Med Math
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Transcript of Med Math
Med Math
Tips for success
Pick one method, that is easiest for YOUStudy itLearn itPractice itPractice itPractice it
Topics
Apothecary SystemWeight and Temperature ConversionsMetric SystemMed Math Administration Doses Weight Based Doses Drip Rate Calculations
Apothecary System
Phased out and replaced by metric systemBasic Units: grain (gr), dram (dr), drop (gtt), ounce, (oz), pint (pt), quart (qt)Equivalents
1dr = 1 tsp = 60 gtts3tsp = 1 Tbsp
Weight Conversion
Fact: 1 kilogram (kg) = 2.2 pounds (lbs)Fact: Weight in kgs X 2.2 = weight in pounds
Conversion Practice
80 kilogram patient, what is weight in pounds
kilograms X 2.2 = pounds
80 X 2.2 = 176 lbs.
Conversion Practice
100 kilogram patient, what is weight in pounds
kilograms X 2.2 = pounds
100 X 2.2 = 220 lbs.
Weight Conversion
Fact: 1 kilogram (kg) = 2.2 pounds (lbs)Fact: Weight in kgs X 2.2 = weight in poundsFact: Weight in pounds / 2.2 = weight in kilograms
Conversion Practice
245 lb patient, what is weight in kilograms
lbs / 2.2 = kilograms
245 / 2.2 = 111.36 kgs
Conversion Practice
140 lb patient, what is the weight in kilograms
lbs / 2.2 = kilograms
140 / 2.2 = 63.63 kilograms
Conversion Practice
The easy way…
Half of weight in pounds, subtract 10%
Example: 180 lbs . . . . . 90
10% of 90 = 981 kilograms
Conversion Practice
180 lb patient, what is the weight in kilograms
lbs / 2.2 = kilograms180 / 2.2 = 81.82 kilograms
KNOW YOUR WEIGHT CONVERSIONS!!!!!
Temperature Conversions
Fahrenheit: Water Freezes at 32º F Water Boils at 212º F
Celsuis: Water Freezes at 0º C Water Boils at 100º C
Temperature Conversions
Fahrenheit CelsiusSubtract 32 from the temperatureMultiply by 0.556 or 5/9
98.6 – 32 = 66.6
66.6 X 0.556 = 37.03 = 37º C
Practice
Convert 103º F to Celsius
103 – 32 = 71
71 X 0.556 = 39.48º C
Temperature Conversions
Celsius FahrenheitMultiply by 1.8Add 32
37º X 1.8 = 66.666.6 + 32 = 96.6º F
Practice
Convert 44º C to Fahrenheit
44 X 1.8 = 79.2
79.2 + 32 = 111.2 º F
On your own
120 º F Celsius76.4 º F Celsuis
60 º C Fahrenheit24 º C Fahrenheit
Metric System
System of 10 (base 10)No fractions only decimalsEASY!
Metric System
Metric System
Deca10Hecto 100Kilo 1000
Deci 0.1Centi 0.01Mili 0.001
Metric System
Gram = gLiter = lKilogram = kgMilliliter = mLMilligram = mgCubic centimeter = ccMicrogram = g
1 L = 1000 mL1 mL = 1 cc1 g = 1000 mg1 mg = 1000 g1cc = 1 mL1 g = 0.001 mg1 mg = 0.001 g
The math
Adding – keep the decimal points in lineSubtracting – see aboveMultiplying – multiply without regard to decimals then add decimal placesDividing – make the divisor a whole number and add zeroes to the dividend
Addition
4.3795+ 5.2389---------------
9.6184
Subtraction
9.6184- 5.2389---------------
4.3795
Multiplication
34.76X 4.935-------------- 17154060
Add decimal places = 5 171.54060 = 171.5406
Division
.75 / .995 75 / 99.5 move
decimal--------------0.7537
Converting
1g = 1000mg so… g mg X1000
1mg = 1000 µg so… mg g X 1000
1g = ???? g = 1,000,000 g
Converting
500mL = 0.5L so… mL L / 1000
The Bottom Line…To convert from the base to mili X
1000To convert from mili to the base / 1000To convert from mili to X 1000To convert from base to X 1000000
Standard Administration
The long formula
dose desired X volume on hand
Volume to administer = ------------------------------------
dose on hand
Example
Orders call for 0.5mg Atropine for symptomatic bradycardia. You have 1mg in 10 mL pre-filled syringe
0.5 mg X 10 mL------------------ = volume to
administer 1.0 mg
Example
mg’s cancel out0.5 X 10mL = 5mL
0.5 mg X 10 mL------------------ = 5 mL
1.0 mg
Another Example
You have 100mg Furosemide in a 10mL vial. The order is for 40mg
80 mg X 10 mL------------------ = volume to
administer 100 mg
Example
mg’s cancel out80 X 10mL = 800mL/100 = 8
80 mg X 10 mL------------------ = 8 mL
100 mg
Catching on?
Try it on your own
Benadryl – 50 mg in 2 mLOrders are for 12.5 mgShow your work
Benadryl
12.5 mg X 2 mL------------------ = volume to
administer 50 mg
12.5 X 2 = 25 / 50 = 0.5 mL
The easy way
Set up an equationCross MultiplyDivideSound like algebra?
The easy way
Order is for 45 mg BenadrylYou have 50 mg in 2 mL
50 45--- --- 2 X
The easy way
50 45--- --- 2 X
Multiply 45 X 2 = 90Divide 90 by 50 = 1.8
So… you would administer 1.8 mL = 45 mg
Another example
Order is for 3 mg ValiumYou have 10 mg in 2 mL
10 3--- -- 2 X
Another example
10 3--- -- 2 X
Multiply 3 X 2 = 6Divide 6 by 10 = 0.6
So… you would administer 0.6 mL = 3 mg
Finally, the good stuff
Order is for 145 µg of Fentanyl CitrateYou have 300 mcg in 5 mL
300 145----- ----- 5 X
The good stuff
300 145----- ----- 5 X
Multiply 145 X 5 = 725Divide 735 by 300 = 2.42 = 2.4
So… you would administer 2.4 mL = 145 mg
Weight Based Dosage
1. Convert weight to kgs.2. Calculate the dose to give3. Calculate the volume to
administer
Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest.
1. Convert the weight to kilograms. 185 / 2.2 = 84 kgsOr 93 – 9.3 = 83.7 = 84 kgs
Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest.
2. Calculate the dose to give 84 kgs X 1.5 mg = 126 mg
Weight Based Dosage
1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest.
3. Calculate the volume to administer
126 mg is the dose we want to give 10 mL pre-filled syringe containing
100 mg
Weight Based Dosage
126 mg X 20 mL------------------ = volume to
administer 200 mg
126 X 20 = 2520 / 200 = 12.6 mL
So, one complete syringe containing 10 mL plus approx. 2.6 mLfrom a second syringe
Weight Based Dosage
Pediatric2mg/kg Benadryl for a 25 lb patient
1. Convert weight to kilograms 25 / 2.2 = 11.36 kgsOr 12.5 – 1.2 = 11.3 kgs
Weight Based Dosage
Pediatric2mg/kg Benadryl for a 25 lb patient
2. Calculate the dose to give 11.3 kgs X 2 mg/kg = 22.6 mg
Weight Based Dosage
Pediatric2mg/kg Benadryl for a 25 lb patient
3. Calculate the volume to administer
22.6 mg X 1 mL-------------------- = 0.45 mL 50 mg
Or the easy way
We know we want 2mg/kgThe child ways 11.3 or roughly 11 kgsThe dose will be 22mg
50 22--- --- 1 X
Or the easy way
50 22--- --- 1 X
22 X 1 = 22 / 50 = 0.44 mL
Drip Rate Calculations
Facts: In a 60 drop set, 60 drops = 1 mL In a 10 drop set, 10 drops = 1 mL In a 15 drop set, 15 drops = 1 mL Medications are usually given in 60 gtt sets Doesn’t mean you cannot give it in a 10 gtt
set A 60 drip set is usually called a microdrip A 10 drip set is usually called a macrodrip
Microdrips
60 gtts = 1 mLIf your dose was 1 mL / hr what would your drip rate be?
1 gtt / minute
Why?60 gtts = 1 mL (our dose)1 drop / min = 60 gtts/hr = 1 mL = 60 gtts
Easy huh?
Let’s try another
Using a 60 drop set, the dose is 30 mL/hr60 gtts = 1 mL30 mL = 1800 gtts1800 gtts/60 min = 30 gtts/min
And another
Using a 60 drop set, the dose is 45 mL/hr60 gtts = 1 mL 45 mL = 2700 gtts2700 gtts / 60 min = 45 gtts / hr
Dose not in mL/hror
mL/min?
No sweat…
Understanding Concentration of drug in fluid
A liter bag of fluid = 1000 cc or 1000 mLIf you add 800 mg of a drug to 1000 mL of fluid, what would ur ratio of drug to fluid be?
800 mg X mg---------- --------1000 mL 1 mL
Drug in fluid
800 mg X mg---------- --------1000 mL 1 mL
800 X 1 = 800 / 1000 = 0.8 mg/mL
Drug in fluid
400 mg X mg---------- --------250 mL 1 mL
400 X 1 = 400 / 250 = 1.6 mg / mLConvert mg mcg Dopamine1.6 X 1000 = 1600 mcg / mL
You do it
You add 1 gram of Lidocaine to 250 mL NSThe answer should be in mg/mL
Survey Says….
1 gm = 1000 mg
1000 mg in 250 mL = 4mg/mL
Not mL/hr but mg/min
Lidocaine 2mg/minMixed 1gm/250ml
1000mg = 1gm1000mg/250ml = 4mg/ml
Drip rate = 30gtts/min
Why?
4mg/mlThe dose is 2mg/minUsing a microdrip (60) 60gtts=1ml4mg/min = 602mg/min = 301mg/min = 15
The Math
Drug order (mg/min) X IV Drip rate (gtts/ml)
-------------------------------------------Drug concentration (mg/ml) X 1min
2mg/min X 60 gtts/ml--------------------------
4mg/ml X 1min
2mg/min X 60 gtts/ml--------------------------
4mg/ml X 1min
2 X 60 120-------- = ---4 X 1 4
30 gtts
Putting it ALL together
Dopamine
Weight BasedOver time (mcg/kg/min)
Weight based over time
Order is for 7mcg/kg/minDrug on hand is 800 mgDrip Set is 60gtts/mlPt weight is 220 lbsIV solution 500mL NS
1. Convert Weight from lbs to kgs2. Convert measurements (mgs
µg)3. Determine µg/mL4. Formula
Step 1: Convert Weight
220 lbs kgs220 / 2.2 = 100 kgs
Step 2: Convert Measurements
800 mg µgMg µg = X 1000800,000 µg
Step 3: Determine µg/mL
800,000 µg / 500 mL1600 µ / mL
Step 4: Formula
Drug order (µg/kg) X weight (kgs) X drip rate
---------------------------------------------------Concentration on hand (µg/ml) X
time (min)
Step 4: Formula
7 µg/kg X 100 kgs X 60 gtts/mL---------------------------------------
1600 µg/mL X 1 min
7 X 100 = 700 X 60 = 4200
4200 / 1600 = 26.25 = 26 gtts/min
Another
Order is for 5 µg/kg/minDrug on hand is 800 mg = 800,000 µg60 Drop setPt weighs 175 lbsIV solution 500 mL NS
Step 1: Convert Weight
175 lbs / 2.2 = 79.5 ~ 79 kgs87.5 – 8.7 = 78.8 ~ 79 kgs
Step 2: Convert Measurements
800 mg µg800,000 µg
Step 3: Determine µg/mL
800,000 mcg / 500 mL1600 mcg / mL
Step 4: Formula
Drug order X weight X drip rate---------------------------------------
Conc on hand X time
5 mcg/kg X 79 kgs X 60-----------------------------1600 mcg/mL X 1 min
Step 4: Formula
5 X 79 X 60 = 2370023700 / 1600 = 14.81 ~ 15 gtts/min
An easy check to your work
For 5 µg / kg / minTake weight in pounds (175)Drop the last digit (17)Subtract 1 (16) in the ballpark, not completely accurate