Module B:
Basic Math for
Pharmacology
Basic Math
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Addition
Subtraction
Multiplication
Division
Roman Numerals
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I=1
V=5
X = 10
L = 50
C = 100
D = 500
M = 1000
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Examples:
VII =
XV =
III =
IX =
IV =
XIX =
XIV =
Fractions
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Simple
Proper
Improper
Mixed numbers
Complex
Fractions
• Reducing to lowest terms
– Divide N & D with a common D
• Changing improper fractions
– Top number is larger than the bottom,
divide bottom # into top#.
- Write the remainder as a fraction and
reduce to lowest terms
Fractions
• Change mixed #’s into improper
fractions
– Multiply the whole # by the bottom #
– Add total to the top #
– Write sum at top; bottom remains same
Fractions
• Adding and subtracting fractions
– If same bottom #, then add the top,
bottom remains same.
– If D is different, then find the lowest
common D.
• Adding and Subtracting mixed
numbers
Fractions
• Multiple a Whole # by a fraction
– Always reduce to the lowest term
– Always change improper fractions
• Multiplying two fractions
– Use cancellation to speed the process
Fractions
• Multiplying Mixed #s
– Change to an improper fraction
• Dividing Fractions
– Invert the divisor
Decimals
• Decimal Places
– Numbers on left of decimal are whole numbers
– Number on the right of the decimal are as
follows:
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Tenths
Hundredths
Thousandths
Ten thousandths
Decimals
• Adding
• Subtracting
Decimals
• Rounding the answer
• Multiplying decimals
• Dividing decimals
– Make the divisor a whole # by moving the
decimal
– Move the decimal in the dividend the same
amount of places as in the divisor.
– Place directly above in bracket
Decimals
• Change decimals to common fractions
– Remove decimal
– Place appropriate D
– Reduce to lowest terms
Percents
• Change percents to fractions
– Ommit percent sign
– Use 100 as D
– Reduce fraction
Percent
• Change percent to decimals
– Omit percent sign
– Insert a decimal point 2 places to the
left.
Ratios
• Indicate the relationship of one
quantity to another
– Form of fraction
– Form of ratio
Proportions
• Shows how 2 equal ratios are related
• Three factors are known
• One factor is unknown (x)
Systems
of Measurements
Household
Apothecary
Metric
Household
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Most often used by people at home
Least accurate
Used by nurse in teaching patients
Should not be relied on in hospital
setting
Household
Unit
Abbreviation
Equivalent
Drop
gtt
none
teaspoon
tsp (t)
1T = 3t
Tablespoon
tbs (T)
Apothecary System
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Ancient system “Old English”
Not very accurate
Use Roman Numerals
The symbol is placed in front of the
number.
• Change to metric system when
possible.
Apothecary
• Weight
Unit
Abbreviation
Equivalent
Grain
gr
***
Apothecary
• Volume Unit
Abbreviation Equivalent
Quart
qt
Pint
pt
Fluidounce
Dram
oz
Minim
m
qt 1 = pt 2
qt 1 = oz 32
pt 1 = oz 16
oz 1=
8 drams
Metric System
• Base Units
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Wt - gram
Volume – liter
Length – meter
Prefixes
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Centi
Milli
Micro
Deca
Hecto
Kilo
Metric System
Weight
Volume
Length
Unit
Abbreviation
Equivelent
gram
g
1 g = 1000mg
Milligram
mg
1 mg = 1000mcg
microgram
Mcg
kilogram
kg
1 kg = 1000g
liter
L
1 L = 1000ml
mililiter
ml
1ml = 1cc
Cubic cent.
cc
1cc = 1 ml
Meter
m
1m=100cm=1000mm
centimeter
cm
1cm =10mm
milimeter
mm
Other Common Drug
Measures
• Units = U
• Milli unit = mU
• Milli equivalent
Conversions
• Use:
– Ratio and Proportion
• 1 step problems
• 2 step problems
• (know) = (want to know)
X:Y
=
X:Y
mg : g
=
mg : g
Conversions between
systems
Metric
Apothecary
Household
Conversion Equivalents
1T
1L
pt 1
1g
gr xv
gr 1
1t
3t
1oz
qt 1
500 ml
1 cup
1 kg
1lb
60mg
5 ml
15ml
30 ml
pt 2
oz 16
250 ml
2.2 lbs
16 oz
½ oz
6t
oz 32
2 cups
oz 8
4 cups
Drug Calculations
Perform Calculation by
• Ratio and Proportion
or
• Dimensional Analysis
or
• Formula
– D/H x Q = X
Ratio & Proportion
• Ratios you many see:
– Wt or strength of a drug in a tab or
capsule
• Example: 50mg: 1 tab
• Meaning : each tablet has 50 mg
• Weight or strength of a drug in a
volume
• Example = 50mg:2ml
• Meaning = 50 mg in 2ml of volume
Ration & Proportion
• When administering medication
you can give
– Tablets, Capsules, and ml (in a
syringe)
• Remember:
– The ratios must be written in the
same sequence of measurements
Ratio & Proportion
• One step Ratio & Proportion
• Two step Ratio & Proportion
Dimensional Analysis
1) Identify the desired unit.
2) Identify the equivalent needed and set
up in fraction form.
3) Write the equivalent in fraction format,
keeping the desired unit in the numerator
of the fraction.
4) Be sure to label all factors in the
equation.
5) Identify undesired units and cancel them.
6) Perform the mathematical process
indicated.
Dimensional Analysis
• By flipping the fraction, no value is
changed.
• Remember: They are ratios in
fraction form.
• Starting the equivalent incorrectly
will not allow you to eliminate desired
units.
• Knowing when the equation is set up
correctly is an important part of
using Dimensional Analysis.
Formulas
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D/H x Q = X
D = Dose desired
Hand = have on hand
Q = the quantity or the unit of
measure that contains the dose.
Formulas
• Memorize the formula
• Place the information from the
problem into the formula in the
correct position, with all terms in the
formula labeled correctly.
• Make sure all measures are in the
same units and system of measure or
a conversion must be done before
calculating the dose.
International Units
o Units
o Milliunits
Reconstitution of
medications
• Stability of the drug
• Powder mixed with diluent or solvent
• Reconstitute medication before
giving to client