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