Transcript Practice Basics

Chapter 14: Pharmacy Calculations
Learning Outcomes
 Explain importance of standardized approach for math
 Convert between fractions, decimals, percentages
 Convert between different systems of measurement
 Perform & check key pharmacy calculations:
 to interpret prescriptions
 involving patient-specific information
Key Terms
 Alligation method
 Apothecary system
 Avoirdupois system
 Body mass index (BMI)
 Body surface area (BSA)
 Days supply
Key Terms
 Denominator
 Fraction
 Household system
 Ideal body weight (IBW)
 Metric system
 Numerator
 Proportion
 Ratio
 Ratio strengths
Review of Basic Math
 Arabic numerals (0,1,2,3)
 Roman numerals
 ss = 1/2
 L or l = 50
 I or i = 1
 C or c = 100
 V or v = 5
 M or m = 1000
 X or x = 10
Roman Numeral Basics
 More than 1 numeral of same quantityadd them
 Locate smaller numerals
 smaller numerals on right of largest numeral(s)

add small numerals to largest numeral
 smaller numerals on left of largest numeral(s)

subtract smaller numerals from largest numeral
 Example: XXI = 10 + 10 + 1 = 21
 Example: XIX = 10 + 10 – 1 = 19
Numbers
 Whole numbers (0, 1, 2)
 Fractions (1/4, 2/3, 7/8
 Mixed numbers (1 ¼ , 2 ½ )
 Decimals (0.5, 1.5, 2.25)
Fractions
 Fraction represents part of whole number
 less than one
 quantities between two whole numbers
 Numerator=number of parts present
 Denominator=total number of parts
 Compound fractions or mixed numbers
 whole number in addition to fraction ( 3 ½)
Fractions in Pharmacy
 IV fluids include
 1/2 NS (one-half normal saline)
 1/4 NS (one-quarter normal saline)
 3/4 teaspoon
 Med errors may occur if someone mistakes the / for a 1
Simplify or Reduce Fractions
 Find greatest number that can divide into numerator
and denominator evenly
 Fractions should be represented in simplest form
 Example: Simplify the fraction 66/100
 66 divided by 2 ⇒ 33
 100 divided by 2 ⇒ 50
 This fraction cannot be reduced further because no
single number can be divided into both 33 and 50
evenly
 Answer: 33/50
Adding Fractions
1. Make sure all fractions have common denominators
Example: 3/4 + 2/3


3/4 * 3/3 = 9/12
2/3 * 4/4 = 8/12
2. Add the numerators

9/12 + 8/12 = 17/12
3. Reduce to simplest fraction or mixed number

17/12 = 1 5/12
Subtracting Fractions
1. Make sure all fractions have common denominators
 Example: 1 7/8 – ½


1 7/8=1 + 7/8=8/8 + 7/8=15/8
1/2 * 4/4 = 4/8
2. Subtract the numerators

15/8 – 4/8 = 11/8
3. Simplify the fraction
 subtract 8 from the numerator to represent one whole
number
 11/8 = 1 3/8
Multiplication
1. Multiply numerators
 Example: 9/10 * 4/5

9 * 4 = 36
2. Multiply denominators.

10 * 5 = 50
3. Express answer as fraction
9/10 * 4/5 = 36/50
4. Simplify fraction
 36 divided by 2 = 18
50 divided by 2 = 25
 Final answer = 18/25
Division
 Convert 2nd fraction to its reciprocal & multiply
 Example: 2/3 ÷ 1/3
1. 1/3 is converted to 3/1.
2. Multiply 1st fraction by 2nd fraction’s reciprocal

2/3 * 3/1 = 6/3
3. Simplify fraction




6 divided by 3 = 2
3 divided by 3 = 1
6/3=2/1=2
Final answer = 2
Decimals
 Decimals are also used to represent quantities less
than one or quantities between two whole numbers
 Numbers to left of decimal point represent whole
numbers
 Numbers to right of decimal point represent quantities
less than one
100.000
hundreds, tens, ones, tenths, hundredths, thousandths
Decimal Errors
 Medication errors can occur
 decimals are used incorrectly or misinterpreted
 sloppy handwriting, stray pen marks, poor quality faxes
 copies can lead to misinterpretation
 To avoid errors
 use decimals appropriately
 never use trailing zero- not needed ( 5 mg, not 5.0 mg)
 always use leading zero (0.5 mg not .5mg)
Convert Fractions to Decimals
 If whole number present, that number is placed to left
of decimal, then divide fraction
 Example:
 1 2/3 → place 1 to left of decimal: 1.xx
 To determine numbers to right of decimal
 divide: 2/3 = 0.6667
 Final answer = 1.6667
 In most pharmacy calculations, decimals are rounded
to tenths (most common) or other as determined
Rounding Decimals
 To round to hundredths
 look at number in thousandths place
 if it is 5 or larger increase hundredths value by 1
 if it is less than 5, number in hundredths place stays the
same
 in either case, number in thousandths place is dropped
 Example: Round 1.6667 to hundreths
 look at number in thousandth place 1.6667
 final answer is 1.67
 Pharmacy numbers must be measureable/practical
Percentages
 Percentages are blend of fractions & decimals
 Percentage means “per 100”
 Percentages can be converted to fractions by placing
them over 100
 Example:

78% =78/100
 Percentages convert to decimals
 Remove % sign & move decimal point two places to the
left
 Example: 78% = 0.78
Ratios and Proportions
 A ratio shows relationship between two items
 number of milligrams in dose required for each
kilogram of patient weight (mg/kg)
 read as “milligrams per kilogram”
 Proportion is statement of equality between two ratios
 Units must line up correctly
 (same units appear on top of equation & same units
appear on bottom of equation)
 May need to convert units to make them match
Proportion Example
 Standard dose of a medication is 4 mg per kg of
patient weight
 If patient weighs 70 kg, what is correct dose for this
patient?
 Set up proportion:
4mg/kg=x mg/70kg
 x represents unknown value
(in this case, number of mg of drug in dose)
Solve the Proportion
 Using algebraic property
 if a/b=c/d then ad=bc
 Solve for x:
4mg/kg=x mg/70kg
4mg*70kg=1kg*xmg
isolate x by dividing both sides by 1kg:
4mg*70kg = 1kg*xmg
1kg
1kg
Completing the Problem
4mg*70kg = 1kg*xmg
1kg
1kg
Units cancel (kg) to give this equation:
4mg*70=x mg
Therefore: 280mg=x mg
A patient weighing 70kg receiving 4mg/kg should
receive 280mg
Metric System
 Most widely used system of measurement in world
 Based on multiples of ten
 Standard units used in healthcare are:
 meter (distance)
 liter (volume)
 gram (mass)
 Relationship among these units is:
 1 mL of water occupies 1 cubic centimeter & weighs 1
gram
Metric Prefixes
 “Milli” means one thousandth
 1 milliliter is 1/1000 of a liter
 Oral solid medications are usually mg or g
 Liquid medications are usually mL or L
Metric Conversions
 Stem of unit represents type of measure
 Note relationship & decimal placement
0.001 kg = 1 gram = 1000 mg = 1000000 mcg
 1 kilogram is 1000 times as big as 1 gram
 1 gram is 1000 times as big as 1 milligram
 1 milligram is 1000 times as big as 1 microgram
 Converting can be as simple as moving decimal point
Other Systems in Pharmacy
 Apothecary System
 developed in Greece for use by physicians/pharmacists
 has historical significance & has largely been replaced
 The Joint Commission (TJC) recommends

avoid using apothecary units (institutional pharmacy)
 Apothecary units still used in community pharmacy
 Common apothecary measures still used
 grain is approximately 60-65 mg
 dram is approximately 5 mL
Other Systems in Pharmacy
 Avoirdupois System
 French system of mass: includes ounces & pounds
 1 pound equals 16 ounces
 Household System
 familiar to people who like to cook
 teaspoons, tablespoons, etc.
 good practice to dispense dosing spoon or oral syringe

with both metric & household system units
Common Conversions
2.54 cm = 1 inch
1 kg = 2.2 pounds (lb)
454 g = 1 lb
28.4 g= 1 ounce (oz) but may be rounded to 30 g = 1 oz
5 mL = 1 teaspoon (tsp)
15 mL = 1 tablespoon (T)
30 mL = 1 fluid ounce (fl oz)
473 mL = 1 pint (usually rounded to 480 mL)
Household Measures
 1 cup = 8 fluid ounces
 2 cups = 1 pint
 2 pints = 1 quart
 4 quarts = 1 gallon
Conversions
 Formula for converting Fahrenheit temp (TF) to
Celsius temp (TC):
TC=(5/9)*(TF-32)
 Formula for converting Celsius temp ((TC ) to
Fahrenheit temp (TF): TF=(9/5)*(TC +32)
Common Temps
Celsius °
Fahrenheit°
Normal Body Temp
37°
98.6°
Freezing
0°
32°
Boiling
100°
212°
Military Time
 Institutions use 24-hour clock
 24-hour clock=military time
 does not include a.m. or p.m.
 does not use colon to separate hours & minutes
 Examples:
0100=1 AM
1300=1 PM
2130 = 9:3o PM
Conversions
 Example: How many mL in 2.5 teaspoons?
 Set up proportion, starting with the conversion you know:
5 mL per 1 tsp or 5mL/tsp
 Match up units on both sides of =
5mL/tsp= __ mL/__ tsp
 Fill in what you are given & put x in correct area
5mL/tsp= x mL/2.5tsp
 Now solve for x by cross multiplying and dividing:
5mL*2.5tsp=1tsp*x mL so 12.5mL=x mL
 Answer: There are 12.5mL in 2.5 tsp
Patient-Specific Calculations
 Three examples of patient-specific calculations
body surface area
2. ideal body weight
3. body mass index
1.
Body Surface Area (BSA)
 Value uses patient’s weight/height & expressed as m2
 Example:
man weighs 150 lb (68.2 kg), stands 5’10” (177.8 cm) tall
BSA=1.8 m2
 BSA used to calculate chemotherapy doses
 Several BSA equations available
 find out which equation is used at your institution
 Hospital computer systems will usually calculate the
BSA value
Ideal Body Weight (IBW)
 Ideal weight is based on height & gender
 Expressed as kg
 Common formula for determining IBW:
 IBW (kg) for males = 50 kg + 2.3(inches over 5’)
 IBW (kg) for females = 45.5 kg + 2.3(inches over 5’)
IBW Example
 Calculate IBW for 72-year-old male 6’2” tall
 Formula: IBW (kg) for males = 50 kg + 2.3(inches over 5’)
 IBW (kg) = 50 kg + 2.3(14)
 IBW = 82.2 kg
 Example:
 calculate IBW for 52-year-old female 5’9” tall.
 IBW (kg) = 45.5 kg + 2.3(9)
 IBW = 66.2 kg
Body Mass Index (BMI)
 Measure of body fat based on height & weight
 Determines if patient is
 underweight
 normal weight
 overweight
 obese
 BMI is not generally used in medication calculations
Key Pharmacy Calculations
 Pediatric dosing determined by child’s weight
 Example: diphenhydramine syrup: 5 mg/kg per day
 if child weighs 43 lb, how many mg per day?
Convert values to the appropriate units
x=19.5 kg
Determine dose
5mg/kg=xmg/19.5kg
5mg*19.5kg=1kg*xmg
x=97.5mg of diphenhydramine
Days Supply
 Evaluate dosing regimen to determine
 how much medication per dose
 how many times dose is given each day
 how many days medication will be given
 Example: Metoprolol 50 mg po bid for 30 days
only 25 mg tablets available
1. dose is 50 mg-requires two 25-mg tablets
2. dose is given bid (twice daily) 2 tabs* 2 = 4 tabs/day
3. given for 30 days, so 4 tabs/day*30 days = 120 tablets
Concentration & Dilution
 Mixtures may be 2 solids added together
 percentage strength is measured as weight in weight
(w/w) or grams of drug/100 grams of mixture
 Mixtures may be 2 liquids added together
 Percentage strength measured as volume in volume
(v/v) or mL of drug/100mL of mixture
 Mixtures may be solid in liquid
 percentage strength is measured as weight in volume
(w/v) or grams of drug per 100mL of mixture
Standard Solutions
 To determine how much dextrose is in 1 liter of D5W
 weight (dextrose) in volume (water) mixture (w/v)
 Set up proportion-start with concentration you know
& then solve for x
 Make sure you have matching units in the numerators
& denominators
 D5W means 5% dextrose in water=5 g/100 mL
 Start with 5 g/100 mL
 Convert 1 liter to mL so that denominator units are mL
on both sides of equation
Standard Solutions
 How much dextrose is in 1 liter of D5W?
 Steps to solve the problem
 5g/100mL=xg/1000mL
 5g*1000mL=100mL*xg
 divide each side by 100mL to isolate x
 perform calculations & double check your work
 50g=x There are 50 grams of Dextrose in l liter of D5W
Alligation Method
 It may be necessary to mix concentrations above and
below desired concentration to obtain desired
concentration
 Visualize alligation as a tic-tac-toe board:
Conc you have
Conc you want
Parts of each
Alligation
 Add 5% and 10% to obtain 9%
%Conc you have
%Conc you want
5%
9%
10%
# of parts of each
Alligation
 Add 5% and 10% to obtain 9%
 Subtract crosswise to get # of parts of each
%Conc you have
%Conc you want
5%
10-9=1 Part
9%
10%
# of parts of each
Alligation
 Add 5% and 10% to obtain 9%
 Subtract crosswise to get # of parts of each
 Need 1 part of 5% solution & 4 parts of 10% solution
 Total parts=5 parts
%Conc you have
%Conc you want
5%
# of parts of each
10-9=1 Part
9%
10%
9-5=4 Parts
Alligation
 Determine how much you need to mix by using
proportions relating to parts
 If you want a total of 1 L or 1000 mL set up like this:
1 part/5 parts=x mL/1000 mL
x=200mL of 5%
Since total is 1000 mL, 1000mL-200mL=800mL of 10% solution
%Conc you have
%Conc you want
5%
# of parts of each
10-9=1 Part
9%
10%
9-5=4 Parts
Another Solution
 Another method to solve similar problems mixing 2
concentrations to obtain a 3rd concentration
somewhere between original 2 concentrations:
 C1V1 = C2V2
 You need to know 3 of these values to solve for the 4th
Specific Gravity
 Specific gravity is ratio of weight of compound to
weight of same amount of water
 Specific gravity of milk is 1.035
 Specific gravity of ethanol is 0.787
 Generally, units do not appear with specific gravity
 In pharmacy calculations, specific gravity & density are
used interchangeably
 specific gravity = weight (g)
volume(mL)
Chemotherapy Calculations
 System of checks & rechecks important in chemotherapy
 Example: medication order is received for amifostine
200 mg/m2 over 3 minutes once daily 15–30 minutes prior
to radiation therapy
patient is 79-year-old man weighing 157 lb & standing 6’ tall
BSA is 1.9 m2
What is the dose of amifostine for this patient?
Solution
 Set up equation
 Ordered dose of amifostine 200mg/m2
 BSA is 1.9 m2
 200mg/m2=xmg/1.9m2
Note how units match up
200mg*1.9m2 =1m2 *xmg Now divide both sides by 1m2
380mg=xmg
The correct dose of amifostine is 380mg