Module B: Basic Math for Pharmacology

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Module BBasic Math for Pharmacology
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Basic Math

• Addition
• Subtraction
• Multiplication
• Division

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Roman Numerals

• I 1
• V 5
• X 10
• L 50
• C 100
• D 500
• M 1000

• Examples
• VII
• XV
• III
• IX
• IV
• XIX
• XIV

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Fractions

• Simple
• Proper
• Improper
• Mixed numbers
• Complex

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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

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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

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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

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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

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Fractions

• Multiplying Mixed s
• Change to an improper fraction
• Dividing Fractions
• Invert the divisor

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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

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Decimals

• Adding
• Subtracting

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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

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Decimals

• Change decimals to common fractions
• Remove decimal
• Place appropriate D
• Reduce to lowest terms

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Percents

• Change percents to fractions
• Ommit percent sign
• Use 100 as D
• Reduce fraction

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Percent

• Change percent to decimals
• Omit percent sign
• Insert a decimal point 2 places to the left.

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Ratios

• Indicate the relationship of one quantity to
  another
• Form of fraction
• Form of ratio

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Proportions

• Shows how 2 equal ratios are related
• Three factors are known
• One factor is unknown (x)

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Systemsof Measurements

• Household
• Apothecary
• Metric

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Household

• Most often used by people at home
• Least accurate
• Used by nurse in teaching patients
• Should not be relied on in hospital setting

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Household
Unit Abbreviation Equivalent
Drop gtt none
teaspoon tsp (t) 1T 3t
Tablespoon tbs (T)
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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.

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Apothecary

• Weight

Unit Abbreviation Equivalent
Grain gr
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Apothecary
Unit Abbreviation Equivalent
Quart qt qt 1 pt 2 qt 1 oz 32
Pint pt pt 1 oz 16
Fluid- ounce oz oz 1 8 drams
Dram
Minim m

• Volume

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Metric System

• Base Units
• Wt - gram
• Volume liter
• Length meter
• Prefixes
• Centi
• Milli
• Micro
• Deca
• Hecto
• Kilo

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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 1m100cm1000mm
centimeter cm 1cm 10mm
milimeter mm
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Other Common Drug Measures

• Units U
• Milli unit mU
• Milli equivalent

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Conversions

• Use
• Ratio and Proportion
• 1 step problems
• 2 step problems
• (know) (want to know)
• X Y X Y
• mg g mg g

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Conversions between systems

• Metric Apothecary
  Household

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Conversion Equivalents
1g 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
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Drug Calculations
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Perform Calculation by

• Ratio and Proportion
• or
• Dimensional Analysis
• or
• Formula
• D/H x Q X

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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 50mg2ml
• Meaning 50 mg in 2ml of volume

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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

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Ratio Proportion

• One step Ratio Proportion
• Two step Ratio Proportion

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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.

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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.

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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.

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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.

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International Units

• Units
• Milliunits

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Reconstitution of medications

• Stability of the drug
• Powder mixed with diluent or solvent
• Reconstitute medication before giving to client