Drug Math

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Drug Math

• Natalie Capps, MNSc

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Objectives

• Demonstrate analysis of basic algebraic and math
  calculations
• Discuss math calculation formulas
• Demonstrate utilization of dimensional analysis
• Convert medications to administer the appropriate
  dosage
• Identify and define commonly used medical and
  pharmacological terminology and abbreviations

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Roman Numerals

• If the numeral of lesser value follows one of
  greater value it is added to that numeral
• Xi 10 1 11
• Numeral of the same value are repeated
• Xx 10 10 20
• If a numeral of lesser value precedes one of
  greater value it is subtracted from it
• Xix 10 10 1 19

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Fractions

• A fraction may be reduced if the numerator and
  denominator are both evenly divisible by the same
  number
• 2 1
• 4 2
• When two fractions have like numerators, the
  fraction with the smaller denominator represents
  the larger fraction
• 1 is larger than 1
• 3 6

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Fractions

• If two fractions have like denominators, the
  fraction with the larger numerator is the larger
  fraction.
• 2 is larger than 1
• 3 3
• Fractions with unlike numerators and unlike
  denominators must be changes to fractions with
  like denominators before determining their size
• 1 1 must be changed to 2 3 to compare
• 3 2 6 6

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Fractions

• To add or subtract fractions with like
  denominators, the denominator remains the same
  and the numerators are either added or subtracted
• 2 3 5
• 6 6 6

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Fractions

• To add or subtract fractions with unlike
  denominators, find the least common denominator
  by finding the smallest number divisible by both
  denominators
• 1 1 must be changed to 2 3
• 3 2 6 6

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Multiplication and division of Fractions

• To multiply fractions, multiply all of the
  numerators and then all of the denominators
• 1 x 1 1
• 2 3 6
• To divide fractions, invert the second fraction
  then follow the rules of multiplication.
• 2 1 2 x 3 6
• 4 3 4 1 4

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Multiplication and division of Fractions

• When changing an improper fraction to a mixed
  number, divide the numerator by the denominator.
  The quotient becomes the whole number and the
  remainder is the numerator of the new fraction
• 6 1 2 1 1
• 4 4 2

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Multiplication and division of Fractions

• When changing a mixed number to an improper
  fraction, multiply the whole number by the
  denominator, then add to that product the
  numerator. The resulting number is the numerator
  of the improper fraction.
• 1 2 6
• 4 4
• Mixed numbers are multiplied or divided by first
  converting them to improper fractions

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Decimals

• 0.12345
• The 1 is in the tenths place, the 2 is in the
  hundredths place, the 3 is in the thousandths
  place, the 4 is in the ten thousandths place, 5
  is in the hundred thousandths place.
• When adding or subtracting decimals, place the
  numbers in a column with the decimal points
  aligned. Then add or subtract from right to
  left.
• 0.01
• 0.2
• 0.002
• 0.212

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Decimals

• When miltiplying decimal numbers, the product
  contains as many decimal places as the sum of the
  decimal places n the nubmers being multiplied.
  If there are not enough numbers for correct
  placement of the decimal point, add as many zeros
  as necessary to the left of the answer.
• 0.25 0.12
• x0.2 x0.2
• 0.050 24 0.024

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Decimals

• To change a fraction to a decimal, the numerator
  is divided by the denominator.
• To multiply by 10, 100 or 1000, count the number
  of zeros and more the decimal point that number
  of places to the right
• To divide by 10, 100, or 1000, count the number
  of zeros and move the decimal point that number
  to the left

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Decimals

• To simplify a complex fraction, invert the
  denomiator and multiply the numerator by the
  denominator
• 2 2 1 2 x 2 4
• 1/2 2 1
• To change a decimal to a percent, multiply by 100
  or move the decimal two places to the right.
  Divide by 100 or more two places to the left to
  change a percent to a decimal.
• To change a fraction to a percent, change the
  fraction to a decimal first.

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Review of Rounding Rules for UAMS

• Remember with basic rounding, round at the end of
  the problem
• When converting pounds to kilograms, round to the
  nearest 10th
• Drops and units are too small to divde into
  parts. Round to the nearest whole number
• Tablets can be given whole or divided in half
• IV fluids can be calculated in drops per minute,
  cc per hour or milliliters per hour

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Dimensional Analysis

• Dimensional analysis is defined as a method of
  problem solving that changes one unit of
  measurement to another of multiplying that unit
  by a conversion factor
• Conversion factor is the component that produces
  a change in the form of a quantity or expression
  without changing the value
• EX 1 foot 12 inches or 1 ft or 12 inches
• 12 in
  1 ft

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Basic Rules

• Fractions in dimensional analysis represent
  relationships between two items
• There is 500mg of Penicillin in 25ml of Normal
  Saline
• 500mg 25 ml
• 25 ml 500 mg

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Basic Rules

• Begin your problem by identifying what unit of
  measurement you are looking for
• Ms. Smith is to receive 25mg of Zofran IM. The
  drug is available in a vial with 50mg in 1 ml.
  How many ml will you administer?

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Basic Rules

• One side of an equation can be multiplied by a
  conversion factor without changing the value of
  the equation
• The problem is correctly set up when all labels
  cancel from both the numerator and the
  denominator except the label that is desired in
  the answer

1 foot 12 inches
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Basic Rules

• Ms. Smith is to receive 25mg of Zofran IM. The
  drug is available in a vial with 50mg in 1 ml.
  How many ml will you administer?
• ml 1 ml x 25 mg
• 50 mg 1

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Systems of Measurement

• Metric
• weight gram
• Volume liter
• Length meter
• International Units
• Insulin 400 IU
• Heparin 5000U
• Household/Apothecary
• Drop
• Tablespoon/Teaspoon 1T 15 ml
• Ounce 1 ounce 30 ml
• Grain

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Systems of Measurement

• Milliequivalent (mEq)
• Represents how many grams of a drug are present
  in 1 ml of a normal solution

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Systems of Measurement

• Percentage ()
• Represents the number of grams of drug per 100 ml
  of solution
• A 1000cc IV bag is labeled 5 Dextrose in water.
  How many grams of Dextrose will it contain?

• 1000 x 0.05 (or 5) 50 grams
• b. 5 x 1000 50
• 100

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Conversions
1 L 1000 ml

• Liters to milliliters
• Kilograms to grams
• Milliliters to ounces
• Grains to milligrams
• Pounds to kilograms

1 kg 1000 g
30 ml 1 oz
1 gr 60 mg
2.2 lbs 1 kg
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Abbreviations

• a.c. Before meals
• q.i.d. 4 xs per day
• OU both eyes
• s without
• q.h.s each night _at_ bedtime
• p.r.n. when neccesary

• m.g. milligrams
• Lbs pounds
• s.q. subcutaneously
• m.l. milliliters
• gtts drops
• ad lib as desired

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Nurses Role

• Checking the medication order with the medication
  administration record
• 5 rights
• Right patient
• Right dose
• Right drug
• Right time
• Right route

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Nurses Role

• Drug forms
• Tablets scored tablets, enteric coated
• Capsules extended release, gelatin capsules
• Suspension or solution

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Nurses Role

• Components of a label
• Generic name-name derived from the chemical
  components of the drug ex acetaminophen
• Trade name-registered name given by the drug
  manufacturer ex Tylenol
• Strength of the drug
• Drug form
• Expiration Date
• Total amount of medication

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Algebra Review

• The unknown component that you are seeking to
  solve (X) is a variable
• The variable must be isolated on one side of the
  equation in order to solve the equation
• For example 3x 2 8
• 3x 2 2 8 2
• 3x 6
• 3x 6
• 3 3
• x 2

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Dimensional Analysis Problems

• Dosages are always expressed in relation to the
  drug form or unit of measure
• Ex 1 ml 5 mg or 1 tab 2 g
• 1ml or 1 tablet
• 5 mg 2 g
• When these factors are used in dimensional
  analysis equations they are expressed in terms of
  fractions

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Dimensional Analysis Problems

• A medication is ordered for 1500 mg. The solution
  strength available is 500mg per ml. How many ml
  must you prepare?
• Unit of measurement being calculated? ml
• ml 1 ml x 1500 mg 1500ml 3 ml
• 500 mg 500

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• All other factors entered so that each successive
  numerator matches the previous denominator to
  cancel out, leaving only the units of measurement
  being calculated
• You have 500 cc to run over 1 hour. The tubing
  for infusion released 20 gtts per 1 cc. How many
  gtts per minute will you administer the drug?
• gtts 20 gtts 500cc 1 hr
• min 1 cc 1 hr 60 mins

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Dimensional Analysis Problems

• If there is extraneous information, it will not
  cancel out
• When metric conversions are required, incorporate
  the conversion factor into the equation

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Dimensional Analysis Problems

• An order to give the patient 0.5 mg from an
  available strength of 200 mcg per ml. How many
  ml will be administered?
• Unit of measurement being calculated?
• ml x x
  2.5 ml

ml
1 ml 200 mcg
1000 mcg 1 mg
0.5 mg
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Dimensional Analysis Problems

• When there is a fraction in the denominator, the
  bottom fraction cannot be inverted
• Mg/kg/day mg mg x 1
• kg/day kg day

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Basic Rules

• Analyze the problem
• Conversion factor needed?
• Write neatly
• Reduce fractions by common denominators
• Always place a zero in front of the decimal
• Once you have arrived at the answer, ask yourself
  if this is a reasonable amount
• Recalculate