 g
Bacitracin 4.0 g
Polymixin B 320 mg
Liquid Petrolatum 150 g
White Petrolatum 343.18 g
Want to make 1500 g of antibiotic
ointment. How much polymixin B do I
need?
1500 g = Conversion Factor = 3
500 g
3 * 320 g = 960 mg of polymixin B
Change % to amounts.
Bulk
Compounding
Using Percent
Ex: D1 is 6%. Total weight is 400 g.
How much D1?
6 g = x g x = 6 g * 400 g = 24 g
100 g
400 g
100 g
Making
Preparations by
Percent
Bulk Compound
Percents
1 Convert to amounts.
2 Derive Conversion
Factor.
3 Multiply each step by
the Conversion Factor.
When you double a recipe given in
percent, the amount will double but
the percent will remain the same.
If you are measuring very small amounts,
the scale may not be sufficiently
accurate due to its margin of error.
Aliquot Method
Balance of Sensitivity comes from
manufacturer.
Permissible Margin of Error determined by
whoever controls the pharmacy.
1 x Balance Sensitivity
Permissible Margin of Error
Ex: A class A balance has a sensitivity of
6 mg. According to the pharmacist, the
order can have up to a 2% margin of
error.
1 * 6 mg = 300 mg
0.02
Under 300 mg should NOT
be measured via this scale.
Pharmacy
Business
Mathematics
Mark-Up
Mark-Up as an
Amount Example
Mark-Up as a
Percent
Mark-up can be written as an
amount or as a percent.
How much “profit” is made on
a sale?
“Profit” is the difference
between cost and selling
price.
“Profit” = Selling Price – Cost
The cost is $8.00. The markup is $20.00. What is the
selling price?
Cost + Mark-Up = Selling Price
$8.00 + $20.00 = $28.00
Mark-up expressed as a
percentage is the amount of
mark-up for each $100 of Cost:
% Mark-Up = Amt of Mark-Up
100
Cost
Mark-Up as a
Percent Example
If the mark-up is 30% and the
item cost is $60, what is the
amount of mark-up?
30 = Mark-Up
100
60
Mark-Up = 30 * 60 = $18.00
100
Selling Price = $60 + $18 = $78
Increase by a
Percent: From
Cost to Selling
Price
1 Add 100% to percent markup.
2 Change to a decimal (move
decimal 2 places to the left).
3 Multiply by cost.
Cost is $40. % Mark-Up is
80%. What is the price?
Increase by a
Percent Example
100% + 80% = 180%
180% => 1.8
1.8 * $40 = $72
Be sure to use labels ($).
(Cost + Incidental Expenses) *
(100% + % Mark-Up) = Selling
Price
Gross and Net
Profit
Gross Profit = Selling Price (Cost + Incidental Expenses)
Net Profit = Gross Profit * (Net
Profit Expressed as a % of
Gross Profit)
“Discount” or Sale
Price (Mark-Off)
Sale Price
Example
1 Subtract % Mark-Off from
100.
2 Change to a decimal by
moving decimal 2 places to the
left.
3 Multiply by Selling Price.
Lotion is marked 30% off. The
original Selling Price is $12.50.
What is the new Sale Price?
100 – 30 = 70
70 => 0.7
0.7 * $12.50 = $8.75
Sequential
Discount vs
Aggregate
Discount
Mark-Up Profit,
Mark-Off Profit or
Loss Example
A sale offers a 20% Discount. You
have a 10% coupon. What happens
if you get both discounts in either
order versus combining discounts?
$1.00 * 0.8 = $0.80 * 0.9 = $0.72
$1.00 * 0.9 = $0.90 * 0.8 = $0.72
$1.00 * 0.7 = $0.70
An item costs $400.00. Store policy
is a 50% Mark-Up. After 1 month
the item is marked off 50%. What is
the profit or loss if an item sells
immediately versus after 1 month?
$400 * 1.5 = $600 ( - $400 = +$200)
$600 * 0.5 = $300 ( - $400 = -$100)