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Lecture 14 - Hospital Calculations

Tech Lectures®

For the Pharmacy Technician

P.O. Box 19357 Denver, CO 80219-0357

303-984-9877

It is respectfully requested by the Author that no part of this Tech Lecture®

be reproduced or transmitted in any form, by any means without express

written consent. Joe Medina CPhT, B.S Pharmacy

Tech Lectures® Copyright 2013

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You are extremely lucky in having selected this Tech Lecture® in that if you study this lecture and Lecture 13, Pharmacy Calculations I carefully, you will know all you need to know in the solving of calculation type problems in the Pharmacy setting. joe Medina

Pharmacy Calculations for the Pharmacy Technician

This is Lecture II of Pharmacy Calculations a continuation of Lecture 1 that will cover different aspects of calculations required by the Pharmacy Technician. With careful attention and practice the Pharmacy Technician should become very proficient in number crunching required in the Hospital setting.

It will be assumed that the student using this Tech Lecture® is already competent in basic math skills of addition, subtraction, fractions and decimals. If this is not the case then a review of these topics may be necessary before

continuing this Tech Lecture®. This particular Tech Lecture® will build upon itself, therefore it is recommended that you begin on page one.

Calculators

In the Pharmacy setting you will always find several calculators laying around. The use of calculators is vital in the correct computation required in dosage calculations. Utilization of a calculator is not only encouraged but

expected while using this Tech Lecture®.

Sample Problems

Please follow the sample problems carefully to ensure that you understand the process of solving the different type of calculations you may encounter in the pharmacy setting.

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Review of material in Lecture 13 Ratio and Proportion Ratio - A ratio states a relationship between two quantities a / b or c / d a. how two quantities relate to each other a is to b or c is to d Proportion: Two equal ratios from a proportion a / b = c / d a. an expression of equality between two terms

Equation - is a statement that two terms are equal and are joined by the equal (=) sign.

a c _____ = _______ is the same as a / b = c / d b d

Example: 5 apples / 1 box = 15 apples / 3 boxes This equation states that 5 apples per 1 box is equal to 15 apples per 3 boxes a. This is a true statement 5 apples 15 apples ------------ = ------------- 1 box 3 boxes

Example: 5g / 100 ml = 50 g / 1000 ml This equation states that 5g per 100ml is equal to 50g per 1000 ml a. This is a true statement 5g 50g ------- = -------- 100ml 1000 ml

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Solving a Ratio and Proportion type problem A Proportion consists of four terms. If three of the four terms are

known, the fourth can be calculated Sample Problem 1: In one basket farmer joe has four oranges. How many oranges will farmer joe have in six baskets?

Solve: 1. Read Problem carefully a. try to figure out what is being asked for b. try to figure out four terms needed in the ratio and proportion c. try to figure out what the unknown variable is

2. Set up problem in a ratio & proportion equation a / b = c / d

a. note that units must be equal in both numerator and

denominator in this case ------------> numerator: basket(s) denominator: oranges

3. Solve for x a. cross-multiply four oranges times six baskets = 24 b times c = one basket times x oranges = 1 x a times d =

b. Divide so that x equal one 24 ______ = 24 24 divided by 1 x = 24 1 x

4. Attach units -------> oranges a. 24 oranges (answer)

a one basket six baskets c ___________ = ___________ b four oranges x oranges d

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Ratio and Proportion is the most common form of problem solving in the field of pharmacy. There are few Arithmetic problems, save for the simplest, that cannot most directly be solved by this method:

Important: Three conditions must be met when using ratio and proportion 1. The numerators must have the same units 2. The denominators must have the same units 3. Three of the four parts must be known

Steps necessary to solve Ratio and Proportion type problems: 1. Read problem carefully 2. Set-up 3. Cross Multiply 4. Divide so that x = 1 5. Attach units

If : a / b = c / d then a = bc / d b = ad / c c = ad / b d = bc / a

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Percents Percent (%) means “by the hundred” or “in a hundred”. A percent is actually a fraction, but a fraction with a specific denominator: The denominator is always 100. Example: 50 % “ means 50 parts in 100 parts , or 50 / 100, or 1/2 Example: 50 / 100 = 50% 25 / 100 = 25% 10 / 100 = 10% 12.5 / 100 = 12.5% In the Pharmacy setting especially Hospital, Percents come up with the preparation of Intravenous solutions (IV’s).

Example: 50% Dextrose 1000 ml IV bag a. means 50g of Dextrose per 100 ml in this IV bag b. so how many grams of Dextrose in the whole bag? Set-Up 50g / 100ml = x g / 1000 ml x = 500 grams (Answer) c. so how many mls will give you a 10 grams of Dextrose? Set-Up 50 g / 100ml = 10 g / x ml x = 20 mls (Answer)

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Practice Problem Set V 1. Convert the following fractions to Percent a. 60/100 = ___________ % b. 80/100 = ___________ % c. 12/100 = ___________ %

2. Convert the following Percents to fractions d. 50% = _____________ e. 12.5% = _____________ f. 99% = _____________

3. Solve the following using Ratio & Proportion You have a 70% Dextrose solution, How many grams in: __________ g. 50 ml of solution __________ h. 75ml of solution __________ i. 20 ml of solution

You have a 50% Dextrose solution, how many mls will give you: __________ j. 25 g of Dextrose __________ k. 35 g of Dextrose __________ l. 10 g of Dextrose

m. You have a liquid that contains 100mg / 10ml. What is the percent of this liquid? hint: note your liquid is 100mg / 10 ml. To solve this you will need to first convert to gms / 100ml

Answers to these questions can be found in Appendix I in back of this Tech Lecture®

Doodle Space

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Percent Solution Formula In the preparation of Hyperalimentation or TPN’s this formula is a handy tool at solving Percent Changes. [ See Tech Lectures® Lecture - Hyperalimentations ]

Have % Want % ____________ = _______________ Total Volume x Volume needed Required Sample Problem 10: The physician wants a 35% Solution of Dextrose 1000ml. You have

a 50% Solution of Dextrose 1000ml. How will you make up what the physician wants ?

Set-Up Use the Percent Solutions Formula Have % : 50% Dextrose is what you have Want % : 35% Dextrose is what the Physician wants Total Volume Required : 1000ml Total Volume Needed : x ml 50 / 1000 = 35 / x x = 700 ml (Dextrose 50% needed to make) To make you use 700 ml Dextrose 50% Solution and then add (qsad) Sterile Water until you have 1000 ml as ordered by the physician.

[ qsad means quantity sufficient to make total volume ]

Answer: Dextrose 50% Solution : 700 ml Sterile Water (qsad) : 300 ml Total Volume : 1000 ml

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Sample Problem 11: You are to make the following TPN (Total Parenteral Nutrition)

TPN Order ( want ) What you have :

Aminosyn 4.25% Aminosyn 8.5% 1000 ml Dextrose 25% Dextrose 70% 1000 ml Additives: KCl 20 mEq KCl 2mEq / ml 10 ml MVI 10 ml MVI 10 ml NaCl 24 mEq NaCl 4.4mEq / ml 20 ml Total Volume is to be 1000 ml

How much of each ingredient do you need to prepare this TPN ? Aminosyn Set-Up Percent Solutions Formula 8.5 / 1000 = 4.25 / x ml Dextrose Set-Up Percent Solutions Formula 70 / 1000 = 25 / x ml KCl Set-Up Ratio and Proportion 2 / 1 = 20 / x MVI Set-Up No Set-Up needed NaCl Set-Up Ratio and Proportion 4.4 / 1 = 24 / x Sterile Water Set-Up qsad for a volume of 1000 ml

882.45 ml + x = 1000 ml

x = 500 ml Aminosyn

x = 357 ml Dextrose

x = 10 ml KCl

Just add 10 ml MVI

x = 5.45 ml NaCl

x = 117.55 ml

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Practice Problem Set VI 1. Solve the following Pediatric TPN order: TPN Order ( want ) What you have Aminosyn 2.5% Aminosyn 8.5% 500 ml Dextrose 7. 5% Dextrose 50% 1000 ml Additives: KCl 4mEq KCl 2mEq/ml 10 ml Ca Gluconate 2 mEq Ca Gluconate 4.4mEq/ml 25 ml Ped MVI 5 ml Ped MVI 10 ml Total Volume to be 250ml How much of each ingredient do you need to prepare this TPN ? a. Aminosyn 8.5% _________________ ml b. Dextrose 50% _________________ ml c. Kcl 2mEq/ml _________________ ml d. Ca Gluconate 4.4mEq/ml _________________ ml e. Pediatric MVI _________________ ml f. Sterile Water (qsad) _________________ ml

g. The physician wants a 35% solution of Dextrose 1000ml. You have a 70% solution of Dextrose 1000ml. How will you make up what the physician wants? hint: Figure out how many ml’s of Dextrose 70% you need to prepare then figure out how much Sterile Water is needed to make the total volume 1000 mL

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Calculation of Children’s Doses The average doses in the U.S.P. (United States Pharmacopia) and other drug Reference sources are for adults. For drugs that can be taken by a child doses are generally not given thus the following formulas were developed but rarely used:

Normally doses for children are given by body weight in Kg. If you know the child’s body weight you can solve for the prescribed dose by again using Ratio & Proportion: Sample Problem 12: An Antibiotic IV was prescribed for little Baby joe. The dose is to be 15mg / Kg twice a day. Little baby joe weighs only 12 lbs. How much drug is to be given for one dose?

Read Problem Carefully Little baby joe weighs only 12 lbs but the dose is mg / Kg. You need to convert lbs to Kg. Set-Up 2.2 lb / 1Kg = 12 lb / x Kg x = 5.45 Kg (baby joe’s weight) Set-Up 15mg / 1 Kg = x mg / 5.45 Kg x = 81.75 mg ( Answer )

Young’s Rule: age of child (in years) -------------------------- x Adult dose = dose for child age of chld (in years) + 12

Clark’s Rule: weight of child (in pounds) --------------------------------- x Adult dose = dose for child 150 lb

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Drops / minute

Sometimes you will be given a drop factor of which you are asked to find the amount of drops per minute to set your pump. In this case you will first need to find out how many mls per minute then simply multiply your answer times the drop factor to find drops per minute.

Sample Problem 11 Order: KCL 10 mEq and K Acetate 15 mEq in D5W 1000 ml to run over 8 hours.

How many drops per minute would I set my pump if the drop factor is 12 drops per ml?

To solve this you would need two pieces of information

a. The flow rate in mls / hour b. Total volume prescribed

Set-Up have = want conversion 1. 1000 ml / 8 hour = x ml / 1 min notice units on bottom do not match…need to change to minutes note: 1 hour = 60 minutes

2. 1000 ml / 480 min = x ml / 1 min

x = 2.08 ml / minute From this answer we can come up with the final answer or drops per minute by simply multiplying your answer times your drop factor: 1. (2.08) (12 drops) = 24.96 gtts / minute (Answer) x can be rounded to 25 gtts / minute

For Flow rate problems always find ml’s per minute first then if there is a drop factor just multiply your answer times the drop factor to get drops / minute.

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Temperature Type Problems: Two formulas express the relationship between the Fahrenheit and Celsius (Centigrade) temperature scales:

Sample Problem 13: Oral Polio Virus Vaccine (Poliovax®) should be stored in a temperature not to exceed 46 degrees Fahrenheit. What is this temperature in Centigrade? Set-Up C = 5/9 ( F - 32 ) C = 5/9 ( 46 - 32 ) C = 5/9 ( 14 ) C = 7.78 degrees (Answer)

Farenheit = 32 + 9/5 C Centigrade = 5/9 ( F - 32 )

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Review of Calculations This Section was added to ensure that you have more examples to follow in understanding of Ratio & Proportion Type of Problems. The understanding of these type of problems will allow the Pharmacy Technician the ability to solve 95% of all Pharmacy Calculation type problems encountered.

Three conditions must be met when using ratio and proportion

1. The numerators must have the same units 2. The denominators must have the same units 3. Three of the four parts must be known

Steps Necessary to solve a Ratio and Proportion type problem 1. Read problem carefully 2. Set-up 3. Cross Multiply 4. Divide so x = 1 5. Attach units

Other info: 1. Always look for a conversion you have 2. Always look for a conversion you want Have Conversion = Want Conversion

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Sample Problem 14 750mg is equal to how many grams ? 1. Set-Up a. find a conversion that relates to this question -----> 1000mg / 1 gram 1000 mg 750 mg --------------- = ------------- 1 gm x gm 2. Cross Multiply ( 1000 ) ( x ) = ( 750 ) ( 1 ) 1000 x = 750 3. Divide so x is equal to 1 10000 x 750 ---------- = ----------- 1000 1000 x = 0.75 4. Attach units x = 0.75 grams

Any problems that deals with using a percent solution to get another percent solution use the Percent Solutions Formula Have % Want % ---------------- = ---------------- Total Volume x Volume Required needed to make

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Sample Problem 15 325mg is equal to how many grains? 1. Set - Up a. Find a Conversion that relates to this question --------> 60mg / 1 grain 60 mg 325 mg -------------- = ------------- 1 grain x grain 2. Cross Multiply (60) ( x ) = ( 325 ) ( 1) 60 x = 325 3. Divide so x is equal to 1 60 x 325 --------- = ---------- 60 60 x = 5.41 4. Attach Units x = 5.41 grains

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Sample Problem 16 A prescription reads for Erythromycin 150mg every six hours for ten days. You have on the shelf a bottle of Erythromycin 250mg / 5ml 150 ml. How much erythromycin is needed for one dose? 1. Set-Up Find a conversion that relates to this question -------> 250mg / 5 ml 250mg 150 mg ----------- = ------------- 5 ml x ml 2. Cross Multiply ( 250 ) ( x ) = ( 150 ) ( 5 ) 250 x = 750 3. Divide so x is equal to 1 250 x 750 -------- = ------- 250 250 x = 3 4. Attach units x = 3 ml

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Sample Problem 17 You have an IV that needs MgS04 (Magnessium Sulfate) 10 mEq. You have on hand a bottle of MgS04 4 mEq / ml. How much MgS04 do you need to inject into this IV bag? 1. Set-up Find a conversion that relates to this question -----> 4 mEq / 1 ml 4 mEq 10 mEq -------- = ---------- 1 ml x ml 2. Cross Multiply ( 4 ) ( x ) = ( 10 ) ( 1 ) 4 x = 10 3. Divide so x is equal to 1 4 x 10 ------- = ------- 4 4 x = 2.5 4. Attach units x = 2.5 ml

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Sample Problem 18 You have an order for 20% Dextrose 500ml. You have a 1000 ml bag of Dextrose 70%. How much of the Dextrose 70% do you need to use to make Dextrose 20% 500ml? How much sterile water to you need? 1. Set-Up This is a Percent Solution to another Percent Solution. Use formula 70 % 20 % ---------- = ------------ 500 ml x ml 2. Cross Multiply ( 70 ) ( x ) = ( 20 ) ( 500 ) 70 x = 10000 3. Divide so x is equal to 1 70 x 10000 -------- = ----------- 70 70 x = 142.86 4. Attach units

x = 142.86 ml of the 70% Solution 5. qsad to 500ml of Sterile Water 500 ml - 142.86 ml = 357 ml of Sterile Water

Have % Want % ----------- = ------------- Total Volume x Volume Required to make

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Rounding Off When number crunching on your calculator you may encounter decimal numbers that extend beyond the decimal point and make the dose extremely difficult or impossible to attain. Rounding off of numbers is permissible in the Pharmacy Setting generally to the tenth place. Although in some IV admixtures, rounding off should be in the hundredth place. Generally a need to follow Pharmacy protocol is necessary to attain the correct dose. Examples: 7.84 degrees Celsius can be rounded off to 8 degrees Celsius 81.75 mg Pediatric IV Antibiotic dose should not be rounded off 5.45 ml of NaCl dose in a TPN order can be rounded off to 5.5 ml Doodle Space

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Appendix I - Practice Problem Sets Answers Practice Problem Set V a. 60% Problem Set VI b. 80% c. 12% a. 73.5 ml Aminosyn 8.5% d. 50/100 b. 37.5 ml Dextrose 50% e. 12.5/100 c. 2 ml KCl f. 99/100 d. 0.45 ml Ca Gluconate g. 35 g e. 5 ml Pediatric MVI h. 52.5 g f. qsad 131.8 ml Sterile Water to make 250ml i. 14 g g. 500 ml Dextrose 70% should be used to make and j. 50 ml add 500 ml Sterile Water to make 1000 ml k. 70 ml l. 20 ml m. 1000mg / 100ml or 1 gram / 100 ml or 1 %

End of Lecture 14 - Hospital Calculations

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Lecture 14 - Hospital Calculations Worksheet Part II - Word Problems

1. You have a 70% solution of Dextrose 1000ml. How many Kg of Dextrose is in 400 ml of this solution?

a. 280 Kg b. 28 Kg c. 2.8 Kg d. 0.28 Kg

2. You receive an order for Vancomycin (Vancocin®) 10mg/Kg 500ml to be infused over 90 minutes. The patient is five foot eleven inches tall and weighs 165lb. What dose is needed for this patient?

a. 750 mg b. 500 mg c. 250 mg d. 125 mg

3. How much of a 20% Dextrose Solution 1000ml is needed to make a 8% Dextrose solution 125ml.

_______ ml 4. How much Sterile Water is needed for problem number 3? _______ ml 5. You are asked by the Pharmacist to add 45 mEq of Ca Gluconate in an IV bag of D5% 1000ml. You have on the shelf concentrated vial of Ca Gluconate 4.4mEq / ml 50 ml. How many ml’s of this concentrated vial needs to be added to the IV bag?

a. 1.2 ml b. 10.2 ml c. 0.12 ml d. 2.4 ml

6. How much Dextrose would be found in a D5W 1000ml bag?

a. there is 5 grams of Dextrose in this bag b. there is 250 grams of Dextrose in this bag c. there is 50 grams of Dextrose in this bag d. there is 500 grams of Dextrose in this bag

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7. A Liter of D5%W with KCL 20mEq was started at 10pm at a flow rate of 100mL per hour. At 3am the rate was changed to 200mL per hour. At what time will this IV need to be replaced? a. 5:00 am b. 5:30 am c. 6:00 am d. 6:30 am 8. How much D20W 1000 mL and D5W 1000 mL is needed to make a D12W 500 mL?

a. D20W 466.7 mL and D5W 533.3 mL b. D20W 266.7 mL and D5W 233.3 mL c. D20W 233.3 mL and D5W 266.7 mL d. D20W 533.3 mL and D5W 466.7 mL

9. D5W 800mL is to run over 6 hours. If the drop factor is 12 drops / mL, what would the flow rate be in drops / minute?

a. 21 gtts / min b. 27 gtts / min c. 31 gtts / min d. 43 gtts / min

10. A solution that is 120mg / 10 ml would be what percent ?

a. 1.2% b. 2.4% c. 3.6% d. 4.2%

Once your questions are answered, place your answers to the answer sheet on the following website https://form.jotform.com/61905069950966 If you ARE an NCPT member there is no charge. If you are NOT an NCPT member you must pay a 10.00 fee on answer form or you can become a two year member on the same form by paying 30.00 for a two year membership and get 36 hours of CE for free. https://form.jotform.com/30880859625970