Lions And Tigers And Bears

Lions and Tigers and Bears … oh my! IV rates and conversions and equivalents … oh no!! Plus more fun math …

Mary J Aigner RN, MSN, FNPC

Mary J. Aigner RN, MSN, FNPC

Ratio & Proportion Method 

What’s a ratio? 

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Two number related to each other

Why care? 

Meds often expressed in ratio form

Eg. 125mg/1 tablet or 125 mg:1 tablet 250mg/10ml or 250 mg:10 ml

proportion shows two equal ratios eg. 4/12 = 1/3 or 4:12 = 1:3 

A proportion problem is missing one element of the ratio 

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To solve, cross multiply  

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Eg. 4:X = 1:3 Multiply outer numbers (4, 3) Multiply inner numbers (X,1)

4X3 = 12, X times 1 means X equals one, thus X = 12

But … 

You can use DA or Dimentional Analysis to solve problems

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Just be aware that there are many ways to do the same thing

Med example 

Dose ordered is 375mg and you have tablets of 150mg … how many are needed?

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375mg:X = 150mg:1 tablet   

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(The two mg cross each other out) Multiply outer (375 X 1 = 375) Multiply inner (150 times X = 150 X)

Thus 375 = 150X, Divide 375 by 150 Result is 2.5 tablets

Doing this same problem with DA 

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We want 375 mg of medicine and need to know how many tabs We have tablets that are 150mg each Want #/tab, Have 375mg/1 X 1 tab/150mg (cross out mg) Write:375/1 X 1 tab/150 which results in 375/150, divided out is 2.5 tab Correct me if I’m wrong!

Another way to use the proportion method is to determine percents 

What is 75% of 4? 3 is what percent of 4? 75% of what number is 3?

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Method:   

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Part/whole = percent/100

Or in ratio form 3:4 = 75:100 Multiply outer 3x100 = 300 and Multiply inner 4 x 75 = 300)

Percent – the number with the percent sign Part – the number with the word is Whole – the number with the word of

Figuring out IV flow rates Flow Rate = (Volume) administrative set/time 

Identify the values of each factor   

Flow rate (volume) administrative set Time

Keep in mind that terminology may vary for each factor

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Other terms for factors Factor Flow rate Volume

Other name(s) Drip rate Drop rate ------

Administrative Set, drip set factor, microdrip Time -------

Units Represented gtts/min or µgtts/min cc, ml, or l gtts/ml, or µgtts/ml Min (divide by 60 to get hrs)

Plug identified values in … 

Flow rate = volume (admin set)/time    

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(Volume times admin set divided by time) Eg. Volume is 250 ml Administrative set is 15 gtts/ml Time is 100 min

Thus Flow rate = 250 ml X 15 gtts/ml / 100 min.   

(cross out ml, result is gtts/min) 250X15=3750, divided by 100 = 37.5 gtts/min or 38 gtts min Can’t give half a drop so round up

Other IV info that is helpful 

Some meds are measured in units 

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Eg. Penicillin, heparin, insulin, pitocin

Definitions: 

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Solute: dissolved substance (such as Na in 0.9% NS or Dextrose in D5W) Solvent: liquid in which solute is dissolved Percent concentration: number of grams of solute in 100 ml of solution or solvent Titration: adjusting infusion or IV dosage over time to obtain measurable response

Examples of IV solutions: 

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D5W means 5% dextrose in 100 parts water or 5 g dextrose in 100 ml water  So in 1000 ml, there would be 5 g dextrose x 10 or 50 g dextrose 10% Na means 10%/10parts/10 g Na in 100 ml water  So in 1000 ml, there would be 10 g Na x 10 or 100 g Na What about Normal Saline? 0.9% NS?  0.9 g Na or 0.9 parts Na per 100 ml water  0.9 x 10 (to make 1000 ml) = 9 g Na in 100 ml

Solve for Time Flow rate = volume (admin set)/time 

Ordered is 2 liters of 0.9% NS @ 75mcgtts/min (µgtts/min)

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Thus write as: 75 µgtts/min=2000 ml times 60 µgtts/min / X min 

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2000ml x 60 totals 120000:X min = 75:1 

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Cross out two µgtts/min

Multiply outer and inner values

120000 = 75 X, therefore X = 120000/75 or 1600 minutes  

Divide by 60 to get hours Answer is 26 hours and 40 min.

What about with an IV pump? 

Set to run at ml/hr

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Total infusion time = volume to infuse 

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Either ml/min or ml/hr

Run an IV of 500 ml for 6 hrs?  

6 hrs = 500 ml. Divide 500 by 6 = 83.3 ml/hr or 83 ml/hr

Word Problems 

Figure out from the text   

What is being asked? What info is extraneous (if any)? What is important information?

Mrs. G will start Zoloft 25 mg PO qd and increase by 25 mg weekly until she reaches 100 mg. How many weeks will this take?

Words are just words  

Half-life Metabolism

Medicine A is metabolized in the kidney and has a half-life of 16 hours. If she takes 20 mg at 0900 in the morning, at what time will approximately 10 mg be in her system? To answer: Add 16 hours to 0900 or 0900 plus 12 hours = 2100 plus another 4 hours = 2500 or 0100 the next morning. In this case, the information about the kidney was just extra information.

What about calories? 

How many calories per gram?   

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Protein = 4 (kilo)calories/gram Carbohydrates = 4 (kilo)calories/gram Fat = 9 (kilo)calories/gram

So – figuring out calories means multiplying caloric value (either 4 or 9) times the number of grams then adding up totals

And fluid counts?  

Convert if necessary from oz to ml Then add

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Eg. 12 oz coffee = 12 x 30 = 360 ml Eg. 4 oz OJ = 4 x 30 = 120 ml Eg. 8 oz water = 8 x 30 = 240 ml

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Total? 360 + 120 + 240 = 720 ml

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References & Sources for More Practice 

Just plain math (good for parents who help with homework) 

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http://amby.com/educate/math/

Nurse’s math problems 

http://www.accd.edu/sac/nursing/math/

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http://www.delta.edu/tlc/TLCStdy/Support/mathforsci

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This site has good links, quizzes for practice, and explains very clearly

Practice, Practice, Practice