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# Med Math

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### Med Math

1. 1. Med Math
2. 2. Tips for success <ul><li>Pick one method, that is easiest for YOU </li></ul><ul><li>Study it </li></ul><ul><li>Learn it </li></ul><ul><li>Practice it </li></ul><ul><li>Practice it </li></ul><ul><li>Practice it </li></ul>
3. 3. Topics <ul><li>Apothecary System </li></ul><ul><li>Weight and Temperature Conversions </li></ul><ul><li>Metric System </li></ul><ul><li>Med Math </li></ul><ul><ul><li>Administration Doses </li></ul></ul><ul><ul><li>Weight Based Doses </li></ul></ul><ul><ul><li>Drip Rate Calculations </li></ul></ul>
4. 4. Apothecary System <ul><li>Phased out and replaced by metric system </li></ul><ul><li>Basic Units: grain (gr), dram (dr), drop (gtt), ounce, (oz), pint (pt), quart (qt) </li></ul><ul><li>Equivalents </li></ul><ul><ul><ul><li>1dr = 1 tsp = 60 gtts </li></ul></ul></ul><ul><ul><ul><li>3tsp = 1 Tbsp </li></ul></ul></ul>
5. 5. Weight Conversion <ul><li>Fact: 1 kilogram (kg) = 2.2 pounds (lbs) </li></ul><ul><li>Fact: Weight in kgs X 2.2 = weight in pounds </li></ul>
6. 6. Conversion Practice <ul><li>80 kilogram patient, what is weight in pounds </li></ul><ul><li>kilograms X 2.2 = pounds </li></ul>80 X 2.2 = 176 lbs .
7. 7. Conversion Practice <ul><li>100 kilogram patient, what is weight in pounds </li></ul><ul><li>kilograms X 2.2 = pounds </li></ul>100 X 2.2 = 220 lbs.
8. 8. Weight Conversion <ul><li>Fact: 1 kilogram (kg) = 2.2 pounds (lbs) </li></ul><ul><li>Fact: Weight in kgs X 2.2 = weight in pounds </li></ul><ul><li>Fact: Weight in pounds / 2.2 = weight in kilograms </li></ul>
9. 9. Conversion Practice <ul><li>245 lb patient, what is weight in kilograms </li></ul><ul><li>lbs / 2.2 = kilograms </li></ul>245 / 2.2 = 111.36 kgs
10. 10. Conversion Practice <ul><li>140 lb patient, what is the weight in kilograms </li></ul><ul><li> lbs / 2.2 = kilograms </li></ul>140 / 2.2 = 63.63 kilograms
11. 11. Conversion Practice <ul><li>The easy way… </li></ul><ul><li>Half of weight in pounds, subtract 10% </li></ul><ul><li>Example: 180 lbs . . . . . 90 </li></ul>10% of 90 = 9 81 kilograms
12. 12. Conversion Practice <ul><li>180 lb patient, what is the weight in kilograms </li></ul><ul><li>lbs / 2.2 = kilograms </li></ul><ul><li>180 / 2.2 = 81.82 kilograms </li></ul>
13. 13. KNOW YOUR WEIGHT CONVERSIONS!!!!!
14. 14. Temperature Conversions <ul><li>Fahrenheit: </li></ul><ul><ul><li>Water Freezes at 32 º F </li></ul></ul><ul><ul><li>Water Boils at 212º F </li></ul></ul><ul><li>Celsuis: </li></ul><ul><ul><li>Water Freezes at 0 º C </li></ul></ul><ul><ul><li>Water Boils at 100º C </li></ul></ul>
15. 15. Temperature Conversions <ul><li>Fahrenheit  Celsius </li></ul><ul><li>Subtract 32 from the temperature </li></ul><ul><li>Multiply by 0.556 or 5/9 </li></ul><ul><li>98.6 – 32 = 66.6 </li></ul>66.6 X 0.556 = 37.03 = 37 º C
16. 16. Practice <ul><li>Convert 103 º F to Celsius </li></ul><ul><li>103 – 32 = 71 </li></ul>71 X 0.556 = 39.48 º C
17. 17. Temperature Conversions <ul><li>Celsius  Fahrenheit </li></ul><ul><li>Multiply by 1.8 </li></ul><ul><li>Add 32 </li></ul><ul><ul><li>37 º X 1.8 = 66.6 </li></ul></ul><ul><ul><li>66.6 + 32 = 96.6º F </li></ul></ul>
18. 18. Practice <ul><li>Convert 44 º C to Fahrenheit </li></ul><ul><ul><li>44 X 1.8 = 79.2 </li></ul></ul><ul><ul><li>79.2 + 32 = 111.2 º F </li></ul></ul>
19. 19. On your own <ul><li>120 º F  Celsius </li></ul><ul><li>76.4 º F  Celsuis </li></ul><ul><li>60 º C  Fahrenheit </li></ul><ul><li>24 º C  Fahrenheit </li></ul>
20. 20. Metric System <ul><li>System of 10 (base 10) </li></ul><ul><li>No fractions only decimals </li></ul><ul><li>EASY! </li></ul>
21. 21. Metric System
22. 22. Metric System <ul><li>Deca 10 </li></ul><ul><li>Hecto 100 </li></ul><ul><li>Kilo 1000 </li></ul><ul><li>Deci 0.1 </li></ul><ul><li>Centi 0.01 </li></ul><ul><li>Mili 0.001 </li></ul>
23. 23. Metric System <ul><li>Gram = g </li></ul><ul><li>Liter = l </li></ul><ul><li>Kilogram = kg </li></ul><ul><li>Milliliter = mL </li></ul><ul><li>Milligram = mg </li></ul><ul><li>Cubic centimeter = cc </li></ul><ul><li>Microgram =  g </li></ul><ul><li>1 L = 1000 mL </li></ul><ul><li>1 mL = 1 cc </li></ul><ul><li>1 g = 1000 mg </li></ul><ul><li>1 mg = 1000  g </li></ul><ul><li>1cc = 1 mL </li></ul><ul><li>1  g = 0.001 mg </li></ul><ul><li>1 mg = 0.001 g </li></ul>
24. 24. The math <ul><li>Adding – keep the decimal points in line </li></ul><ul><li>Subtracting – see above </li></ul><ul><li>Multiplying – multiply without regard to decimals then add decimal places </li></ul><ul><li>Dividing – make the divisor a whole number and add zeroes to the dividend </li></ul>
25. 25. Addition <ul><li>4.3795 </li></ul><ul><li>+ 5.2389 </li></ul><ul><li>--------------- </li></ul><ul><li>9.6184 </li></ul>
26. 26. Subtraction <ul><li>9.6184 </li></ul><ul><li>- 5.2389 </li></ul><ul><li>--------------- </li></ul><ul><li>4.3795 </li></ul>
27. 27. Multiplication <ul><li>34.76 </li></ul><ul><li>X 4.935 </li></ul><ul><li>-------------- </li></ul><ul><li> 17154060 </li></ul><ul><li>Add decimal places = 5 </li></ul><ul><li> 171.54060 = 171.5406 </li></ul>
28. 28. Division <ul><li>.75 / .995 </li></ul><ul><li> 75 / 99.5  move decimal </li></ul><ul><li>-------------- </li></ul><ul><li>0.7537 </li></ul>
29. 29. Converting <ul><li>1g = 1000mg so… g  mg X 1000 </li></ul><ul><li>1mg = 1000 µg so… mg   g X 1000 </li></ul><ul><li>1g = ????  g = 1,000,000  g </li></ul>
30. 30. Converting <ul><li>500mL = 0.5L so… mL  L / 1000 </li></ul><ul><li>The Bottom Line… </li></ul><ul><li>To convert from the base to mili X 1000 </li></ul><ul><li>To convert from mili to the base / 1000 </li></ul><ul><li>To convert from mili to  X 1000 </li></ul><ul><li>To convert from base to  X 1000000 </li></ul>
31. 31. Standard Administration <ul><li>The long formula </li></ul><ul><li> dose desired X volume on hand </li></ul><ul><li>Volume to administer = ------------------------------------ </li></ul><ul><li> dose on hand </li></ul>
32. 32. Example <ul><li>Orders call for 0.5mg Atropine for symptomatic bradycardia. You have 1mg in 10 mL pre-filled syringe </li></ul><ul><li>0.5 mg X 10 mL </li></ul><ul><li>------------------ = volume to administer </li></ul><ul><li> 1.0 mg </li></ul>
33. 33. Example <ul><li>mg’s cancel out </li></ul><ul><li>0.5 X 10mL = 5mL </li></ul><ul><li>0.5 mg X 10 mL </li></ul><ul><li>------------------ = 5 mL </li></ul><ul><li> 1.0 mg </li></ul>
34. 34. Another Example <ul><li>You have 100mg Furosemide in a 10mL vial. The order is for 40mg </li></ul><ul><li>80 mg X 10 mL </li></ul><ul><li>------------------ = volume to administer </li></ul><ul><li> 100 mg </li></ul>
35. 35. Example <ul><li>mg’s cancel out </li></ul><ul><li>80 X 10mL = 800mL/100 = 8 </li></ul><ul><li>80 mg X 10 mL </li></ul><ul><li>------------------ = 8 mL </li></ul><ul><li> 100 mg </li></ul>
36. 36. Catching on?
37. 37. Try it on your own <ul><li>Benadryl – 50 mg in 2 mL </li></ul><ul><li>Orders are for 12.5 mg </li></ul><ul><li>Show your work </li></ul>
38. 38. Benadryl <ul><li>12.5 mg X 2 mL </li></ul><ul><li>------------------ = volume to administer </li></ul><ul><li> 50 mg </li></ul><ul><li>12.5 X 2 = 25 / 50 = 0.5 mL </li></ul>
39. 39. The easy way <ul><li>Set up an equation </li></ul><ul><li>Cross Multiply </li></ul><ul><li>Divide </li></ul><ul><li>Sound like algebra? </li></ul>
40. 40. The easy way <ul><li>Order is for 45 mg Benadryl </li></ul><ul><li>You have 50 mg in 2 mL </li></ul><ul><li>50 45 </li></ul><ul><li>--- --- </li></ul><ul><li> 2 X </li></ul>
41. 41. The easy way <ul><li>50 45 </li></ul><ul><li>--- --- </li></ul><ul><li> 2 X </li></ul><ul><li>Multiply 45 X 2 = 90 </li></ul><ul><li>Divide 90 by 50 = 1.8 </li></ul><ul><li>So… you would administer 1.8 mL = 45 mg </li></ul>
42. 42. Another example <ul><li>Order is for 3 mg Valium </li></ul><ul><li>You have 10 mg in 2 mL </li></ul><ul><li>10 3 </li></ul><ul><li>--- -- </li></ul><ul><li> 2 X </li></ul>
43. 43. Another example <ul><li>10 3 </li></ul><ul><li>--- -- </li></ul><ul><li> 2 X </li></ul><ul><li>Multiply 3 X 2 = 6 </li></ul><ul><li>Divide 6 by 10 = 0.6 </li></ul><ul><li>So… you would administer 0.6 mL = 3 mg </li></ul>
44. 44. Finally, the good stuff <ul><li>Order is for 145 µ g of Fentanyl Citrate </li></ul><ul><li>You have 300 mcg in 5 mL </li></ul><ul><li>300 145 </li></ul><ul><li>----- ----- </li></ul><ul><li> 5 X </li></ul>
45. 45. The good stuff <ul><li>300 145 </li></ul><ul><li>----- ----- </li></ul><ul><li> 5 X </li></ul><ul><li>Multiply 145 X 5 = 725 </li></ul><ul><li>Divide 735 by 300 = 2.42 = 2.4 </li></ul><ul><li>So… you would administer 2.4 mL = 145 mg </li></ul>
46. 46. Weight Based Dosage <ul><li>Convert weight to kgs. </li></ul><ul><li>Calculate the dose to give </li></ul><ul><li>Calculate the volume to administer </li></ul>
47. 47. Weight Based Dosage <ul><li>1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest. </li></ul><ul><li>1. Convert the weight to kilograms. </li></ul><ul><ul><li>185 / 2.2 = 84 kgs </li></ul></ul><ul><ul><li>Or </li></ul></ul><ul><ul><li>93 – 9.3 = 83.7 = 84 kgs </li></ul></ul>
48. 48. Weight Based Dosage <ul><li>1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest. </li></ul><ul><li>2. Calculate the dose to give </li></ul><ul><ul><li>84 kgs X 1.5 mg = 126 mg </li></ul></ul>
49. 49. Weight Based Dosage <ul><li>1.5 mg/kg Lidocaine for a 185 lb patient in cardiac arrest. </li></ul><ul><li>3. Calculate the volume to administer </li></ul><ul><ul><li>126 mg is the dose we want to give </li></ul></ul><ul><ul><li>10 mL pre-filled syringe containing 100 mg </li></ul></ul>
50. 50. Weight Based Dosage <ul><li>126 mg X 20 mL </li></ul><ul><li>------------------ = volume to administer </li></ul><ul><li> 200 mg </li></ul>126 X 20 = 2520 / 200 = 12.6 mL So, one complete syringe containing 10 mL plus approx. 2.6 mL from a second syringe
51. 51. Weight Based Dosage <ul><li>Pediatric </li></ul><ul><li>2mg/kg Benadryl for a 25 lb patient </li></ul><ul><li>Convert weight to kilograms </li></ul><ul><ul><ul><li>25 / 2.2 = 11.36 kgs </li></ul></ul></ul><ul><ul><ul><li>Or </li></ul></ul></ul><ul><ul><ul><li>12.5 – 1.2 = 11.3 kgs </li></ul></ul></ul>
52. 52. Weight Based Dosage <ul><li>Pediatric </li></ul><ul><li>2mg/kg Benadryl for a 25 lb patient </li></ul><ul><li>2. Calculate the dose to give </li></ul><ul><ul><li>11.3 kgs X 2 mg/kg = 22.6 mg </li></ul></ul>
53. 53. Weight Based Dosage <ul><li>Pediatric </li></ul><ul><li>2mg/kg Benadryl for a 25 lb patient </li></ul><ul><li>3. Calculate the volume to administer </li></ul><ul><ul><li>22.6 mg X 1 mL </li></ul></ul><ul><ul><li>-------------------- = 0.45 mL </li></ul></ul><ul><ul><li>50 mg </li></ul></ul>
54. 54. Or the easy way <ul><li>We know we want 2mg/kg </li></ul><ul><li>The child ways 11.3 or roughly 11 kgs </li></ul><ul><li>The dose will be 22mg </li></ul><ul><li>50 22 </li></ul><ul><li>--- --- </li></ul><ul><li> 1 X </li></ul>
55. 55. Or the easy way <ul><li>50 22 </li></ul><ul><li>--- --- </li></ul><ul><li> 1 X </li></ul><ul><li>22 X 1 = 22 / 50 = 0.44 mL </li></ul>
56. 56. Drip Rate Calculations <ul><li>Facts: </li></ul><ul><ul><li>In a 60 drop set, 60 drops = 1 mL </li></ul></ul><ul><ul><li>In a 10 drop set, 10 drops = 1 mL </li></ul></ul><ul><ul><li>In a 15 drop set, 15 drops = 1 mL </li></ul></ul><ul><ul><li>Medications are usually given in 60 gtt sets </li></ul></ul><ul><ul><li>Doesn’t mean you cannot give it in a 10 gtt set </li></ul></ul><ul><ul><li>A 60 drip set is usually called a microdrip </li></ul></ul><ul><ul><li>A 10 drip set is usually called a macrodrip </li></ul></ul>
57. 57. Microdrips <ul><li>60 gtts = 1 mL </li></ul><ul><li>If your dose was 1 mL / hr what would your drip rate be? </li></ul><ul><li>1 gtt / minute </li></ul><ul><li>Why? </li></ul><ul><li>60 gtts = 1 mL (our dose) </li></ul><ul><li>1 drop / min = 60 gtts/hr = 1 mL = 60 gtts </li></ul>
58. 58. Easy huh?
59. 59. Let’s try another <ul><li>Using a 60 drop set, the dose is 30 mL/hr </li></ul><ul><li>60 gtts = 1 mL </li></ul><ul><li>30 mL = 1800 gtts </li></ul><ul><li>1800 gtts/60 min = 30 gtts/min </li></ul>
60. 60. And another <ul><li>Using a 60 drop set, the dose is 45 mL/hr </li></ul><ul><li>60 gtts = 1 mL </li></ul><ul><li>45 mL = 2700 gtts </li></ul><ul><li>2700 gtts / 60 min = 45 gtts / hr </li></ul>
61. 61. Dose not in mL/hr or mL/min?
62. 62. No sweat…
63. 63. Understanding Concentration of drug in fluid <ul><li>A liter bag of fluid = 1000 cc or 1000 mL </li></ul><ul><li>If you add 800 mg of a drug to 1000 mL of fluid, what would ur ratio of drug to fluid be? </li></ul><ul><li>800 mg X mg </li></ul><ul><li>---------- -------- </li></ul><ul><li>1000 mL 1 mL </li></ul>
64. 64. Drug in fluid <ul><li>800 mg X mg </li></ul><ul><li>---------- -------- </li></ul><ul><li>1000 mL 1 mL </li></ul><ul><li>800 X 1 = 800 / 1000 = 0.8 mg/mL </li></ul>
65. 65. Drug in fluid <ul><li>400 mg X mg </li></ul><ul><li>---------- -------- </li></ul><ul><li>250 mL 1 mL </li></ul><ul><li>400 X 1 = 400 / 250 = 1.6 mg / mL </li></ul><ul><li>Convert mg  mcg  Dopamine </li></ul><ul><li>1.6 X 1000 = 1600 mcg / mL </li></ul>
66. 66. You do it <ul><li>You add 1 gram of Lidocaine to 250 mL NS </li></ul><ul><li>The answer should be in mg/mL </li></ul>Survey Says…. 1 gm = 1000 mg 1000 mg in 250 mL = 4mg/mL
67. 67. Not mL/hr but mg/min <ul><li>Lidocaine 2mg/min </li></ul><ul><li>Mixed 1gm/250ml </li></ul>1000mg = 1gm 1000mg/250ml = 4mg/ml Drip rate = 30gtts/min
68. 68. Why? <ul><li>4mg/ml </li></ul><ul><li>The dose is 2mg/min </li></ul><ul><li>Using a microdrip (60) 60gtts=1ml </li></ul><ul><li>4mg/min = 60 </li></ul><ul><li>2mg/min = 30 </li></ul><ul><li>1mg/min = 15 </li></ul>
69. 69. The Math <ul><li>Drug order (mg/min) X IV Drip rate (gtts/ml) </li></ul><ul><li>------------------------------------------- </li></ul><ul><li>Drug concentration (mg/ml) X 1min </li></ul>2mg/min X 60 gtts/ml -------------------------- 4mg/ml X 1min
70. 70. <ul><li>2mg/min X 60 gtts/ml </li></ul><ul><li>-------------------------- </li></ul><ul><li>4mg/ml X 1min </li></ul>2 X 60 120 -------- = --- 4 X 1 4 30 gtts
71. 71. Putting it ALL together
72. 72. Dopamine <ul><li>Weight Based </li></ul><ul><li>Over time (mcg/kg/min) </li></ul>
73. 73. Weight based over time <ul><li>Order is for 7mcg/kg/min </li></ul><ul><li>Drug on hand is 800 mg </li></ul><ul><li>Drip Set is 60gtts/ml </li></ul><ul><li>Pt weight is 220 lbs </li></ul><ul><li>IV solution 500mL NS </li></ul>
74. 74. <ul><li>Convert Weight from lbs to kgs </li></ul><ul><li>Convert measurements (mgs  µg) </li></ul><ul><li>Determine µg/mL </li></ul><ul><li>Formula </li></ul>
75. 75. Step 1: Convert Weight <ul><li>220 lbs  kgs </li></ul><ul><li>220 / 2.2 = 100 kgs </li></ul>
76. 76. Step 2: Convert Measurements <ul><li>800 mg  µg </li></ul><ul><li>Mg  µg = X 1000 </li></ul><ul><li>800,000 µg </li></ul>
77. 77. Step 3: Determine µg/mL <ul><li>800,000 µg / 500 mL </li></ul><ul><li>1600 µ / mL </li></ul>
78. 78. Step 4: Formula <ul><li>Drug order ( µg/kg) X weight (kgs) X drip rate </li></ul><ul><li>--------------------------------------------------- </li></ul><ul><li>Concentration on hand (µg/ml) X time (min) </li></ul>
79. 79. Step 4: Formula <ul><li>7 µg/kg X 100 kgs X 60 gtts/mL </li></ul><ul><li>--------------------------------------- </li></ul><ul><li>1600 µg/mL X 1 min </li></ul>7 X 100 = 700 X 60 = 4200 4200 / 1600 = 26.25 = 26 gtts/min
80. 80. Another <ul><li>Order is for 5 µg/kg/min </li></ul><ul><li>Drug on hand is 800 mg = 800,000 µg </li></ul><ul><li>60 Drop set </li></ul><ul><li>Pt weighs 175 lbs </li></ul><ul><li>IV solution 500 mL NS </li></ul>
81. 81. Step 1: Convert Weight <ul><li>175 lbs / 2.2 = 79.5 ~ 79 kgs </li></ul><ul><li>87.5 – 8.7 = 78.8 ~ 79 kgs </li></ul>
82. 82. Step 2: Convert Measurements <ul><li>800 mg  µg </li></ul><ul><li>800,000 µg </li></ul>
83. 83. Step 3: Determine µg/mL <ul><li>800,000 mcg / 500 mL </li></ul><ul><li>1600 mcg / mL </li></ul>
84. 84. Step 4: Formula <ul><li>Drug order X weight X drip rate </li></ul><ul><li>--------------------------------------- </li></ul><ul><li>Conc on hand X time </li></ul>5 mcg/kg X 79 kgs X 60 ----------------------------- 1600 mcg/mL X 1 min
85. 85. Step 4: Formula <ul><li>5 X 79 X 60 = 23700 </li></ul><ul><li>23700 / 1600 = 14.81 ~ 15 gtts/min </li></ul>
86. 86. An easy check to your work <ul><li>For 5 µg / kg / min </li></ul><ul><li>Take weight in pounds (175) </li></ul><ul><li>Drop the last digit (17) </li></ul><ul><li>Subtract 1 (16)  in the ballpark, not completely accurate </li></ul>