Module B:Module B:Basic Math for Basic Math for PharmacologyPharmacology
Module B:Module B:Basic Math for Basic Math for PharmacologyPharmacology
Basic Math• Addition• Subtraction• Multiplication• Division
Roman Numerals• I = 1• V = 5• X = 10• L = 50• C = 100• D = 500• M = 1000
• Examples:• VII =• XV =• III =• IX =• IV = • XIX =• XIV =
Fractions• 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:
• 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)
SystemsSystemsof Measurementsof Measurements
SystemsSystemsof Measurementsof Measurements
HouseholdHouseholdApothecaryApothecary
MetricMetric
Household• Most often used by people at
home• Least accurate• Used by nurse in teaching patients• Should not be relied on in hospital
setting
HouseholdUnit Abbreviation Equivalent
Drop gtt none
teaspoon tsp (t) 1T = 3t
Tablespoon tbs (T)
Apothecary System• 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
• VolumeUnit Abbreviation
Equivalent
Quart qt qt 1 = pt 2qt 1 = oz 32
Pint pt pt 1 = oz 16
Fluid-ounce
oz oz 1= 8 drams
Dram
Minim m
Metric System• Base Units
– Wt - gram– Volume – liter– Length – meter– Prefixes
• Centi• Milli• Micro• Deca• Hecto• Kilo
Metric System
Unit Abbreviation Equivelent
Weight gram g 1 g = 1000mg
Milligram mg 1 mg = 1000mcg
microgram Mcg
kilogram kg 1 kg = 1000g
Volume liter L 1 L = 1000ml
mililiter ml 1ml = 1cc
Cubic cent. cc 1cc = 1 ml
Length 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 Equivalents1g gr xv
gr 1 60mg
1 t 5 ml
1 T 3 t 15ml ½ oz
1oz 30 ml 6 t
1L qt 1 pt 2 oz 32 4 cups
pt 1 500 ml oz 16 2 cups
1 cup 250 ml oz 8
1 kg 2.2 lbs
1lb 16 oz
Drug CalculationsDrug CalculationsDrug CalculationsDrug 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 Analysis1) 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• 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 Unitso Unitso Milliunits
Reconstitution of medications
• Stability of the drug• Powder mixed with diluent or
solvent• Reconstitute medication before
giving to client