MEDICATION MATH Jose A Martinez MSN RN Nursing

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

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

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

OBJECTIVES d e t s i l s. e v m i t • Ability to solve for unknowns using e c h t e j b w o the systems of measurements o r n e k h t o s listed in the syllabus and your text u e b r a a l l bookere y s r Th you in MED MATH / JAM / 2003

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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. MED MATH / JAM / 2003

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

Roman Numerals 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! MED MATH / JAM / 2003

Roman Numerals 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] )) MED MATH / JAM / 2003

Roman Numerals • 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” MED MATH / JAM / 2003

A Roman en nd Numerals t ire , re us em mem ing pi • The only fraction we will b er: with is “ 1/2”. the re wwork “ 0 ith the ” i th Ro sc ez m • The fraction red ero “ 1/2” an is written ite ! I s b as “ss” d t nv uil o t ent t a he ing n • The number “i A ss” an be ra would read as “ 1 1/2” bs d MED MATH / JAM / 2003

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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). MED MATH / JAM / 2003

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

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

General Review: Fractions To do any operation with fractions you must work with the COMMON DENOMINATOR MED MATH / JAM / 2003 ARITHMATIC: 1/4 + 1/3 = ( multiply denominators [4 x 3=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: Decimals Most medications are ordered in metric measures that use decimals not fractions. MED MATH / JAM / 2003 . Capoten 6 25 mg . Digoxin 0 125 mg Sometimes the decimal is ignored! This can be a fatal mistake!

General Review: Decimals Do not underestimate the power of the decimal. Many medications need only a small amount to be effective. MED MATH / JAM / 2003 Capoten 6. 25 mg Digoxin 0. 125 mg “Capoten 6 and 25 hundredths mg” “Digoxin zero point one hundred and twentyfive thousandths mg”

General Review: Decimals 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! MED MATH / JAM / 2003 Capoten 6. 25 mg Digoxin 0. 125 mg “Capoten 6 point 25 mg” “Digoxin zero point one-two-five mg”

General Review: Decimals 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. MED MATH / JAM / 2003 0. 11 x 0. 33= 0. 11 T ! O x 0. 33 N YET E D R ’ 33 U HE O IS Y 33 N FI 363 The answer requires a 4 decimal number

General Review: Decimals 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) MED MATH / JAM / 2003 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 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 MED MATH / JAM / 2003

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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 MED MATH / JAM / 2003 In the example given on the left 3 is the numerator 4 is the denominator The expression could be written as 3/4

General Review: Proportion A proportion is an equation of two ratios. The terms of the 1 st ratio have a relationship to the terms of the 2 nd ratio, e. g, : 3: 4 : : 6: 8 MED MATH / JAM / 2003 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.

General Review: Proportion In the example 3: 4 : : 6: 8 4 and 6 are the means 3 and 8 are the extremes MED MATH / JAM / 2003 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 If the example is written as a fraction 3/4 = 6/8 4 and 6 are the means 3 and 8 are the extremes MED MATH / JAM / 2003 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.

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

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 : 0. 125 mg or 0. 125 mg This means that 1 tablet contains 0. 125 mg of the drug MED MATH / JAM / 2003

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

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

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

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

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

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

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

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

The Metric System 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 MED MATH / JAM / 2003

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

The Metric System 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 MED MATH / JAM / 2003

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

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

The Metric System To convert a smaller unit to a larger one, divide by moving the decimal point 3 places the left (smaller) (larger) 100 m. L = __ L 100 m. L = 0. 1 L MED MATH / JAM / 2003 To convert a larger unit to a smaller one, multiply by moving the decimal 3 places to the right (larger) (smaller) 0. 75 g = ___ mg 0. 75 g = 750 mg

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

The Apothecaries’ System 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 m. L 1 fluid ounce = 30 m. L 1 fluid ounce = 8 fluid drams 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 ny a m w o h used d see ! n d a n i f n e n h a c c t i u k o n y w s o n r o u o o p y s a n i e t k Loo nt sized e r e f f i d MED MATH / JAM / 2003

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

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

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

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

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

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

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

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

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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! MED MATH / JAM / 2003

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

CONVERTING - Within and Between Systems 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) MED MATH / JAM / 2003

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

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

CONVERTING - Within and Between Systems 8 mg = _____ g 1000 mg : 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 MED MATH / JAM / 2003

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

CONVERTING - Within and Between Systems Example: The doctor orders, “gr 1/100” of a certain drug. The drug comes as 0. 3 mg per tablet. The nurse will administer ___ tablet(s). This is a typical type of drug conversion problem that nurses respond to every day. MED MATH / JAM / 2003

CONVERTING - Within and Between Systems gr 1/100 = _____ mg STEP #1 (This is a conversion between systems) [Apothecaries’] [Metric] Equivalent: gr 1 = 60 mg gr 1 : 60 mg : : gr 1/100 : x mg 60 x 1/100 = x 60/100 - x x = 0. 6 mg - This is how much we need MED MATH / JAM / 2003

CONVERTING - Within and Between Systems x = 0. 6 mg - this is how much we need Now we need to know how many tablets of 0. 3 mg strength the nurse will give: 0. 3 : 1(tablet) : : 0. 6 : x 0. 3 x = 0. 6 or 0. 6 / 0. 3 = 2 tablets MED MATH / JAM / 2003 STEP #2

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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 MED MATH / JAM / 2003

Converting Between Temperature Systems There is an easy way to remember which system to use: °F °C WATER BOILS 212 100 WATER FREEZES 32 0 THE FAHRENHEIT SCALE HAS MORE NUMBERS - IT COVERS MORE AREA MED MATH / JAM / 2003

Converting Between Temperature Systems SO - IF YOU HAVE A TEMPERATURE IN FAHRENHEIT AND WANT TO CONVERT TO CENTIGRADE - YOU AUTOMATICALLY KNOW YOUR ANSWER WILL BE A SMALLER EM A S E H T NUMBER S I HAS MP IT TE G E N H I T R U R S E A B E M FM O REME Y A W D! R E U G O N T CHA JUS MED MATH / JAM / 2003

Converting Between Temperature Systems LET’S WORK WITH 2 EXAMPLES OF TEMPERATURE CONVERSION °F °C 100. 4 °F = ? °C ? °F = 37. 3 °C REME MBER - THE MAKE MED MATH / JAM / 2003 ANSW SENS E ER M UST

Converting Between Temperature Systems 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 MED MATH / JAM / 2003

Converting Between Temperature Systems 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 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 12 noon on standard time simply add 12 to the time. • 1: 00 pm + 12 = 1300 hrs • 5: 00 pm + 12 = 1700 hrs ETC. MED MATH / JAM / 2003

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

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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 15 mg 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 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 15 mg 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. 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 15 mg scored tablets. The most appropriate nursing action is to: B. Administer 1/2 tablet You recall that 1 grain = 60 mg. So now we set up the ratio: gr 1 : 60 mg : : gr 1/4 : x 1 x = (60 x 1/4) (Set it us then cross multiply. ) 1 x = (60 / 4) 1 x = 15 mg If we need 15 mg and the tablet is 15 mg, 1/2 of this amount would not give the correct dosage. Go to the next Choice. 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 15 mg scored tablets. The most appropriate nursing action is to: C. Administer 1 tablet You recall that 1 grain = 60 mg. So now we set up the ratio: gr 1 : 60 mg : : gr 1/4 : x 1 x = (60 x 1/4) (This is where the action is!) 1 x = (60 / 4) 1 x = 15 mg If we need 15 mg and the tablet is 15 mg, 1 tablet will give us the amount we need. Let’s complete the exercise and look at the last Choice. 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 15 mg scored tablets. The most appropriate nursing action is to: D. Administer 1 1/2 tablets You recall that 1 grain = 60 mg. So now we set up the ratio: gr 1 : 60 mg : : gr 1/4 : x 1 x = (60 x 1/4) (This is where the action is!) 1 x = (60 / 4) 1 x = 15 mg If we need 15 mg and the tablet is 15 mg, 1 1/2 tablets will give us too much. Choice “C” is the most appropriate nursing action. 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 15 mg 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. MED MATH / JAM / 2003

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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. 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 1 st 13 chapters. Complete chapters 14 - 26 before end of RNSG 1205 MED MATH / JAM / 2003