2. MED MATH / JAM / 2003 MEDICATION MATH MEDICATION MATH Jose A. Martinez,MSN,RN Nursing Instructor

3. MED MATH / JAM / 2003 OBJECTIVES Ability to calculate basic arithmetic and convert Arabic numerals to Roman numerals and reverse this process Demonstrate correct use of symbols and abbreviations

4. MED MATH / JAM / 2003 Ability to convert measurements of weights and volumes in household, apothecaries’ and metric systems OBJECTIVES

5. MED MATH / JAM / 2003 Ability to solve for unknowns using the systems of measurements listed in the syllabus and your text book OBJECTIVES

6. MED MATH / JAM / 2003 Ability to solve for unknowns using the systems of measurements listed in the syllabus and your text book OBJECTIVES There are other objectives listed in your syllabus - know them.

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8. MED MATH / JAM / 2003 INTRODUCTION Knowledge of basic math is a necessary component of dosage calculation that nurses need to know to prevent medications errors and ensure the safe administration of medications.

9. MED MATH / JAM / 2003 Be Fully Advised: If given incorrectly, the drug given to cure or help the client can kill them! INTRODUCTION

10. MED MATH / JAM / 2003 Roman Numerals This system developed by Romans uses letters to describe amounts. (there is no ‘zero’ (0) in this system!) Used primarily in the APOTHECARIES’ system: “gr x” = grains 10

11. MED MATH / JAM / 2003 I or i = one II or ii = two III or iii = three From this point on - working with Roman Numerals becomes a little more complex and certain rules must be followed! Roman Numerals

12. MED MATH / JAM / 2003 V or v = five IV or iv = four VI or vi = six Certain numbers are immediately subtracted from other numbers (5 - 1 = 4 or v - i= iv) Some are added (e.g,, (5 + 1= 6 or v + i = vi [6] )) Roman Numerals

13. MED MATH / JAM / 2003 The only fraction we will work with is “1/2”. The fraction “1/2” is written as “ss” The number “i ss” would be read as “1 1/2” Roman Numerals

14. MED MATH / JAM / 2003 The only fraction we will work with is “1/2”. The fraction “1/2” is written as “ss” The number “i ss” would be read as “1 1/2” Roman Numerals And, remember: the Romans built an entire empire with the zero! Inventing and using the “0” is credited to the Arabs

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16. MED MATH / JAM / 2003 Arabic Numerals These are the numbers that we used in our every day activities - 1, 2, 3, 10, 1/3 … etc. The Arabic system developed the ‘zero’ (0).

17. MED MATH / JAM / 2003 General Review: Fractions NUMERATOR: How many parts of the whole you are taking DENOMINATOR: How many equal parts the whole is divided into Remember, the ‘de-nom’ is always below!

18. MED MATH / JAM / 2003 Types: Proper Improper Mixed 1/8, 5/6, 7/8 3/2, 6/5, 8/7 3 1/3, 5 1/8, 9 1/2 General Review: Fractions

19. MED MATH / JAM / 2003 To do any operation with fractions you must work with the COMMON DENOMINATOR ARITHMATIC: 1/4 + 1/3 = ( multiply denominators [4x3=12] to get com.de., then divide individual de. [4/12=3. So:1/4=3/12 ) 1/4= 3/12 1/3= 4/12 7/12 General Review: Fractions

20. MED MATH / JAM / 2003 General Review: Decimals Most medications are ordered in metric measures that use decimals not fractions. Capoten  6. 25 mg Digoxin 0. 125 mg Sometimes the decimal is ignored! This can be a fatal mistake!

21. MED MATH / JAM / 2003 Do not underestimate the power of the decimal. Many medications need only a small amount to be effective. Do not underestimate the power of the decimal. Many medications need only a small amount to be effective. Capoten  6.25 mg Digoxin 0.125 mg “Capoten  6 and 25 hundredths mg” “Digoxin zero point one hundred and twenty- five thousandths mg” General Review: Decimals

22. MED MATH / JAM / 2003 A decimal error in giving a med can mean that the client gets 10 or 100 or even 1000 x the ordered amount of drug - this can become toxic in no time at all! Capoten  6.25 mg Digoxin 0.125 mg “Capoten  6 point 25 mg” “Digoxin zero point one-two-five mg” General Review: Decimals

23. MED MATH / JAM / 2003 It is MOST IMPORTANT to place a zero (0) in front of the decimal point to indicate that it is a fraction when there is no whole number before it. 0.11 x 0.33= 0.11 x0.33 33 3 6 3 The answer requires a 4 decimal number General Review: Decimals YOU’RE NOT FINISHED YET!

24. MED MATH / JAM / 2003 In this example a 4 decimal placed number is required because there are 2 places (0.11) to be added to another 2 places (0.33) 0.11 x 0.33= The partial answer is 363 and we now add a “0” to the left most space and then add a decimal point. 0.0363 is the answer General Review: Decimals

25. MED MATH / JAM / 2003 Three Steps To Correctly Writing a Decimal: 1.- The whole number. (If there is no whole number, write zero [0] ). 2.- The decimal point to indicate the place value of the right-most number 3.- The decimal portion of the number Three Steps To Correctly Writing a Decimal: 1.- The whole number. (If there is no whole number, write zero [0] ). 2.- The decimal point to indicate the place value of the right-most number 3.- The decimal portion of the number General Review: Decimals

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27. MED MATH / JAM / 2003 General Review: Ratio A ratio is used to indicate a relationship between two numbers. These numbers are separated by a colon (:), e.g., 3:4 In the example given on the left 3 is the numerator 4 is the denominator The expression could be written as 3/4

28. MED MATH / JAM / 2003 General Review: Proportion A proportion is an equation of two ratios. The terms of the 1st ratio have a relationship to the terms of the 2nd ratio, e.g,: 3:4 :: 6:8 Read as follows: “3 is to 4 equals 6 is to 8” The two terms in a proportion are called means extremes - Do not confuse these terms.

29. MED MATH / JAM / 2003 In the example 3:4 :: 6:8 4 and 6 are the means 3 and 8 are the extremes The product of the means = the product of the extremes: 4 x 6 = 24 3 x 8 = 24 24 = 24 The answer is verified; the ratios are equal, the proportion is true. General Review: Proportion

30. MED MATH / JAM / 2003 If the example is written as a fraction 3/4 = 6/8 4 and 6 are the means 3 and 8 are the extremes The product of the means = the product of the extremes: 4 x 6 = 24 3 x 8 = 24 24 = 24 The answer is verified; the ratios are equal, the proportion is true. General Review: Proportion

31. MED MATH / JAM / 2003 Solving for x in Ratio & Proportion In this example:12 : 9 :: 8 : x 12 : 9 :: 8 : x “X” still marks the spot! X = 6 12 x = 72 (multiply the means and extremes) 72 = 12x (divide both 12 x sides of the equation by the number in front of the x to obtain the value for x

32. MED MATH / JAM / 2003 Dosage Calculations using Ratio & Proportion R-P may be used to represent the weight of a drug that is in tablet or capsule form: 1 tab 1 tab : 0.125mg or 0.125mg This means that 1 tablet contains 0.125mg of the drug

33. MED MATH / JAM / 2003 R & P may be used to represent the weight of a drug in a certain volume of solution: 1 mL 1 mL : 250 mg or 250 mg This means that 1 mL contains 250 mg of the drug Dosage Calculations using Ratio & Proportion

34. MED MATH / JAM / 2003 The doctor orders 40 mg of a certain drug. The drug comes in a vile: “80 mg per 2 mL”. How many mL does the nurse give? Dosage Calculations using Ratio & Proportion The most important step is to set up the equation correctly.

35. MED MATH / JAM / 2003 Dosage Calculations using Ratio & Proportion The most important step is to set up the equation correctly. 80 mg : 2 mL :: 40 mg : x WHAT PHARMACY SENT This is the way the drug manufacturer packaged this medication. This is what is written on the package you are holding in your hand! Left Side Of The Equation

36. MED MATH / JAM / 2003 Dosage Calculations using Ratio & Proportion The most important step is to set up the equation correctly. 80 mg : 2 mL :: 40 mg : x WHAT DOCTOR ORDERED

37. MED MATH / JAM / 2003 Dosage Calculations using Ratio & Proportion The most important step is to set up the equation correctly. 80 mg : 2 mL :: 40 mg : x WHAT YOU NEED TO GIVE

38. MED MATH / JAM / 2003 The doctor orders 40 mg of a certain drug. The drug comes in a vile: “80 mg per 2 mL”. How many mL does the nurse give? Dosage Calculations using Ratio & Proportion 80 mg : 2 mL :: 40 mg : x multiply means (2 x 40) = 80 multiply extremes (80 x x ) 80 x

39. MED MATH / JAM / 2003 The doctor orders 40 mg of a certain drug. The drug comes in a vile: “80 mg per 2 mL”. How many mL does the nurse give? Dosage Calculations using Ratio & Proportion 80 x = 80 80 / 80 = 1 x = 1 mL The nurse gives 1 mL of the drug.

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41. MED MATH / JAM / 2003 The Metric System THE ONLY ONE WHO HAS ANY- THING TO WORRY ABOUT CONCERNING THE METRIC SYSTEM IS THE “INCH” WORM !!!

42. MED MATH / JAM / 2003 The international decimal system of weights and measures Three basic units of measure: GRAM: basic unit for weight LITER: basic unit for volume METER: basic unit for length You can expect to see more items with Grams and Liters then with Meters The Metric System

43. MED MATH / JAM / 2003 Memorize: gram = g milligram = mg kilogram = kg microgram = mcg liter = L milliliter = mL The Metric System

44. MED MATH / JAM / 2003 Memorize: Kilo 1000 one thousand x Centi 0.01 one hundredth part Milli 0.001 one thousandth part of Micro 0.000001 one millionth part of The Metric System

45. MED MATH / JAM / 2003 Memorize: 1 kilogram [kg] =1,000 grams [g] 1 gram [g]=1,000 milligrams [mg] 1 milligram [mg] =1,000 micro- grams [mcg] The Metric System

46. MED MATH / JAM / 2003 Memorize: 1 liter = 1,000 milliliters [mL] or 1,000 cubic centimeters [cc] 1 milliliter [mL] = 1 cubic centimeter [cc] The Metric System

47. MED MATH / JAM / 2003 To convert a smaller unit to a larger one, divide by moving the decimal point 3 places the left (smaller) (larger) 100mL = __ L 100mL = 0.1 L To convert a larger unit to a smaller one, multiply by moving the decimal 3 places to the right (larger) (smaller) 0.75g = ___ mg 0.75g = 750 mg The Metric System

48. MED MATH / JAM / 2003 The Apothecaries’ System Particulars 1.- The measures used are approximations 2.- Roman and Arabic numerals are used in this system

49. MED MATH / JAM / 2003 The Apothecaries’ System Particulars 3.- Fractions are used to express a quantity less then one 4.- The symbol ss is used for the fraction 1/2

50. MED MATH / JAM / 2003 Memorize : 1 grain [gr] = 60 or 65 milligrams [mg] gr 15 = 1 g [15 grains = 1 gram] 1 fluid dram = 60 minims 1 fluid dram - 4 or 5 mL 1 fluid ounce = 30 mL 1 fluid ounce = 8 fluid drams The Apothecaries’ System

51. MED MATH / JAM / 2003 The Household System The household system is used for doses given primarily at home. This is the least accurate of the three system because of different sizes of measuring instruments used - Look in your own kitchen and see how many different sized teaspoons you can find!

52. MED MATH / JAM / 2003 Memorize: Drop (gtt) Teaspoon (t, tsp.) [60 gtt = 1 tsp] Tablespoon (T, tbs) [3 tsp = 1 tbs] Cup (C) [16 tbs = 1C] Pint (pt) [2C = 1 pt] Quart (qt) [2pt = 1 qt] The Household System

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54. MED MATH / JAM / 2003 Approximate Equivalents of Household, Apothecaries’ and Metric Measurements The Systems This symbol is NOT the number “3” it is the DRAM sign

55. MED MATH / JAM / 2003 Approximate Equivalents of Household, Apothecaries’ and Metric Measurements Don’t confuse these symbols:  and  = fluid ounce,  = dram

56. MED MATH / JAM / 2003 Approximate Equivalents of Household, Apothecaries’ and Metric Measurements

57. MED MATH / JAM / 2003 Approximate Equivalents of Household, Apothecaries’ and Metric Measurements

58. MED MATH / JAM / 2003 “grains 15” Approximate Equivalents of Household, Apothecaries’ and Metric Measurements

59. MED MATH / JAM / 2003 Approximate Equivalents of Household, Apothecaries’ and Metric Measurements

60. MED MATH / JAM / 2003 Approximate Equivalents of Household, Apothecaries’ and Metric Measurements

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62. MED MATH / JAM / 2003 CONVERTING - Within and Between Systems It is very important that every nurse is proficient in converting between all three systems of measure. Your client’s life depends on your accuracy!

63. MED MATH / JAM / 2003 The nurse has a professional, ethical and legal responsibility to ensure safe practice. CONVERTING - Within and Between Systems HOW WOULD YOU FEEL IF ONE OF YOUR FAMILY WAS GIVEN THE WRONG DOSE OF A DRUG?

64. MED MATH / JAM / 2003 POINTS FOR CONVERTING 1- Memorize the equivalents 2- Use these as conversion factors 3- Follow basic math principles 4- Follow the system used (metric uses decimals, Apothecaries’ uses fractions) CONVERTING - Within and Between Systems

65. MED MATH / JAM / 2003 RULES FOR R & P 1- State known equivalent 1st 2- Add incomplete ratio on the other side of = sign 3- Units written in same sequence (mg : g = mg : g) 4- Label terms accurately CONVERTING - Within and Between Systems

66. MED MATH / JAM / 2003 Example: 8mg = _____ g (How many grams are in 8 milligrams?) CONVERTING - Within and Between Systems

67. MED MATH / JAM / 2003 8mg = _____ g 1000mg : 1 g :: 8 mg : xg [Known equiv.] [Unknown equiv.] 1 x 8 = 1000 x (x) 8/1000 = 1000 x /1000 x = 8/1000 x = 0.008 g CONVERTING - Within and Between Systems

68. MED MATH / JAM / 2003 Example: gr 1/100 = _____ mg (How many milligrams are in 1/100 grains?) CONVERTING - Within and Between Systems

69. MED MATH / JAM / 2003 Example: The doctor orders, “gr 1/100” of a certain drug. The drug comes as 0.3mg per tablet. The nurse will administer ___ tablet(s). This is a typical type of drug conversion problem that nurses respond to every day. CONVERTING - Within and Between Systems

70. MED MATH / JAM / 2003 gr 1/100 = _____ mg (This is a conversion between systems) [Apothecaries’] [Metric] Equivalent: gr 1 = 60mg gr 1 : 60mg :: gr 1/100 : x mg 60 x 1/100 = x 60/100 - x x = 0.6 mg - This is how much we need CONVERTING - Within and Between Systems STEP #1

71. MED MATH / JAM / 2003 x = 0.6 mg - this is how much we need Now we need to know how many tablets of 0.3mg strength the nurse will give: 0.3 : 1(tablet) :: 0.6 : x 0.3x = 0.6 or 0.6 / 0.3 = 2 tablets CONVERTING - Within and Between Systems STEP #2

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73. MED MATH / JAM / 2003 Converting Between Temperature Systems Two more items before we leave the area - since there are 2 scales that can be used to measure a client’s temperature we need to know how this is done

74. MED MATH / JAM / 2003 There is an easy way to remember which system to use: °F °C WATER BOILS 212100 WATER FREEZES 32 0 THE FAHRENHEIT SCALE HAS MORE NUMBERS - IT COVERS MORE AREA Converting Between Temperature Systems

75. MED MATH / JAM / 2003 SO - IF YOU HAVE A TEMPERATURE IN FAHRENHEIT AND WANT TO CONVERT TO CENTIGRADE - YOU AUTOMATICALLY KNOW YOUR ANSWER WILL BE A SMALLER NUMBER Converting Between Temperature Systems REMEMBER THE TEMP IS THE SAME - JUST OUR WAY OF MEASURING IT HAS CHANGED!

76. MED MATH / JAM / 2003 LET’S WORK WITH 2 EXAMPLES OF TEMPERATURE CONVERSION °F °C 100.4 °F = ? °C ? °F = 37.3 °C REMEMBER - THE ANSWER MUST MAKE SENSE Converting Between Temperature Systems

77. MED MATH / JAM / 2003 LET’S LOOK AT THE FORMULA CELCIUS TO FAHRENHEIT °F = (°C X 1.8) + 32 °F = 37.3 °C = ? °F °F = (37.3 X 1.8) + 32 = °F = 67.14 + 32 = °F = 99.14 Converting Between Temperature Systems

78. MED MATH / JAM / 2003 LET’S LOOK AT THE FORMULA FAHRENHEIT TO CELCIUS °C = (°F - 32) X 0.55 °C = 100.4 °F = ? °C °C = (100.4 - 32) X 0.55 = °C = 68.4 X 0.55 = °C = 37.6 Converting Between Temperature Systems

79. MED MATH / JAM / 2003 Standard and Military Time Systems Last item: For military time do not use a.m. or p.m. For times after 12noon on standard time simply add 12 to the time. 1:00pm + 12 = 1300hrs 5:00pm + 12 = 1700hrs ETC.

80. MED MATH / JAM / 2003 Standard and Military Time Systems Last item: For converting from military time to standard time just subtract: 1300hrs - 12 = 1:00pm 1700hrs - 12 = 5:00pm

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82. MED MATH / JAM / 2003 TEST TAKING SKILLS The nurse has a medication calculation to make: Drug Order: gr 1/4 po of phenobarbital t.i.d. The Supply is: phenobarbital 15mg scored tablets. The most appropriate nursing action is to: A. Verify the order B. Administer 1/2 tablet C. Administer 1 tablet D. Administer 1 1/2 tablets

83. MED MATH / JAM / 2003 TEST TAKING SKILLS The nurse has a medication calculation to make: Drug Order: gr 1/4 po of phenobarbital t.i.d. The Supply is: phenobarbital 15mg scored tablets. The most appropriate nursing action is to: A. Verify the order This response means that there is something wrong with the question: the wrong drug was supplied by pharmacy - or, they sent the right drug but the wrong dosage form (e.g., liquid form rather than solid), or unscored tablets when the nurse would need scored tablets, or the physician made an error, or the client’s condition has changed and giving the med at this time would be dangerous. MED MATH IS NOT JUST MATH - you have to exercise proper judgment before administering a med. There are no errors with this question.

84. MED MATH / JAM / 2003 TEST TAKING SKILLS The nurse has a medication calculation to make: Drug Order: gr 1/4 po of phenobarbital t.i.d. The Supply is: phenobarbital 15mg scored tablets. The most appropriate nursing action is to: B. Administer 1/2 tablet You recall that 1 grain = 60mg. So now we set up the ratio: gr 1 : 60mg :: gr 1/4 : x (Set it us then cross multiply.) 1 x = (60 x 1/4) 1 x = (60 / 4) 1 x = 15mg If we need 15mg and the tablet is 15mg, 1/2 of this amount would not give the correct dosage. Go to the next Choice.

85. MED MATH / JAM / 2003 TEST TAKING SKILLS The nurse has a medication calculation to make: Drug Order: gr 1/4 po of phenobarbital t.i.d. The Supply is: phenobarbital 15mg scored tablets. The most appropriate nursing action is to: C. Administer 1 tablet You recall that 1 grain = 60mg. So now we set up the ratio: gr 1 : 60mg :: gr 1/4 : x (This is where the action is!) 1 x = (60 x 1/4) 1 x = (60 / 4) 1 x = 15mg If we need 15mg and the tablet is 15mg, 1 tablet will give us the amount we need. Let’s complete the exercise and look at the last Choice.

86. MED MATH / JAM / 2003 TEST TAKING SKILLS The nurse has a medication calculation to make: Drug Order: gr 1/4 po of phenobarbital t.i.d. The Supply is: phenobarbital 15mg scored tablets. The most appropriate nursing action is to: D. Administer 1 1/2 tablets You recall that 1 grain = 60mg. So now we set up the ratio: gr 1 : 60mg :: gr 1/4 : x (This is where the action is!) 1 x = (60 x 1/4) 1 x = (60 / 4) 1 x = 15mg If we need 15mg and the tablet is 15mg, 1 1/2 tablets will give us too much. Choice “C” is the most appropriate nursing action.

87. MED MATH / JAM / 2003 TEST TAKING SKILLS The nurse has a medication calculation to make: Drug Order: gr 1/4 po of phenobarbital t.i.d. The Supply is: phenobarbital 15mg scored tablets. The most appropriate nursing action is to: C. Administer 1 tablet If you got this sample question correct - congratulations ! If not, take a look at the way this question was constructed and why you chose the answer you did. If you would like additional information on this topic go to page 111 of your Calculate With Confidence textbook. If you got this sample question correct - congratulations ! If not, take a look at the way this question was constructed and why you chose the answer you did. If you would like additional information on this topic go to page 111 of your Calculate With Confidence textbook.

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89. MED MATH / JAM / 2003 CONCLUSION It is simply impossible to overestimate the REAL importance of giving drugs in a safe and appropriate manner as ordered by the doctor. Your knowledge of medication math will help you to fulfill this vital nursing responsibility.

90. MED MATH / JAM / 2003 PRACTICE YOUR SKILLS Do the practice exercise to see how well you have mastered the skills. By next class be sure to have completed all the fill in exercises in the 1st 13 chapters. Complete chapters 14 - 26 before end of RNSG 1205