Pharmacology 1104

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Pharmacology 1104

• Introduction to Drug Calculations
• Brown Mulholland
• (Chpt. 1, 2 4)

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Objectives

• Utilize Roman numerals accurately when
  calculating medications.
• Convert fractions to whole numbers.
• Find lowest common denominators in fractions.
• Add, subtract, multiply, and divide fractions and
  reduce to lowest terms.
• Given two fractions, determine which is greater
  and which is smaller.

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Objectives

• Read decimal fractions.
• Add, subtract, and divide decimals.
• Round decimals to the nearest tenth, hundredth,
  and whole number.
• Solve ratio/proportion problems for x.
• Utilize ratio/proportion to solve one-step metric
  equivalent problems.

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Roman Numerals

• Sometimes used in prescribing medications in the
  Apothecariessystem.
• Uses letter to represent numbers.
• Most common letters ss(1/2), i (1), v (5),
  x(10).
• Add when largest numerals are on the left and the
  smallest is on the right.
• Example vi 6 xv 15 viss 6.5
• Subtract when the smallest numeral is on the left
  and the largest numeral is on the right.
• Example iv 4 ix 9

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Roman Numerals

• Subtract values first then add when the smallest
  numeral is in the middle and the larger numerals
  are on either side.
• Example xiv 14 xix 19
• Roman numerals of the same value can be repeated
  in sequence only up to three times.
• Example x 10 xx 20 xxx 30
• When you can no longer repeat, you need to
  subtract.
• Example 3 iii 4 iv 8 viii

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Fractions

• 4/6 4 numerator / 6 denominator
• Adding fractions with like denominators
• Add the numerators
• Place the answer over the denominator
• reduce the answer to the lowest term by dividing
  the numerator and the denominator by the largest
  number that can divide them both.1/4 1/4 1
  1 / 4 2/4 1/2

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Fractions

• Adding fractions with unlike denominators
• Find the smallest number that denominators of
  each fraction divide into evenly (least common
  denominator)
• Divide the denominator into the least common
  denominator and multiply the results by the
  numerator.
• Add the new numerators and place over the new
  denominator (least common denominator)
• Reduce to the lowest terms.
• 1/4 1/3 ( 4 and 3 will divide into 12 evenly)

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Fractions

• Subtracting fractions with like denominators
• Subtract the numerators
• Place the difference over the denominator
• Reduce to lowest terms
• 3/4 - 1/4 2/4 1/2
• Both numbers divisible by 2

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Fractions

• Subtracting fractions with unlike denominators
• Find the least common denominator and convert
  fractions.
• Subtract the numerators.
• Place the difference over the least common
  denominator.
• Reduce to lowest terms.
• 3/2 - 3/4 (Both 2 4 divisible into 4)
• 4 2 2 x 3 6
• 4 4 1 x 3 3 6/4 - 3/4 6-3 / 4
  3/4

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Fractions

• Multiplying Fractions
• Multiply the numerators
• Multiply the denominators
• Reduce to lowest terms
• 2/3 x 3/4 2x3 / 3x4 6/12
• 6 will divide evenly into 6 and 12
• 6/12 1/2

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Fractions

• Dividing fractions
• Invert the divisor (1/2 becomes 2/1)
• Change the division sign to multiplication
• Multiply the numerators
• Multiply the denominators
• Reduce to the lowest terms
• 1/4 (dividend) 1/2 (divisor)
• 1/4 1/2 1/4 x 2/1 1x2 / 4x1 2/4 1/2

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Sample Problems

• 2/3 1/3 ?
• 2/4 2/6 ?
• 4/6 - 1/6 ?
• 2/3 - 1/4 ?
• 1/3 x 2/6 ?
• 1/150 1/300 ?
• 1/2 100 ?

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Fractions

• Given two fractions, which is greater and which
  is smaller?
• Rule The smaller the bottom number (denominator)
  of a fraction, the greater the fractions value.
• 1/3 or 1/5 which is greater?
• 1/100 or 1/150 which is greater?
• 1/4 or 1/6 which is greater?

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Decimal Fractions (pg.13)

• Rule All whole numbers are to the left of the
  decimal all decimal fractions are to the right
  of the decimal point.
• To read a decimal fraction, read the number to
  the right of the decimal and use the name that
  applies to the place value of the last figure.
• Decimal fractions read with a ths on the end.
• To read a whole number and a fraction, the
  decimal point reads as an and.

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Decimal Fractions

• 0.3 three tenths
• 0.5 five tenths
• 1.3 one and three tenths
• 1.5 one and five tenths
• 0.12 twelve hundreths

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Add, Subtract, Divide Decimals

• 1.24 2.14 3.38
• 1.24 1.02 1.432 0.5
• 2.14 0.89 - 0.112 0.6
• 3.38 1.91 1.320 1.1
• 1.50 2 0.75
• 2.650 4 0.6625

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Round Decimals to nearest 10,100, Whole Numbers

• Calculate one decimal place beyond the desired
  place.
• If the final digit is 4 or less, make no
  adjustment.
• If the final digit is 5 or more increase the
  prior digit by one.
• Drop the final digit.
• Examples
• 0.75 0.8 0.67 0.7 0.125 0.13 0.4
  0.4
• 0.64 0.6 0.164 0.16 0.6 1

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Medication Alert!

• Do not round medication dosages to the nearest
  whole number. This could result in a medication
  overdosage.
• Rule Always round your answers to the nearest
  measurable dose after you verify that the dose is
  correct for that patient.

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Ratio and Proportion

• Ratio Composed of two numbers which are somehow
  related to each other. In dosage problems, ratio
  is used to represent the weight of a drug in a
  certain volume of solution or package.
• Example
• 1 ml 100mg (ml contains 100mg of the drug)
• 1 tablet 50 mg (1 tablet contains 50 mg of the
  drug)

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Ratio Proportion

• Proportion Consists of two ratios separated by
  an equal sign which indicates that the two ratios
  are equal.
• Example
• 1 50 2 100
• 1 ml 50 mg 2 ml 100 mg
• If 1 ml contains 50 mg then 2 ml contains 100mg
• The numbers on the end are called extremes
• The numbers in the middle are called means
• Example
• 1 50 2 100, 1 50 2
  100
• 1 times 100 100
• 50 times 2 100

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Ratio Proportions

• Ratio and proportion is used in dosage
  calculations when only one ratio is known or
  complete, and the other ratio is incomplete.
• Example The doctor orders Lasix 40 mg po stat.
  What you have available is Lasix 20 mg per
  tablet.
• Set up the problem
• What you have Lasix 20 mg per 1 tablet
• What you want Lasix 40 mg per x tablet
• 20 mg 1 tab 40 mg x tab
• 20 x 1 ( 40 )
• 20 x 40
• x 40/20
• x 2 tabs

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Ratio Proportion Pointers

• Set your problem up the same way each time.
• Write what you have (or the known ratio) first
  this comes from the drug label.
• Write what you want second (or the dosage
  ordered).
• Make the x that you are solving for last.
• You must write the ratio in the same sequence of
  measurement units or the answer will be wrong.

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Example mg ml mg ml

• Example The doctor ordered 0.4 mg of Atropine.
  The drugs label reads 1000mcg in 2 ml.
• What you have 1000mcg per 2 ml
• What you want 0.4 mg per ml
• To calculate the correct answer you must first
  convert all measurement units to be the same.

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Convert 0.4 mg to 400 mcg
STEP 1

• 1 mg 1000 mcg 0.4 mg x mcg
• 1x 1000(0.4)
• 1x 400
• x 400/1
• x 400mcg

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Solving the Problem
STEP 2

• What you have 1000 mcg per 2 ml
• What you want 400 mcg per x ml (this is the
  0.4 mg we converted to mcg in step1)
• 1000 mcg 2 ml 400 mcg x ml
• 1000x 2(400)
• 1000x 800
• x 800/1000
• x 0.8 ml

ALWAYS write a zero in front of the decimal point
to prevent errors
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Sample Problems

• 25 mg x g
• 0.3 mg x g
• 2.8 L x ml
• 1000 mg 1 mg 150 mg x mg
• 200 mg 5 ml 300 mg x ml
• 175 mcg 1 tab 350 mcg x tab

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Sample Problems

• Ordered Vistaril 60 mg
• Available Vistaril 100mg/2ml
• Ordered Heparin 2000u
• Available Heparin 6000u/ml

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Sample Problems

• 20 mg is equal to how many gr?
• 60 mg 1 gr 20 mg x gr
• 60 x 20/60 (1/3)
• x 0.333
• 1/4 tsp equals how many milliliters?
• 1 tsp 5 ml 1/4 tsp x
• 1x 5/4
• x 1.25

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Sample Problems

• 0.04 g ____µg
• 1 g 1000mg 0.04 g x mg
• x 40 mg
• 1 mg 1000 µg 40 mg x µg
• x 40,000
• gr 1/6 ____mg
• 1 gr 60 mg 1/6 x mg
• x 60/6
• x 10 mg

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Questions?