A Brief Overview of Pharmacy Calculations for Pharmacy - Free CE ...

A Brief Overview of PharmacyCalculations for PharmacyTechniciansRoman NumeralsRatio & ProportionDecimalsRounding NumbersSystems of MeasurementIV CalculationsRhomell Calara, PharmD, CPhKevin McCarthy, RPhCopyright PharmCon Inc 2010

A Brief Overview of Pharmacy Calculations forPharmacy TechniciansSpeaker: Rhomell Calara has built a solid reputation as Central Florida's premiere Consultant Pharmacist. Rhomell receivedhis Doctorate of Pharmacy from Nova Southeastern University in1997. After he graduated with high honors, he did a residencyin Primary Care/Ambulatory care at the Bay Pines VA Medical Center. Rhomell is currently employed by the Department ofVeterans Affairs as a Clinical/Consultant Pharmacist for the Florida Department of Veterans Affairs and is currently thePresident of Consultant Pharmacists of Central Florida (http://www.ConsultantRx.com).Speaker Disclosure: Rhomell Calara has no actual or potential conflicts of interest in relation to this programThis program has been brought to you by PharmConPharmCon, Inc. is accredited by the Accreditation Council for Pharmacy Education as aprovider of continuing pharmacy education.Legal Disclaimer: The material presented here does not necessarily reflect the views of Pharmaceutical EducationConsultants (PharmCon) or the companies that support educational programming. A qualified healthcare professional shouldalways be consulted before using any therapeutic product discussed. Participants should verify all information and databefore treating patients or employing any therapies described in this educational activity.

A Brief Overview of Pharmacy Calculations forPharmacy TechniciansAccreditation:Technicians: 0798-0000-09-094-L01-TTarget Audience: TechniciansCE Credits: 1.0 Continuing Education Hour or 0.1CEU for techniciansExpiration Date: 11/17/2012Program Overview: Accurately performing pharmaceutical calculations is a critical component in providingpatient care in every pharmacy practice environment and a vital part of any pharmacy technicians’ duty.Although most pharmaceutical calculations are not overly difficult, they do require flawless accuracy.Correct calculations contribute as much to patient outcomes as the newest methods and guidelines fordiagnosis, treatment, and prevention; and errors in calculations can turn the best attempts at optimal patientcare catastrophic. This session will present an overview of pharmacy calculations for technicians.Objectives:• Describe examples of common systems of measurement• Explain the process of percentage, ratio, and proportion and show how they apply to pharmacycalculations• Solve common pharmacy calculations using mathematical skills reviewed in this activityThis program has been brought to you by PharmCon

Introduction Speaker’s credentials and expertise orexperience in this topic. State/review the importance of basic mathin the practice of pharmacy

Program ObjectivesDefine the common systems of measurementExplain the process of percentage, ratio, andproportion and show how they apply topharmacy calculationsBe able to solve practical problems usingmathematical skills discussed in this talk

Roman Numerals Used in writing prescriptions. Used to specify the amounts of ingredientsor quantity to be dispensed. Used in the directions to the patient.

Roman Numeral Symbolsss = one-halfI = oneV = fiveX = tenL = fiftyC = one hundredM = one thousand

Roman Numerals Three Cardinal Rules:#1 If a symbol follows another symbol ofequal or greater value, the two symbols areadded together#2 If a symbol follows another symbol oflower value, the lower value is subtractedfrom the higher valuess= one-halfI = oneV = fiveX = tenL = fiftyC = onehundred#3 First perform any necessary subtraction,then add the resulting values together to getthe final answer

Roman NumeralsQUESTION 1: IX = ?QUESTION 2: CXXII = ?QUESTION 3: 20 = ?

Roman NumeralsQUESTION 1: IX = 9QUESTION 2: CXXII = 122QUESTION 3:20 = XX

Roman Numerals - Real Life

Ratio and Proportion Proportions will be your most used pharmacycalculation Solve most dosage calculations Numerous applications in everyday life Used when two expressions are directly related toone anotherFor instance, if 1 kg of drug cost us $5, how much2 kg cost?both expressions contain cost per weightif they are set up as ratios, once the problem issolved, both ratios should be equalwill

Ratio and ProportionA ratio is the relation between like numbersor values, or a way to express a fractionalpart of a whole. Ratios may be written: As a fraction: 2/3 With the ratio or colon sign: 2:3 Using "per": 2 milliliters per 3 hours(2ml/3hr)

Ratio and ProportionThe strength or concentration of various drugs canbe expressed as a ratio. First, read the label of thedrug and find the strength or concentration.Express this strength as a ratio in fractional form,as in the following examples:Tolnaftate solution, 10 mg per ml = 10 mg/1 mlKanamycin injection, 1.0 gm/3 ml = 1.0 gm/3 mlIsoproterenol inhalation, 1:200 = 1/200

Ratio and ProportionA proportion consists of two equal ratios andis essentially a statement of equalitybetween two ratios. For example:2 4--- = ---5 10

Ratio and ProportionExample 2.You have a 10-ml vial of aminophyllinelabeled "25 mg per ml".How many milliliters must be injected toadminister a dose of 125 mg?

Ratio and ProportionExample 1.You have a 10-ml vial of aminophylline labeled "25 mg per ml".How many milliliters must be injected to administer a dose of125 mg?25 mg 125 mg-------- = -----------1 ml X ml25mg (X) = (1 ml) (125 mg)X = 5 ml

Ratio and ProportionExample 2. How many milliliters must be injectedfrom an ampule of Prochlorperazine labeled "10mg/2 ml" in order to administer a dose of 7.5 mg?

Ratio and ProportionExample 2. How many milliliters must be injected from anampule of Prochlorperazine labeled "10 mg/2 ml" in orderto administer a dose of 7.5 mg?10 mg 7.5 mg-------- = -----------2 ml X ml10mg (X) = (2 ml) (7.5 mg)X = 1.5 ml

Ratio and ProportionA formula calls for 42 capsules of300mg of drug. How many milligramswould be required to make 24capsules?

Ratio and ProportionA formula calls for 42 capsules of 300mg of drug. Howmany milligrams would be required to make 24capsules?300mg = x 7,200 = 171.4 mg42 caps 24 caps 42

Ratio and Proportion – RealLifeOne person's error killed Elisha Crews Bryant,hospital officials said:“a miscalculation overdosed the pregnant 18-yearoldwith a magnesium sulfate meant to slow herlabor. She got 16 grams when she should havegotten 4 grams. The young mother began havingtrouble breathing, went into cardiac arrest andcould not be revived.”

Ratio and Proportion – RealLife Patient received 16 gms Mag. Sulfate, fataldose. Patient should have received 4 gms.How many ML @ 25 gm/50 ml should shehave received?

Ratio and Proportion – Real Life How many ML @ 25 gm/50 ml should shehave received to obtain 4 gms??25 gm 4 gm-------- = -----------50 ml X ml25gm X = 200 gm/mlX = 8 ml

Percentage PreparationsThree types of percentage preparations• Percent weight-in-weight (wt/wt)X Grams / 100 Grams• Percent volume-in-volume (v/v)X Milliliters / 100 Milliliters• Percent weight-in-volume (wt/v)*X Grams / 100 MillilitersMost Common

Percentage Preparations Example 1. How much Potassium Chloridein grams is needed to prepare a 1 Litersolution of 3% KCl solution?

Percentage Preparations Example 1. How much Potassium Chloridein grams is needed to prepare a 1 Litersolution of 3% KCl solution?Answer: 3% = 3 grams / 100mls1 Liter = 1000 mlsNext: 3 grams X grams---------- = -----------100 mls 1000 mlsFinally: x = 30 grams

Decimals–Three general rules when workingwith decimals#1 Never leave a decimal point “uncovered”- too easy to misread and make a mistake#2 Unless working with money, Never add zeros to the right of thedecimal point-the end signifies the accuracy of the number#3 The answer you get can be only as accurate as the least accuratenumber used in the calculation

Rounding Numbers–If the number following the place you arerounding to is 5 or higher, you round up–If the number following the place you arerounding to is 4 or lower, you round down

Try some rounding10.359 to tenths10.40.143 to hundredths0.149.9982 to thousandths9.998

Systems of MeasurementTHREE SYSTEMS–Avoirdupois-(household system)–Metric–Apothecary-(rarely used)

Metric SystemCONVERSION FACTORSMicro – one millionthMilli – one thousandthCenti – one hundredthDeci – one tenthKilo – one thousand

Avoirdupois Conversion Factors3 tsp = 1 tbsp2 tbsp = 1 oz16 oz = 1 pt2 pt = 1 qt4 qt = 1 G16oz = 1 lb

Conversion Factors Between Systems1 tsp = 5 ml1 tbsp = 15 ml1 oz = 30 ml (29.57ml)1 pt = 480 ml (473ml)1 G = 3840 ml(3784ml)1 g = 15.4 gr1 gr = 60 mg (64.8mg)1 kg = 2.2 lb1 lb = 454 g1 oz = 30 gm

Conversions6.3 oz = ? mlArrange the units so they will cancel and solveValue x Conversion Factor = Answer6.3 oz x 30ml = 189 ml1ozThe units of ounces cancel, and you are left with milliliters

ConversionYou receive a prescription for Cefzil250mg/5mls with directions to take 1teaspoonful by mouth twice daily for 10days.• How much drug in milligrams, is in oneteaspoonful?• How much Cefzil in milliliters do you haveto give the patient to last the full 10 days?

Parenteral (IV) Calculations Parenteral calculations deal withadministration of IV fluids Two main concepts you will learn- Flow Rate- Dose per Time

Flow Rate Calculations Flow rate is the speed at which an IV solutionis delivered Function of Volume per Time- usually reported in milliliters per hour The magical formulavolume ÷ time = flow rateAlways be sure which time and volume units you are being asked tosolve forIs it ml/min ? Or l/hr? Something else?

Flow Rate CalculationsA patient receives 1 L of IV solution over a 3 hour period.Calculate the flow rate in ml/hr.Note: the volume given is in liters, but the answer asks formilliliters. If the conversion wasn’t so obvious, we would firstneed to do a conversion of L ml.volume ÷time = flow rate1000 ml ÷ 3 hours = 333 ml/hr

Another Rate ProblemA patient receives 0.75L of IVsolution over a 4 hourperiod. Calculate the flowrate in ml/hr

Another Rate ProblemA patient receives 0.75L of IV solution over a 4 hourperiod. Calculate the flow rate in ml/hrNow the conversion is a bit harder, so we do the math0.75 L x 1000ml = 750ml1 1L750 ml ÷ 4 hours = 188 ml/hr

Solve for Time By manipulating the rate formula, we cansolve for time The equation becomes:volume ÷ rate = time

Solving for TimeIf an IV is run at 125ml/hr, how longwill 1 L last?

Solving for TimeIf an IV is run at 125ml/hr, how long will 1 L last?volume ÷ rate = time1000 ml = 8 hours125ml/hrMilliliters cancel and you are left with the units of hours

Solving for Volume Play with the formula some more, and nowwe can solve for volume The equation becomes:rate x time = volume

Solving for VolumeHow many ml of IVsolution would berequired to run anIV for 12 hours at arate of 60 ml/hr?

Solving for VolumeHow many ml of IV solution would be required to run an IVfor 12 hours at a rate of 60 ml/hr?rate x time = volumeIT’S REALLY JUST A CONVERSION PROBLEM!60 ml x 12 hr = 720 ml1hr 1

Solving for VolumeWhat volume would we need to have onhand if an IV solution is to be run for 100ml/hr for 8.3 hrs?

Solving for VolumeWhat volume would we need to have on hand if anIV solution is to be run for 100 ml/hr for 8.3 hrs?100 ml x 8.3 hr = 830 ml1 hr

Any Questions?ARE YOU READY FOR THE“PHARMACYTECHNICIAN MATHCONTEST”ON-LINE COMPETITION!

This is Pope John the 22 nd , whatwould that be in Roman Numerals?

This is Pope John the 22 nd , whatwould that be in Roman Numerals?Pope John XXII

Question: What number super bowlis illustrated below, and, what teamwon the game?

Question: What number super bowlis illustrated below, and, what teamwon the game?Super Bowl 43, won bythe Pittsburgh Steelers

What is the sum ofXLVI + IXin Roman Numerals?

What is the sum ofXLVI + IXin Roman Numerals?46 + 9 = 55 or LV

• If a customer asked to buy 10 packages ofSudafed, containing 20 tablets of 30 mgPseudoephedrine, how many milligrams ofPseudoephedrine is she purchasing?• Why would she want so much Sudafed?

• If a customer asked to buy 10 packages of Sudafed,containing 20 tablets of 30 mg Pseudoephedrine, howmany milligrams of Pseudoephedrine is he purchasing?10 Packs X 20 Tabs X 30 mg = 6000 mg• Why would she want so much Sudafed?– Key ingredient in the making ofmethamphetamine

• Your customer now has 6000 mg ofPseudoephedrine. If it takes 1800 mg ofPseudoephedrine to make 6 gm of crystalmeth, how many grams can she make?

• Your customer now has 6000 mg of Pseudoephedrine. If ittakes 1800 mg of Pseudoephedrine to make 6 grams ofcrystal meth, how many grams can she make?1800 mg PSE 6000 mg PSE----------------- = ---------------------6 gm Crys Meth X gm CrysMeth(1800mg PSE)( X )=( 6000 mg PSE)(6gm CryMeth)1800 mg X = 36000 mg/gmX = 20 gm

• Your Meth addict now has 20 gm of drug.• She wants to make a nasal solutioncontaining 25% crystal meth. How manyml of normal saline solution does she needto make a 25% solution?

• Your Meth addict now has 20 gm of drug.• She wants to make a nasal solutioncontaining 25% crystal meth. How manyml of normal saline solution does she needto make a 25% solution?25 gm 20 gm PSE----------------- = ---------------------100 ml X ml Saline(25 gm( X )=( 20 gm PSE)(100 ml)X = 80 ml

Pharmacy Technician Josh is travelingin Europe. He needs to fill up his rentalcar. Gas cost only $1.25 per liter.Technician Josh is excited that gas is socheap.What would the cost of gas be ingallons?Hint: 1 pint = 473 milliliters

Pharmacy Technician Josh is travelingin Europe. He needs to fill up his rentalcar. Gas cost only $1.25 per liter.Technician Josh is so excited that gas isso cheap.What would the cost of gas be in473 mlgallons?8 pint 1 liter $1.25-------- x ----------- x ---------- x --------- =$4.73 gal1 pint 1 gal 1000 ml 1 liter

Round to the nearestThousand1) 14,389 _________2) 29,610 _________3) 3,492 _________

Round to the nearestThousand1) 14,389 14,0002) 29,610 30,0003) 3,492 3,000

Round to the nearesttenth1) 0.89 _________2) 2.673 _________3) 2.57 _________

Round to the nearesttenth1) 0.89 0.92) 2.673 2.73) 2.57 2.6

What is the flow rate in ml/hr if1 liter Starbucks Coffee with100% french roast is givenover 12 hours???

83.3 ml/hr(1 liter = 1000 ml)1000 ml/12 hours = 83.3ml/hr

Try and solve this problem ;o)The Recommended dose of meperidine(demerol) is 6mg/kg/24hrs for pain. It is givenin divided doses of every 4 to 6 hours. Howmany milliliters (ml) of demerol injection (50mg/ml) should be administered to a 33 poundchild as a single dose every 6 hours?

1. The first step is to calculate the daily dosefor a 33 pound child6 mg___ = ____x mg1 Kg (2.2 pounds) 33pounds*By inserting the conversion unit 2.2 poundsfor 1kg in the ratio there is no need to do aseparate calculation of the number ofkilograms in 33 pounds.X = 90 mg of demerol per day (24 hours)

2. The next step is to calculate the number ofmilliliters of demerol injection (50 mg/ml)needed for the total daily dose50mg= 90mg1 ml x ml50x = 90X = 1.8 ml every 24 hours

3. The final step is to calculate the number ofmilliliters to be given every 6 hours1.8 ml = x ml24 hrs 6 hrs24x = 10.8X = 0.45 ml**So therefore the amount of demerol(50mg/ml) to be administered is 0.45 mlevery 6 hours **

Any Questions?

Any Questions?