Math for Nurses.pdf - Math for Nurses Winston-Salem State...

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Unformatted text preview: Math for Nurses Winston-Salem State University Variety of calculation types Varying levels of difficulty Must (re)test every semester Junior year: Original, Retake 1, Retake 2 Senior year: Original, Retake 1 Passing grade is defined as: ≥ 80% Prerequisite for giving medications in a clinical setting-if cannot pass in specificed retakes then cannot attend clinical USE ATI as a resource!!!!! 1 Table of Contents Introductory text . . . . . . . . . . . . . . . . . . . . . . . . 1 Problems solved in class . . . . . . . . . . . . . . . . . 19 Easily solved problems (outside class). . . . . . 66 More solved problems (outside class). . . . . . 68 Answers to More solved problems . . . . . . . . 93 2 Why are you learning to make these calculations? It is physically impossible to stock every medication in every possible dosage. APRNs & physicians don’t know (or care) what is in your medication inventory. Nurse must ACCURATELY do the arithmetic to use what is in the inventory and convert it to what the physician or APRN ordered. 3 1 The nurse’s most important role in medicating a patient The nurse is the patient’s last line of defense against receiving an inappropriate medication. Right patient? Right time? Right medication? Right route? Right form? Right dose? Expiration date? 4 Arguments for/against using dimensional analysis For: Formulas are derived from dimensional analysis. If you forget the formula, you have no rational backup. Guessing is not rational! For: By canceling the excess labels before doing the arithmetic, the problem setup is very likely to be correct. (Avoids the generation of an inappropriate or nonsense answer such as: mL2) Against: Dimensional analysis is more work than using formulas. 5 Med-Math question types & sample units of measure Intake/output Counting (tablets, units of medication) Mass (weight) Volume (mL, Liter) Rate (drops/min, mL/hr, mg/min, units/hr) Time-based (what time will the IV bag empty?) Reconstitution IV rate changes 6 2 Time Abbreviations – Use of the “q” abbreviation is discouraged, but remains prevalent. q4h – every 4 hours q8h – every 8 hours q12h – every 12 hours qd – every day (1 time/day) bid – every 12 hours (two times a day) tid – every 8 hours (three times a day) 7 Other Abbreviations Mass (weight): microgam (mcg) milligram (mg) gram (g) kilogram (Kg) pounds (lbs, #) Volume: milliliter (mL) = (cc) do not use “cc” liter (L) teaspoon (tsp) ounce (oz) tablespoon (tbs) cup (C) 8 Other Abbreviations continued Time: Count: hour (h, hr) minute (min) tablet (tab) drop = gtt [Latin: gutta or guttae] (singular plural) Unit [quantity of certain medications] mEq [milliequivalents for electrolytes] tablet 9 3 Rate definition Rate = flow (These two words mean the same thing) How much medication AND how quickly? Volume & Time (gtt/min, mL/hr) Mass & Time (mg/min) Counting & Time (tablets/dose, Units/hr) mL/hr is the default flow for IV pumps 10 Graphic representation of grams, milligrams and micrograms 11 Introduction to problem solving Answer exactly what you are being asked to find. Not what you think the question means. Not what you think the question should ask. Determine the label for the answer. NOTE: The answer label should be, but may not always be explicitly stated in the problem. Example: IV flow through a pump implies mL/hr. 12 4 Problem solving strategy (1) Based upon the question, determine what the answer’s label will be and place it to the right of the previous lines. Then place an equal sign (=) to the right of the label. (2) The numerator of term immediately to the right of the answer’s numerator label must match the answer’s numerator label. You may require a conversion factor such as (1,000 mcg/1 mg) to force the correct label in the 1st numerator. 13 Problem solving strategy (3) If the question asks you to find (for example) mL/hr, set up the following generic statement. The intention is to cascade as many labels as you need so that the labels that do not appear in the answer are arithmetically canceled. (x to x, y to y and z to z; leaving mL per hr, as required in the answer) mL = hr mL * x * y * z x y z hr 14 Problem solving strategy Include medication order, medication source and other factors to cancel labels that are not used in the answer. (examples that may be relevant: patient weight, drip set ratio, time factors and conversions) Notice that all parts of the formula contain PAIRS of data. Examples: gtt/mL, mg/hr, mg/mL, g/L, “something”/dose, mg/Kg/day By definition: a microdrip set = 60 ggt/mL By definition: a macrodrip set = 10, 15 or 20 gtt/mL 15 5 Rounding Rules *Always follow special directions in the question. Verify the rounding rules with your instructor. Typical rules follow: WSSU Division of Nursing rules for rounding on drug calculations are to be included on all testing materials presented to the students for evaluation and testing and in the course syllabus. Rules for rounding were developed based on best practice evidence in current drug calculation texts and recommendations from the National Council of State Boards of Nursing. In the event of any type of calculation that is not covered by this policy then faculty are directed to include clear directions for rounding on the quiz, midterm, or final exam affected by this event. Round drops to nearest WHOLE number If you have 24.42 gtts/min, the answer will be 24 gtts/min If you have 24.51 gtts/min, the answer will be 25 gtts/min Round weights (kg), infusion rates, and dosages (ml, mg, mcg, etc.) to the nearest TENTHS place If you have 3.4445 ml, the answer will be 3.4 ml If you have 3.4664 ml, the answer will be 3.5 ml If you have 4.544 kg, the answer will be 4.5 kg If you have 4.557 kg, the answer will be 4.6 kg If you have 10.434 mg, the answer will be 10.4 mg If you have 10.475 mg. the answer will be 10.5 mg If you have 24.42 ml/hr, the answer will be 24.4 ml/hr If you have 24.56 ml/hr, the answer will be 24.6 ml/hr 16 Problem with an explicit answer Order: 400 mg of med. Supply: 125 mg per 5 mL. How many mL will you give? 5 mL ? mL = -----125 mg * 400 mg --------1 an number over “1” makes the numerator obvious & does not = 16 mL change the numerator’s value. 17 Problem with an implied answer Order: 400 mg of med. Supply: 125 mg per 5 mL. 5 mL * 400 mg ? mL = ---------------125 mg 1 = 16 mL All further examples are typed on these slides as follows: mL = (5 mL/125 mg) * (400 mg/1) = 16 mL 18 6 Class Problem mg/min Determine the mg/min required to administer when the flow and solution concentration are given. The medication is infusing at 32 mL/hr. The IV volume is 250 mL. The amount of dissolved medication is 700 mg. If necessary, round answer to 1 decimal place. See next slide for important considerations. 19 Class Problem mg/min Identify the pairs of data: 250 mL & 700 mg 1 hour and 32 mL Orient the pairs as required to satisfy the answer’s label and cancel all other labels. Which conversion “tool” will you use to change the hours to minutes? 20 Answer - mg/min Determine the mg/min required to administer when the flow and solution concentration are given. The medication is infusing at 32 mL/hr. The IV volume is 250 mL. The amount of dissolved medication is 700 mg. mg/min=(700mg/250mL) * (32mL/hr) * (1 hr/60min) = 1.49 Round up to 1.5 mg/min ___1____ . _4__ --9-- mg/min rounds to: ___1____ . _5__ - mg/min 21 7 Class Problem – mcg/min Determine how many mcg/min are infusing if the IV contains 240 mg of medication per 500 mL and is infusing at 16 mL/hr. If necessary, round answer to 1 decimal place. This problem does not have mcg in any of the data; therefore, put a conversion “tool’ for mcg and mg immediately to the right of the equal sign (=). Then cascade and orient the rest of the data so that labels not appearing in the answer’s label are canceled. 22 Answer – mcg/min Determine how many mcg/min are infusing if the IV contains 240 mg of medication per 500 mL and is infusing at 16 mL/hr mcg/min = (1000mcg/mg) *(240mg/500mL) * (16mL/hr) * (hr/60min) = 218 mcg/min 23 Class Problem – mL/hr The provider has ordered 2 mcg/min. The nurse has 5 mg per 250 mL. The flow rate is _________________ mL/hr. If necessary, round answer to 1 decimal place. 24 8 Answer – mL/hr The provider has ordered 2 mcg/min. The nurse has 5 mg per 250 mL. The flow rate is _________________ mL/hr mL/hr = (250mL/5mg) * (1 mg/1000mcg) * (2 mcg/min)* (60min/1 hr) = 6 mL/hr 25 Class Problem – mL/hr The provider ordered a medication at the rate of 46 mcg/Kg/min. The client weighs 72.7 Kg. The medication is supplied as 300 mg in 75 mL of solution. The client should receive ______________mL/hr. If necessary, round answer to 1 decimal place. When using a 3-part component (e.g., mcg/Kg/min), always use the 1st component in the numerator (mg) and everything else in the denominator. For example: mg Kg/min 26 Answer – mL/hr The provider ordered a medication at the rate of 46 mcg/Kg/min. The client weighs 72.7 Kg. The medication is supplied as 300 mg in 75 mL of solution. The client should receive ______________mL/hr mL/hr = (75mL/300mg) * (1 mg/1000mcg) * (46mcg/Kg/1 min) * (72.7 Kg/1) * (60min/1 hr) = 50.163 rounds up to 50.2 mL/hr 27 9 Class Problem - tablets A medication comes out of the bottle as 2.5mg/tablet. Give 2.5mg tid. If necessary, round answer to 1 decimal place. (1) How many tablets/dose? (2) How many tablets daily? 28 Answer - tablets A medication comes out of the bottle as 2.5mg/tablets. Give 2.5mg tid. (1) How many tablets/dose? (Each 1 dose = 2.5 mg.) tabs/dose = (1 tab/2.5mg) * (2.5mg/1 dose) = 1 tablet/dose (2) How many tablets daily? (tid = 3 doses/day) tabs/day = (1 tab/2.5mg) * (2.5mg/dose) * (3doses/day) = 3 tablet/day 29 Class Problem – mg/day The provider ordered 2 mg/Kg/day IV for a 16 pound infant. The infant should receive _____________mg per day. If necessary, round answer to 2 decimal places. 30 10 Answer – mg/day The provider ordered 2 mg/Kg/day IV for a 16 pound infant. The infant should receive _____________mg per day. mg/day = (2mg/Kg/day) * (1 Kg/2.2 lbs) * (16 lbs/1) =14.545 round up to 14.55 mg/day 31 Class Problem – determine the label and solve the problem A medication is ordered for your patient at 80 mg/Kg/24 hours every 8 hours. The child weighs 18 lbs. How many mg of medication will you administer at each dose? If necessary, round answer to 1 decimal place. 32 Answer – determine the label and solve the problem A medication is ordered for your patient at 80 mg/Kg/24 hours every 8 hours. The child weighs 18 lbs. How many mg of medication will you administer at each dose? mg/dose= (80mg/Kg/24hrs) * (8hrs/dose) * (1 Kg/2.2 lbs) * (18 lbs/1) = 218.182 rounds down to 218.2 mg/dose 33 11 Class Problem – gtt/min Calculate the drip rate of 1,000 mL of medication to infuse over 10 hours using an infusion set that delivers 15gtt/mL. How many drops/min? If necessary, round answer to 1 decimal place. 34 Answer – gtt/min Calculate the drip rate of 1,000 mL of medication to infuse over 10 hours using an infusion set that delivers 15gtt/mL. gtt/min= (15gtt/mL) * (1,000 mL/10 hrs) * (1 hr/60 min) = 25gtt/min 35 1 Liter bag of medication 4 AM 5 AM 6 AM 7 AM Expectation What is observed 1,000 mL 1,000 mL 900 mL ? mL 800 mL ? mL 700 mL ? mL 600 mL ? mL 500 mL ? mL 400 mL 600 mL 8 AM 9 AM 10 AM 0 mL Drip chamber 7 tubing To the patient 36 12 Class Problem – Is the IV setup working as expected? The IV above was started at 4 AM. At 10 AM 600 mL remain in the bottle. Is the IV running on time? (Refer to previous slide for mL/hr) 37 Answer – Is the IV setup working as expected? The IV above was started at 4 AM. At 10 AM 600 mL remain in the bottle. Is the IV running on time? (4 AM to 10 AM) = 6 hrs running time. (1,000 mL/10 hrs) = 100 mL/hr. (100 mL/hr * 6 hrs/1) = 600 mL should be used in 6 hours. (1,000 mL – 600 mL) = 400 mL should still be in the bottle. Therefore: bottle is emptying too slowly – NO: not on time. Patient may have laid on the tubing and caused it to crimp. There are other possible reasons for the delayed emptying. 38 Conversion factors to memorize 1 oz = 30 mL 8 oz = 1 cup = 240 mL ====================== 16 oz = 1 pint = 32 oz = 1 quart = 128 oz = 1 gallon = 500 mL 1,000 mL = 1 liter 4,000 mL 39 13 Class Problem – Intake & Output 12 hour I/O for patient Smith on 4/7/2008: 4 oz cranberry juice 175 mL urine 1/2 cup oatmeal 2 slices of toast 120 mL yellow vomit 8 oz black coffee 1/2 cup flavored gelatin 100 mL diarrhea a tuna fish sandwich 3 oz cream of mushroom soup 6 oz 1% milk 230 mL urine 16 oz water 1 pint ice cream 2 tsp liquid medication 1 tbs liquid medication IV @ 150mL for 3 hrs 1 cup applesauce What is the intake? ______________ What is the output? ______________ Net gain or net loss of fluid? _______ 40 Answer - Intake 4 oz cranberry juice 4 oz * 30 mL/oz = 120 mL 8 oz black coffee 8 oz * 30 mL/oz = 240 mL 1/2 cup flavored gelatin 4 oz * 30 mL/oz = 120 mL 3 oz cream of mushroom soup 3 oz * 30 mL/oz = 90 mL 6 oz 1% milk 6 oz * 30 mL/oz = 180 mL 16 oz water 1 pint = 500 mL 1 pint ice cream 1 pint = 500 mL 2 tsp liquid medication 2 tsp * 5 mL/tsp = 10 mL 1 tbs liquid medication 1 tbs * 15 mL/tbs = 15 mL IV @ 150 mL for 3 hrs 150 mL/hr * 3 hr = 450 mL 1 cup applesauce 1 cup * 16 oz/cup = 240 mL Answer: - ---------------------------------------- 2,465 mL 41 Answer - Output & Net gain or loss 175 mL urine 120 mL yellow vomit 230 mL urine 100 mL diarrhea 625 mL Output Input = 2,465 mL Output = 625 mL Net gain = 1,840 mL More fluid was retained than was excreted; therefore, patient has a net gain. 42 14 Class Problem mL/hr with distracters This problem contains distracters. Determine what the answer label is. Then look to see which components of the question will satisfy the requirements for the answer’s label. Ignore everything else. If necessary, round answer to 1 decimal place. An IV of 1,000 mL medication contains 60 mEq of an electrolyte and is set to infuse at 27 drops per minute. The tubing delivers 10gtts/cc. How many mL/hr are you administering? 43 Answer - mL/hr with distracters An IV of 1,000mL medication contains 60 mEq of an electrolyte and is set to infuse at 27 drops per minute. The tubing delivers 10gtts/cc. How many mL/hr are you administering? Be in the habit of rewriting drops to gtt and cc to mL. Remember to find pairs of data that may work for you. 27 gtt/min 10 gtt/mL mL/hr 1,000 mL/mEq Correct answer: mL/hr = (1 ml/10 gtt) * (27 gtt/1 min) * (60 min/1 hr) = 162mL/hr Why is this wrong? mL/hr = (1,000 ml/60 mEq) * (27 gtt/1 min) * (60 min/1 hr) 44 Class Problem – Time-based Unless otherwise specified, and if necessary, round answer to 1 decimal place. 900 mL of medication is ordered to infuse at 80 mL per hour. (1) Assuming that there are no interruptions, how long will it take to empty the bag? (2) If the IV line is started at 2:47 PM, what time will the bag run dry? 45 15 Answer - Calculate the hours 1) Assuming that there are no interruptions, how long will it take to empty the bag? Hours = (1 hr/80 mL) * ( 900 mL/1) = 11.25 hours This answer is expressed in hours and it means 11 and ¼ hours. It is NOT 11 hours and 25 minutes! 46 Answer - Calculate the minutes minutes = (60 min/1 hr) * (0.25 hr/1) = 15 minutes 47 Answer – total run time expressed in hours & minutes (1) Assuming that there are no interruptions, how long will it take to empty the bag? The bag will empty in 11 hours and 15 min. 48 16 Answer - Time bag will theoretically empty (2) If the IV line is started at 2:47 PM, what time will the bag run dry? (from previous page) 2 PM + 11 hours -------> 1 AM 47 minutes + 15 minutes = 62 minutes 1 AM + 62 minutes ------> 2:02 AM 49 Class Problem – Reconstitution Reconstitution problems ask the nurse to dissolve a drug (typically a powder) whose quantity is usually expressed in grams or milligrams in: a specific quantity of a liquid (usually measured in milliliters). Frequently, the liquid is normal saline (0.9% NS) or D5W. Conceptually, this is identical to dissolving 1 teaspoon of table salt in 1 cup of hot water. 50 Class Problem – Reconstitution Order: 350 mg of the drug to be given q8h IV. How many mL will you give per dose? Supply: The drug is available in 500 mg containers. The label tells the nurse to dissolve the powder in 25 mL of normal saline (NS). 51 17 Class Problem – Reconstitution Which pairs of data do you find in the problem? 350 mg every 8 hours. (every 8 hours means: 1 dose.) 500 mg of the powder is dissolved in 25 mL of NS. What is the answer’s label for your calculation? How many mL/dose? Can you isolate all of the components that are required to solve this problem? (YES, of course you can do this!) 52 Answer – Reconstitution mL/dose = (25 mL/500 mg) * (350 mg/dose) = 17.5 mL/dose 53 Class Problem – Reconstitution Order: 250 mg of the drug to be given q8h IV. How many mL will you give per dose? Supply: The drug is available in 1g containers. The label tells the nurse to dissolve the powder in 50 mL of normal saline (NS). The disconnect is between the grams and the milligrams, so use the appropriate conversion “tool.” 54 18 Answer – Reconstitution mL/dose = (50 mL/1 g) * (1 g/1000 mg) * (250 mg/dose) = 12.5 mL/dose 55 Class Problem – Reconstitution Order: 20 mg/Kg of the drug to be given q8h IV. Patient weighs 50 pounds. How many mL will you give per dose? Supply: The drug is available in 500 mg containers. The label tells the nurse to dissolve the powder in 5 mL of normal saline (NS). With which data pair is the “dose” a factor? Why? 56 Answer – Reconstitution mL/dose = (5 mL/500 mg) * (20 mg/1 Kg/1 dose) * (1 Kg/2.2 lbs) * (50 lbs/1) = 4.545 rounds up to 4.55 mL/dose Dose is only related mg/Kg. Any other pair does not make any sense. 57 19 Class Problem – Reconstitution Order: 700,000 Units given IM. How many mL will you give? Supply: The drug is available in 5,000,000 Unit containers. The label tells the nurse to reconstitute (dissolve) the powder in 3.2 mL of normal saline (NS) to yield 1,000,000 Units/mL. This problem contains a distracting pair. To determine what the distracting pair is, you must understand the sequence of the problem’s operation. See picture on next slide. 58 Reconstitution Graphic 5 million Units in 3.2 mL 1 million Units/1 mL The patient Which medication source DIRECTLY affects the patient? 59 Answer – Reconstitution The distracters are the 5 million Units and 3.2 mL. Your reconstituted supply is now 1 million Units/mL. The 5 million units dissolved in the 3.2mL is how you arrived at the 1 million Units/mL. Now they are irrelevant = distractors. mL = (1 mL/1,00,000 Units) * (7.000,000 Units/1) = 0.7 mL 60 20 Class Problem – Reconstitution Order: 500 mg IV every 4 hours. Supply: The drug is available in 1 gram containers. The label tells the nurse to reconstitute (dissolve) the powder in 10 mL of 0.9% NS. THEN further dilute this mixture in 50 mL of NS. Infuse it over 30 minutes. The drip set is 10gtt/mL. 61 Class Problem – Reconstitution Refer to the previous graphic and make a similar picture for this problem. Step-A: How many mL will you use of the 10 mL in which you dissolve the 500 mg of powder? Step-B: How many mL/hr will you give the patient? Step-C: How many drops/min? 62 Answer – Reconstitution This is a multi-step (3) problem. (A) Determine how many mL after mixing the powder (Step-1). mL = (10 mL/1 gram) * (1 gram/1,000 mg) * 500 mg/1) = 5 mL 63 21 Answer – Reconstitution (B) Determine how many mL/hr after diluting the mixture (Step-2). mL/hr = (55 mL/30 min) * (60 min/1 hr) = 110 mL/hr Your picture should tell you why we use 55 mL, not 50 mL. 64 Answer – Reconstitution (C) Determine how many gtt/min: gtt/min = (10 gtt/1 mL) * (110 mL/1 hr) * (1 hr/60 min) = 18.3 rounds down to 18 gtt/min 65 Easily solved problems with answers – [in brackets] Supply: 5 mg/mL. Supply: 10 mg tablets. Order: 50 mg. Order: 30 mg. Supply: 250 mg/5 mL. Order: 1.5 g. Supply: 50 mg tablets. Sup...
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  • Spring '17
  • Dr. Donna
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