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Presents… “Math for Health Care Professionals”

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1 Presents… “Math for Health Care Professionals”
James J. (Jim) De Carlo, RN, MA, BSN, BA Laboratory and Clinical Instructor NYU College of Nursing

2 A story pulled from the headlines…
Actor Dennis Quaid’s newborn twins are hospitalized at a prestigious hospital in California for an infection. Pharmacy technicians and nurses accidentally administer 1000x too much of a anti-clotting drug Heparin. Quaid states that he saw blood splatter across the room as a bandage was replaced on one of his babies. The twins recovered, but Quaid and his wife sue the drugmaker for negligence.

3 Key points from this story…
Dosing mistakes are made, even today, at the best hospitals. Patients are harmed by dosing errors. Nurses are often the last stop in quality control before a drug is administered. Giving 10x, 100x, or 1000x too much, or too little of a drug is a common mistake.

4 Steps for error prevention…
Know “reasonable” doses for commonly prescribed drugs. Be comfortable with numbers and basic math. Process a doctor’s order confidently and accurately. Assess whether a calculated dose is “reasonable.” Always double check with a colleague to ensure proper dosing.

5 Goals for this course… Goal Set 1 (Slides 5-19):
To reinforce basic building blocks of arithmetic. To introduce simple math problems commonly found in healthcare. Goal Set 2(Slides 20-25): To learn about measurements and units systems typically encountered in the healthcare. Goal Set 3( Slides 26-33): To learn how to solve dosage calculation problems with step-by-step solutions to sample problems.

6 Common medical symbols/ abbreviations

7 Anatomy of a “base 10” number
How many ones How many hundreds 5,020,720 WHOLE NUMBERS: Numbers used in counting: (0,1,2,3,etc) used as digits and placed in neat columns! How many tens Got the IDEA?

8 RELAX! Here goes Order of operations… 3+5-2x2-(4-2)=oh my first
last Follow these simple rules: -PARENTHESES -EXPONENTS -MULTIPLICATION (left to right) -DIVISION (left to right) -ADDITION (left to right) -SUBTRACTION (left to right) =3+5-2x2-(4-2) =3+5-2x2-2 Parentheses first = Multiplication second Reversible =8-4-2 Addition third =4-2 Subtraction Left fourth An acronym to remember: Please Excuse My Dear Aunt Sally =2 Subtraction fifth DONE!

9 Addition without a calculator…
A patient is not to consume greater than 300 milligrams of NaCl (salt) in a meal. Can she eat lunch from the cafeteria? (NaCl in one hospital drink) 61 milligrams + (NaCl in one sandwhich) 256 milligrams= ? 256 61 + ones tens hundreds Let's Set It Up 1 Remember: 11 tens is the same as 1 ten and 1 hundred Too much salt 3 7 How many ones? How many hundreds? How many tens?

10 Subtraction without a calculator…
A patient receives 525 milliliters of blood through a transfusion. Soon after, he accidentally cuts himself and loses approximately 256 milliliters of blood How much total blood did he gain? (blood gained) 525 mL - (blood lost) 256 mL = ? 525 256 - ones tens hundreds Let's Set It Up 6 Remember: 5 hundreds and 1 ten is the same as 4 hundreds and 11 tens 4 1 9 1 Remember: 2 tens and 5 ones is the same as 1 ten and 15 ones Done! 2 How many ones? How many hundreds? How many tens?

11 Let's Set It Up ... Multiplication…
Performing an important calculation by hand, in addition to a calculator, is a great way to double check your answer. Let’s consider an example: The doctor asks you to administer 105 milligrams of drug for every kilogram that the patient weighs. If the patient ways 80 kilograms, What is the appropriate drug dosage? Let's Set It Up ...

12 105 15 x 5 5 2 105 + 1575 Finished! hundreds ones tens 2
Multiply ones by ones (carry the 2) 2 5 Multiply ones by hundreds 2 Multiply ones by tens 105 Add it up + 1575 Do it again with the tens! Finished!

13 - 5 600 12 60 - Let's Set It Up Division… mg/kg Division procedure
Let’s try a similar type of problem that involves division. You are working in a pediatric ward. The doctor asks you how much drug the patient has received per kilogram of body weight. The child received 600 milligrams of drug and weighs 12 kilograms. The answer is… Division procedure…again 1. Divide: 12 into 00 2. Multiply: 0 x12 3. Subtract: 0-0 - 4. Nothing left Division procedure 1. Divide: 12 into 60 5 mg/kg Let's Set It Up 600 12 2. Multiply: 5 x12 60 3. Subtract: 60-60 - 4. Bring down: 0

14 Things you must know about fractions…
What is a fraction? A whole number divided by another whole number 5 6 numerator fraction bar denominator How are fractions written? NO! Can a denominator be a number =0? Can the same fraction be written in many ways? YES! Can fractions be added, subtracted, multiplied, and divided? YES!

15 Preparing fractions for addition…
Quick add 1 6 15 42 + Wait… This fraction is not ready ! Both denominators must be the same before addition Let’s multiply 1/6 x 1 Anything times 1 equals itself right? Lets try multiplying 7 x 1 6 = Just another way to represent 1 Anything divided by itself =1 num x num den x den = 7 42 BINGO 22 42 = answer Let’s try adding 7 42 15 + = num + num denom

16 Multiplication of fractions…
Let’s consider a problem: A patient is ordered to drink 3/5 of a can of Ensure® at each meal. The doctor asks you to cut this dose in half. What fraction of the can should she drink now? 3 5 x = ? 1 2 (numerator) (denominator) x = (numerator) x (denominator) Therefore… 3 5 x 1 2 = 3 1 5 2 = x 3 10

17 Division of fractions…
How to do it? 3 5 = ? 1 2 Dividing by a fraction is the same as multiplying by its reciprocal. 1 2 Take its reciprocal 1 2 = 2 1 So… 3 5 = 1 2 3 5 x 2 1 = 6 5

18 Decimal notation… Decimals are used to separate a whole number from its fractional part… Got the IDEA? Whole number Fractional part 1 2 ones tens hundreds thousands tenths hundredths thousandths ten thousandths decimal = 1021.1 1 2 = Two more hundredths 1 2 = Two more thousandths

19 Converting mixed numbers to fractions…
A mixed number is a whole number plus a fraction of a whole number. Example: A patient’s dose is 1 1/2 pills (mixed number). Real Scenario: Her doctor tells you to halve the patient’s dose You immediately think to multiply the patient’s dose by 1/2 Convert the mixed number 1 1/2 to a fraction…here’s how: 1 2 = Multiply Add (2x1)+1 2 = 3 2 Now we can solve by multiplying two fractions: 3 4 = 3 2 1 x

20 Percentages… Percentages are used often in the clinic…they are worth knowing well! “Percentage” actually means per/100. Imagine that a sample of blood is collected from a patient. Let’s say 100 “parts” are collected (parts is an arbitrary unit). If 10 parts are alcohol, what is their blood alcohol percentage? 10 parts per 100= 10% percentages, decimals, and fractions can be interconverted. Move decimal 2 places to the left, remove 100 as denominator 10% 10 100 0.10 Remove % sign, /100 To the right, add % Decimal Percentage Fraction

21 9 8 7 2 4 Fundamentals of rounding…
The doctor asks you to keep track of a patient’s temperature to the nearest degree! You’ve been given a fancy thermometer that shows temperature like this… 9 8 7 2 4 ones tens tenths hundreths thousanths decimal 99 98 Imaginary analog thermometer Column to the right Nearest single degree A reminder about how decimal notation works… All you have to do is ask…is the temperature closer to 99 or 98? The formal way: Find the column to which you are rounding. Look to the columns to the right of that column… If the digit is greater than or equal to 5, round up…99 it is!

22 OK for getting one value,
Precision is not the same thing as accuracy! Healthcare professionals are often asked to weigh patients and monitor weight changes. Reliable measurements are critical for the patient’s health, but not all scales are perfect. Understanding how reliable a measurement is requires knowing the difference between… Precision and Accuracy Precision: How closely clustered multiple measurements are Accuracy: How close a measurement is to the “true” value scale #1 scale #2 11.001 11.002 10.999 multiple measurements 10.300 9.700 10.500 9.900 multiple measurements “Close to the true value” OK for getting one value, not good for tracking of small changes “Highly Reproducible” OK for tracking small changes Precise Accurate Precise Accurate

23 Conceptualizing orders of magnitude…
Not everything in this world comes in the same size. If something is a lot bigger than another thing, how do you describe this difference? Doctors and scientists assign “orders of magnitude” to objects to accurately express this difference. Here is an example: Salaries! $10 thousand $100 thousand $1 million $10 million X 10 Janitor Lawyer CEO Baseball player Lawyer compared with janitor = 1 order of magnitude difference. CEO compared with janitor = 2 orders of magnitude difference. Baseball player compared with janitor = 3 orders of magnitude difference. We’ll get into the metric system a bit later, but… Remember that giving a patient 1 gram of a drug instead of 1 milligram of a drug is the same size difference between a Baseball player’s salary and a janitor’s!

24 Many measurement systems are encountered in the clinic…
METRIC (most common) HOUSEHOLD APOTHECARY

25 Weight and volume… Things typically measured Instrument Used
Typical sizes powdered drugs 25 mg (penicillin) mass scale salt Weight / Mass) 5 g (sugar) digital scale sugar pre-diluted drug measuring cup 0.5 Liter (Ensure®) Volume saline graduated cylinder 300 cc (saline) water pipette nutritional supplement

26 Introduction to the Metric System…
Orders of magnitude 1 micro gram = 1 millionth of a gram 1 milligram = 1 thousandth of a gram 1 centigram = 1 tenth of a gram 1 gram = 1 gram, 1 decagram = 10 grams 1 kilogram = 1 thousand grams 1 megagram = 1 million grams 3 2 1 Metric system prefixes are applied to all units of measurement. To go from mass units to volume units, simply change grams to liters. The logic is identical! Brain teasers: How many micrograms in a gram? 1 million How many milligrams in 10 kilograms? 10 million How many milligrams in half a centigram? 50

27 Cracking conversion problems (dimensional analysis)…
How many days have you been alive? Hmmm… What we need to know to answer this… and all conversion problems! 1. In what units is the answer? Days 2. In what ratio is given, or do we need to provide on our own? Days/Year 3. In what is the quantity to be converted? 21 years All we have to do is: multiply (quantity to be converted) x (known ratio) After canceling units, we should be left with our answer in the correct units; 21 years quantity to be converted years x 365 days 1 year = known ratio days 7665 days units in answer

28 Processing a doctor’s order…
Doctors will often order a patient to take a certain amount of drug, but may not specify exactly how many capsules/tablets, volume he should take. You will be responsible for calculating this. What are the 3 critical pieces of information? The doctor’s order (given) Example: 30 mg of Prozac Quantity to be converted 1 Strength of drug Example: 10mg/capsule Known ratio 2 Units the answer will have capsules Example: 3 Simple Dimensional Analysis 30 mg Prozac Doctor’s order x 1 capsule 10 mg Prozac = Strength of drug 3 capsules Units of answer

29 Making solutions from powders…
Many medicines administered by healthcare professionals are actually drugs dissolved in a liquid vehicle. Problem: You are asked to make 0.5 liter of an antibiotic solution. The final concentration of the solution should be 3 grams antibiotic/1 liter of water. How much antibiotic do you need? Think Dimensional Analysis! In what units is the answer ? Grams In what ratio is given? 3 g/L In what is the quantity to be converted ? 0.5 L = x 3 grams antibiotic 1 Liter H20 Known ratio 0.5 Liter Quantity to be converted 1.5 g antibiotic Units of answer DONE!

30 Parenteral dosages… DONE!
Now that you can make your own drug/liquid mixtures, this next problem should be very easy! Problem: The doctor asks you to administer 300 mg of antibiotic each day. The antibiotic comes as a liquid mixture in a strength of 150 mg/500 ml. How much liquid do you administer each day? Think Dimensional Analysis! What units is the answer in? mL What ratio is given? 150 mg/500 mL What is the quantity to be converted? 300 mg = 150 mg antibiotic 500 mL H20 x Known ratio 300 mg antibiotic Quantity to be converted 1000 mL Units of answer DONE!

31 Calculating infusions…
As we know, drugs often come in liquid form. In cases in which large doses are required, not all the drug can be delivered at once. Depending on the speed at which the patient can absorb or metabolize, the drug healthcare providers must determine a suitable flow rate. A flow rate is simply how much drug is delivered at a time. Let’s consider a problem: The doctor orders a patient to receive 1500 mL of 5% dextrose in water (D5W) over 9 hours. The intravenous delivery system requires you to input a flow rate of milliliters/minute. What do you input? Quantity to be converted The conversion is: Units answer hour mL min 9 hours 1500 mL x 60 min 1 Hour = Known ratio 1 min 2.8 mL

32 Dosage that depends on surface area…
The dosage of some drugs is calculated based on the body surface area of the recipient. Surface area is measured in meters squared (m2). When the total body surface area is known, the correct drug dosage can be determined. Let’s consider a problem: The patient is ordered to receive 5 grams of drug/ m2 of body surface area. The total surface area of the patient is 1.4 m2. What quantity of the drug should he receive? Think Dimensional Analysis! What units is the answer in? Grams What ratio is given? 5 g/m2 What is the quantity to be converted? 1.4 m2 DONE! = 1 m2 5 grams x Known ratio 1.4 m2 Quantity to be converted 7 grams Units of answer

33 Total volume of solution
Calculating strengths of solutions… Calculating strengths of solutions is required for knowing how to make solutions correctly and knowing how much drug is contained in a solution. Strengths of solutions are expressed in percentages. A solution consists of two parts mixed together: Solute and Solven.t Solute: Substance being dissolved or diluted. Solvent: Substance dissolving or diluting the solvent. Liquid solute: Solute and solvent are measured in same units of volume. Volume of solute Total volume of solution = 10 mL of alcohol 100 mL of blood = 10% blood alcohol level “Concentration of liquid solvent”= Solid solute: Solute is measured in mass units. = Grams solute 100 mL of solution (mass) 5 grams of NaCl (salt) 100 mL of water = “Concentration of a solid solvent”= 5% NaCl solution

34 Interconverting Celsius and Fahrenheit…
Two temperatures scales exist: Fahrenheit and Celsius. There may come a time when you are required to interconvert temp values. Online converters exist, but learning to do this conversion by hand helps reinforce understanding. Fahrenheit freezing boiling 32 212 Each degree covers less distance. 4 C ?F Refrigerator temperature Refrigerator tempature 98 F ?C Body temperature Celsius 100 Each degree covers more distance. Conversion: F= (( C ) x 9/5 ) +32) C=(F-32)x 5/9) = (4 x 9/5) + 32 = 39 F =( ) x 5/9 = 37 C

35 Take home points… Comfort with basic math is absolutely required for delivering safe and effective healthcare to patients. Solving a lot of problems helps make concepts “second nature”. Double checking calculations with colleagues or by-hand helps prevent mistakes! Don’t be afraid to ask for help if you struggle with a concept.

36 Production Credits… content creator: Seth A. Zonies B.S.
content consultant: James J. (Jim) De Carlo, RN, MA, BSN, BA © Copyright 2007 Insight Media. All rights reserved.


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