Mastering Dosing Calculations
- 2. TO BECOME A NURSE: YOU HAVE TO LEARN DRUG DOSAGE CALCULATIONS
- 3. ARE THEY EASY? Yes and No Everybody wants to teach you how. Everybody teaches you a different way. Everybody says their way is the best way. But no one will say you don’t need to understand basic math.
- 4. A QUESTION TO ASK YOURSELF Do I want to plug into a formula? Or do I want to really understand?
- 5. SOME QUOTES FOR THOUGHT • “Students who developed logical reasoning skills reported improved confidence in drug dosage calculations.” • “Feedback and discussion reveal that confidence in arithmetic skills can be low even when students are able to pass the end of semester drug dosage calculation exam.” • “It is regarded as acceptable that a formula card or mnemonic can be used to find the correct dose even though this removes any requirement for performing the underlying computation.” • “Emphasize students’ innate powers of logical Europepmc.org/article/med/27138475
- 6. DON’T TAKE THE EASY WAY THINK
- 7. ONE GOOD WAY TO KNOW YOU ARE REALLY THINKING: SEE THAT ALL THE WAYS OF DOING = SAME RESULT. AND THE WAYS ARE: The formula (“desired over have”) Proportions Unit cancellation (also called “dimensional analysis”) Reasoning by logical step AND THE PROS AND CONS ARE: The formula (“desired over have”): can be very confusing – formulas stated and explained in many different ways. Proportions: no issues, somewhat an indirect approach but very logical. Unit cancellation: virtually always works – no brainer once you understand it. Reasoning by logical step: it perhaps can take more time in the short run.
- 8. TAKE A BASIC PROBLEM Order: 4 mg Ativan by injection Available: 2mg/ml solution Problem: how many ml to draw up And let’s start with the famous “desired over have” method: Ordered = “Desired” = D in the formula Available = “Have” = H in the formula “Quantity” = Q in the formula “Amount” = A in the formula 𝐴𝑚𝑜𝑢𝑛𝑡 = 𝐷𝑒𝑠𝑖𝑟𝑒𝑑 𝐻𝑎𝑣𝑒 × 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 = 𝐷 𝐻 × 𝑄 = 4 𝑚𝑔 2 𝑚𝑔 𝑥 1 𝑚𝑙 = 2 𝑚𝑙 (1 is understood)
- 9. DRAWBACKS TO “DESIRED OVER HAVE” You will see different versions of the formula, e.g. some will replace Q with V for “volume” – fine for this particular problem (ml is a volume), but what about when its tablets or capsules? You have to correctly identify the D, H, and Q in each problem to get them plugged in right. You have to memorize the formula. The units of the desired and have must match – if they don’t it throws a monkey wrench into the method: you have to convert the units of either the numerator or denominator so that they do match, and this must be done outside of the formula itself. Finally, this way works in basic drug dosage calculations, but what about IV problems (ml or drop rate, etc.) – NOPE.
- 10. LET’S TRY PROPORTIONS 1 5 = Order: 4 mg Ativan by injection Available: 2mg/ml solution Problem: how many ml to draw up 2 𝑚𝑔 1 𝑚𝑙 = 4 𝑚𝑔 𝑥 𝑚𝑙 Cross multiplying and solving for the amount x: 2𝑥 = 4 2 2 𝑥 = 2 So the answer is draw up 2 ml. NOTE: A shortcut that always works is to multiply the numbers that are diagonal to each other and then divide that result by the 3rd number, as: 4 X 1 = 4 and 4 ÷ 2 = 2
- 11. PROS AND CONS OF PROPORTION • You do have to think of what is happening to set it up (think: there are 2 mg in each ml of solution, but I want 4 mg to go into the patient). • Remember same units on top and bottom of each ratio. • Remember how to solve for x. • Can also be used in more complex problems, but then more than one proportion may be required. (With unit cancellation the extra proportion(s) are worked right into the setup). • For example, if unit conversion is necessary, just use another proportion. For example: I need to covert 4000 mg to g: 4000 𝑚𝑔 𝑥 𝑔 = 1000 𝑚𝑔 1 𝑔 4000 X 1 = 4000 and 4000 ÷ 1000 = 4 so 4g
- 12. HOW ABOUT UNIT CANCELLATION? Order: 4 mg Ativan by injection Available: 2mg/ml solution Problem: how many ml to draw up 4 𝑚𝑔 × 1𝑚𝑙 2 𝑚𝑔 = 2 𝑚𝑙 4 𝑚𝑔 1 × 1 𝑚𝑙 2 𝑚𝑔 = 4 × 1 1 × 2 𝑚𝑙 = 2 𝑚𝑙 Or with everything explicit: Calculator operation: 4 ÷ 1 X 1 ÷ 2 or ignoring the 1’s: 4 ÷ 2 Alternative calculator operations: 4 X 1 ÷ 1 ÷ 2 or ignoring the 1’s: 4 ÷ 2 4 x 1/(1 X 2) or ignoring the 1’s: 4 ÷ 2 When the units cancel you don’t want and the unit you do want is left standing, you can be sure the problem is set up correctly. Multiply key before any number on the top (if a whole number it is the top) and divide key before any number on the bottom = the number part of the answer.
- 13. PROS AND CONS UNIT CANCELLATION • It works for any problem. • It is a no brainer – cancel the units, it is set up correctly. • The order doesn’t matter; I like to start with the simple unit (mg) and then the complex (mg/ml) You have to use the calculator correctly – just remember: on top, multiply, on bottom, divide and OK TO HIT DIVIDED BY KEY MORE THAN ONCE IN A ROW. Looks funny when you flip the complex unit (from g/ml to ml/g – JUST MAKE THE UNITS CANCEL).
- 14. ONE MORE WAY: REASONING BY LOGICAL STEP Also known as: look Ma, no format! Order: 4 mg Ativan by injection Available: 2mg/ml solution Problem: how many ml to draw up I think: OK, I have a solution here with 2 mg of drug in every 1 ml. I need to put 4 mg into the patient. So if every ml has 2 mg, the number of times 2 goes into the 4 that is wanted would be the number of ml needed. OR, more simply given the simple numbers involved in this particular problem: I need 4 g to go into the patient; each 1 ml has 2 g in it; I need twice as much, so 2 ml.
- 15. PROS AND CONS OF LOGICAL REASONING? • You really understand the problem. • But you do need to have the correct understanding, and sometimes our understanding can be wrong – but with practice you can be quite confident. • As for every method we have described: YOU HAVE TO UNDERSTAND BASIC MATH When using logical reasoning the trick is to decide when to multiply, divide, even add or subtract. When you know basic math, the correct decision is intuitive and easy.
- 16. LET’S LOOK AT SOME KINDS OF PROBLEMS We will use unit cancellation to solve them. Basic drug dosage problems • Available: mass/volume • Available: mass/tablet Dosage by weight IV rate calculations • Desired volume/time given– wanted in mL/hr • Desired volume/time and drop factor given – wanted in gtts/min • Desired mass/time and available mass/volume given – wanted in mL/hr Combination IV problems: e.g. given = desired mass drug/kg patient weight/hour, patient weight, and available mass/volume – wanted in mL/hr Other IV problems: calculate total infusion volume or time, adjust manual flow rate Amounts of non-injectable fluids
- 17. BASIC DRUG DOSAGE: AVAILABLE MASS/VOLUME We did this in our example of 4 mg of Ativan by injection and available was 2 mg/mL, and we wanted to know how many mL to inject. Here is another example (with an added twist of unit conversion needed): Order: 0.1 g of drug by injection Available: 30 mg/5 mL solution Problem: how many mL to draw up 0.1 𝑔 × 1000 𝑚𝑔 1 𝑔 × 5 𝑚𝐿 30 𝑚𝑔 = 16.666 … = 16.7 𝑚𝐿 Note: This problem had a number, 5 (not just an understood 1) in the volume. I like to start with the simple unit given (g). This helps me to “follow my nose” through the calculation. The complex unit (mg/mL) is flipped so that the units cancel. Order doesn’t matter, but if you start with the given 30 mg/5mL fact you need to be sure to write the relation with mL on top (because that is the unit of your wanted answer – your answer must have mL “on top” and nothing on the bottom).
- 18. BASIC DRUG DOSAGE: AVAILABLE IS MASS/TABLET Or capsule or whatever. Order: 25 mg of drug PO Available: 50 mg/tablet Problem: how many tablets to administer 25 𝑚𝑔 × 1 𝑡𝑎𝑏𝑙𝑒𝑡 50 𝑚𝑔 = 0.5 𝑡𝑎𝑏𝑙𝑒𝑡 Note: Looks like we are going to have to split that tablet! Again, note how I start with the simple unit given (mg). It helps to “follow my nose,” because I know that unit will have to cancel (I want tablets). If I start with the complex unit I have to think that tablets (the wanted unit) will have to be on the top, but when I start with mg it simply forces me to write the complex unit the right way so that the mg unit cancels.
- 19. DOSAGE BY WEIGHT Order: 1.5 mg of drug per kg of patient weigh Given information: patient weighs 74.8 lb Available: 125 mg/ 2 mL solution Problem: how many mL to draw up This brings in a famous conversion fact: 1 kg = 2.2 lb 74.8 𝑙𝑏 × 1 𝑘𝑔 2.2 𝑙𝑏 × 1.5 𝑚𝑔 1 𝑘𝑔 × 2 𝑚𝐿 125 𝑚𝑔 = .816 = .82 𝑚𝐿 Note: Starting with the simple unit (lb, the patient’s weight) helps us to “follow our nose” canceling units – whatever unit is on the top (and which is not the unit of our answer) must go on the bottom of the next fraction, so that it cancels. As with all unit cancellation, you are done when all the units you don’t want cancel, and the unit you want in your answer remains uncanceled. That is the unit of your answer, and you calculate the number. REMEMBER: numbers on top are multiplied, numbers on the bottom are divided which may mean repeated use of the division key.
- 20. IV RATE: VOLUME/TIME IS GIVEN – CALCULATE ML/HR The flow rate wanted is in mL/hr. This is the usual case with the “electronically regulated infusion pump.” Order: 250 mL of solution to be infused over (per) the next 120 minutes Available: the solution Problem: What is the infusion rate in mL/hr? 250 𝑚𝐿 120 𝑚𝑖𝑛 × 60 𝑚𝑖𝑛 1 ℎ𝑟 = 125 𝑚𝐿 1 ℎ𝑟 Note: you are only given a complex unit (a “per expression”), so you have to start with that. Then you use the conversion fact 1 hr = 60 min. Note in this case we cancel bottom to top (till now it has all been top to bottom). KEEP YOUR EYE ON THE UNIT OF YOUR ANSWER: in this case a complex unit with mL on top and hr on the bottom. A conversion fact is true written either way, but we write it so that min cancel. That way not only does mL remain uncanceled on the top, but hr remains uncanceled on the bottom, which is where you want it! = 125 mL/hr
- 21. IV RATE: VOLUME/TIME IS GIVEN WITH A DROP FACTOR – CALCULATE GTT/MIN The flow rate wanted is gtt/min (gtt = “drops”). This is the usual case with the “manually regulated IV.” Order: 1000 mL of fluid in 10 hrs Drop factor given: 15 gtt/mL Problem: What is the infusion rate in gtt/min? 1000 𝑚𝐿 10 ℎ𝑟𝑠 × 1 ℎ𝑟 60 𝑚𝑖𝑛 × 15 𝑔𝑡𝑡 1 𝑚𝐿 = 25 𝑔𝑡𝑡 1 𝑚𝑖𝑛 = 25 gtt/min Again, note where you are going: you want gtt on top and min on bottom in the answer. We didn’t have to write the order or the drop factor flipped – we simply made sure both hours and mL cancel out and we are left with gtt on top and min on bottom. We cancel both bottom to top and top to bottom as needed. Note that the beginning complex unit (the order) has mL, a volume, on the top because our answer needs to have gtt, a volume, on the top.
- 22. IV RATE: MASS/TIME IS GIVEN – CALCULATE ML/HR Order: 20 mg of drug per hour Available: 500 mg in 250 mL of solution Problem: What is the infusion rate in mL/hr? 250 𝑚𝐿 500 𝑚𝑔 × 20 𝑚𝑔 1 ℎ𝑟 = 10 𝑚𝐿 1 ℎ𝑟 = 10 mL/hr Note: we want mL on top in the answer, so we write the mass and volume relation with volume on the top – mg (which is not in the answer) cancels bottom to top.
- 23. IV PROBLEM: COMBO WITH PATIENT WEIGHT Order: 6 mcg/kg/hr Patient weight: 100 kg To infuse: 12.5 mg drug in 250 mL of fluid Problem: What is infusion rate in mL/hr? 100 𝑘𝑔 × 6 𝑚𝑐𝑔 𝑘𝑔 × ℎ𝑟 × 1 𝑚𝑔 1000 𝑚𝑐𝑔 × 250 𝑚𝐿 12.5 𝑚𝑔 = 12 𝑚𝐿 ℎ𝑟 = 12 mL/hr Note: 6 𝑚𝑐𝑔 𝑘𝑔 ℎ𝑟 1 = 6 𝑚𝑐𝑔 𝑘𝑔 × 1 ℎ𝑟 = 6 𝑚𝑐𝑔 𝑘𝑔 ×ℎ𝑟 Note: Start with the simple unit (kg) which needs to cancel. The given per/per order of mass of drug/patient weight/time is written with the patient weight unit multiplied by the time unit in the denominator. The mass of drug per volume relation is written with volume on the top, because volume is on the top of the wanted answer.
- 24. MORE VARIATIONS ON IV PROBLEMS – SAME METHOD WORKS FINE Infuse 500 mL at 20 gtt/min, factor = 20 gtt per mL. What is the total time in hrs to infuse? 500 𝑚𝐿 × 20 𝑔𝑡𝑡 𝑚𝐿 × 1 𝑚𝑖𝑛 20 𝑔𝑡𝑡 × 1 ℎ𝑟 60 𝑚𝑖𝑛 = 8.333… hr = 8 1/3 hr Infuse the solution over 8 hr at 21 gtt/min, factor = 10 gtt/mL. What is the total volume needed? 8 ℎ𝑟 × 60 𝑚𝑖𝑛 ℎ𝑟 × 21 𝑔𝑡𝑡 𝑚𝑖𝑛 × 1 𝑚𝐿 10 𝑔𝑡𝑡 = 1008 mL The order was 500 mL over 5 hrs, factor = 10 gtt/mL. After 1 hr of infusion, 300 mL remain in the bag. Calculate the adjusted flow rate. Note, just a new problem with 300 mL over 4 hr. 300 𝑚𝐿 4 ℎ𝑟 × 1 ℎ𝑟 60 𝑚𝑖𝑛 × 10 𝑔𝑡𝑡 𝑚𝐿 = 12.5 gtt/min = 13 gtt/min (rounding to full drop).
- 25. CALCULATE AMOUNTS OF NON-INJECTABLE FLUIDS Ordered: wound care q2h for 3 da using 45 mL of 25% solution (available is full strength solution = “medication”). Problem: find the volume of medication and volume of normal saline to mix to prepare enough. First calculate total volume needed: 3 𝑑𝑎 × 12 𝑑𝑜𝑠𝑒𝑠 𝑑𝑎 × 45 𝑚𝐿 𝑑𝑜𝑠𝑒 = 1620 mL Then calculate the volume of medication in that total volume: 1620 𝑚𝐿 × .25 = 405 𝑚𝐿 𝑜𝑓 𝑚𝑒𝑑𝑖𝑐𝑎𝑡𝑖𝑜𝑛 Finally, subtract volume of medication from the total volume to get the volume of normal saline: 1620 𝑚𝐿 − 405 𝑚𝐿 = 1215 𝑚𝐿 𝑜𝑓 𝑛𝑜𝑟𝑚𝑎𝑙 𝑠𝑎𝑙𝑖𝑛𝑒
- 27. CONVENTIONS PER DEPARTMENT PRACTICE TESTS Answers over 1 mL: round to nearest tenth. Answers under 1 mL: round to nearest hundredth. All flow rates are rounded to the nearest whole number. Decimals less than 1: always put a leading zero (e.g., 0.75 mL). Partial tablets written as decimal (e.g., 1.5 tablets). READ THE QUESTION: sometimes it will also tell you how to round. TIPS: “Available” is the same as “On hand.” Don’t type units of your answer if the units are already there after the blank to fill in. Note that “dose” is the order and is usually in mg. “Volume” can be used to indicate any kind of answer, not just mL, but also tablets or capsules. • Capsules can’t be divided; a fractional answer or an answer more than three indicate a possible error. • Tablets can be divided, at least if “scored,” and an answer would usually range from ½ to 3. NOTE: The mass/volume relations come from reading the label. Write so that units cancel.
- 28. Order: 50 mEq PO daily Available: 25 mEq/5 mL Wanted: how many mL to administer ANSWER: 10 mL 50 𝑚𝐸𝑞 × 5 𝑚𝐿 25 𝑚𝐸𝑞 = 10 𝑚𝐿 NOTE: The “PO daily” is not information used in the calculation. You just need to calculate how many mL to draw for each day’s dose. Start with the simple unit (mEq) which you don’t want in your answer, and write the mEq/volume (which is given) so that the units cancel. You want mL for your answer, so it goes on top.
- 29. Order: 1.5 g PO 4X daily Available: 500 mg scored tablets Wanted: amount to administer ANSWER: 3 tablets 1.5 𝑔 × 1000 𝑚𝑔 1 𝑔 × 1 𝑡𝑎𝑏𝑙𝑒𝑡 500 𝑚𝑔 = 3 𝑡𝑎𝑏𝑙𝑒𝑡𝑠 NOTE: The “PO 4X daily” is not used in the calculation. Always interpret the “amount to administer” as per dose, unless specifically asked for the daily total or some other total. Start with simple unit (g) which needs to be converted to mg (because the tablets are given in mg). That cancels g. Then write the mass per tablet so that the mg also cancels (your answer has the units “tablets”). “Tablets” is left standing and that is the unit of your answer.
- 30. Order: 1.4 mg/kg of patient weight Patient weight 34 lb Available: 3 mg/mL Wanted: volume to draw ANSWER: 7.2121... = 7.2 mL 34 𝑙𝑏 × 1 𝑘𝑔 2.2 𝑙𝑏 × 1.4 𝑚𝑔 1𝑘𝑔 × 1 𝑚𝐿 3 𝑚𝑔 = 7.2121 … = 7.2 𝑚𝐿 NOTE: A perfect “follow your nose” example. Start with the simple unit (lb). That unit must go in the denominator to cancel. Then with each relation you have (knowing lb to kg is 1lb = 2.2 kg) write so that the unit on top cancels top to bottom, until what you want, mL, is left standing.
- 31. Order: 100 mL to be infused every 15 min for 5 hours Wanted: infusion pump rate in mL/hr ANSWER: 400 mL/hr 100 𝑚𝐿 15 𝑚𝑖𝑛 × 60 𝑚𝑖𝑛 1 ℎ𝑟 = 400 𝑚𝐿 1 ℎ𝑟 = 400 𝑚𝐿/ℎ𝑟 NOTE: Some problems start with a “complex unit,” in this case mL/min. We want mL/hr for an answer, so we write the relation with mL on top. We don’t want min, we want hr, so we make min cancel bottom to top. That leaves us with mL on top and hr on the bottom for our mL/hr answer. We didn’t use the total time of 5 hours. But what if the order stated more simply: “infuse 2000 mL over 5 hours.” Then: 2000 mL divided by 5 hr = 400 mL/hr. Sometimes the answer is just reducing the fraction given!
- 32. Order: 1500 mL to infuse over 12 hr Given: drop factor = 20 gtt/mL Wanted: manual IV infusion rate in gtt/min ANSWER: 42 gtt/min 1500 𝑚𝐿 12 ℎ𝑟 × 1 ℎ𝑟 60 𝑚𝑖𝑛 × 20 𝑔𝑡𝑡 1 𝑚𝐿 = 42 𝑔𝑡𝑡 1 𝑚𝑖𝑛 = 42 𝑔𝑡𝑡/𝑚𝑖𝑛 NOTE: There is no simple unit to start with, because 1500 mL over 12 hr is a rate of mL/hr. We start with that, because that is volume over time which our answer will also be (just different units). Then we use known and given relations to convert hr to min and mL to gtt (order does not matter, just so what we don’t want cancels, and what we do want remains: gtt on top, and min on bottom). (41.666… = 42)
- 33. Order: infuse a solution of 2g in 500 mL at 4 mg/min. Wanted: flow rate for infusion pump in mL/hr ANSWER: 60 mL/hr 500 𝑚𝐿 2 𝑔 × 1 𝑔 1000 𝑚𝑔 × 4 𝑚𝑔 1 𝑚𝑖𝑛 × 60 𝑚𝑖𝑛 1 ℎ𝑟 = 60 𝑚𝐿 1 ℎ𝑟 = 60 𝑚𝐿/ℎ𝑟 NOTE: No simple unit to start with, so we start with the solution relation with mL on top (for the top of our answer). Then in any order, conversion of g to mg, cancel mg with the given mass to time rate, and conversion of min to hr. However, I always use the natural order: whatever unit that is in what I have just written (a unit I don’t want in my answer), I cancel it with the next thing I write. Sometimes one of the units may have to wait to be cancelled by something later in the series. In this case, units always cancel bottom to top immediately.
- 34. Order: infuse a solution of 5 g in 1000 mL at a rate of 1 mg/kg/hour Patient weight: 50 lb Wanted: flow rate of infusion pump in mL/hr 50 𝑙𝑏 × 1 𝑘𝑔 2.2 𝑙𝑏 × 1 𝑚𝑔 𝑘𝑔 × ℎ𝑟 × 1 𝑔 1000 𝑚𝑔 × 1000 𝑚𝐿 5 𝑔 = 22 𝑚𝐿 1 ℎ𝑟 = 4.5454 … = 5 𝑚𝐿/ℎ𝑟 ANSWER: 4.5454… = 5 mL/hr NOTE: We do have a simple unit to start with, the patient’s weight in lb. We first convert to kg and then use the “per/per” expression so that kg cancels, then since our solution relation has g, we convert to grams (cancelling the mg). Finally we write our solution relation with mL at the top (where it is in the answer). Grams then cancels, and note the hr we want in our answer is still on the bottom uncancelled. In this case all cancellations are top to bottom.
- 35. Order: 900 mL to infuse at 150 mL/hr Wanted: if we start at 0730, when will the infusion be done? ANSWER: 1330 900 𝑚𝐿 × 1 ℎ𝑟 150 𝑚𝐿 = 6 ℎ𝑟 0730 + 6 hr = 1330 Military time: after 1200 = 12N, instead of going back to 0100 (which means 1 AM) we just keep counting: 1 PM =1300, 8 PM = 2000, 11 PM = 2300, 12 midnight = 0000. So, for afternoon time just add 12: 2 PM + 12 = 1400. NOTE: The set up is wonderfully simple for this problem. Start with the simple unit (mL) and cancel the mL which you don’t want leaving the hr that you do. Then, for a change, we ADD to get the ending military time.
- 36. Order: 8.45% NS to infuse at 125 mL/hr over 32 hr Wanted: the total volume needed ANSWER: 4000 mL 32 ℎ𝑟 × 125 𝑚𝐿 ℎ𝑟 = 4000 𝑚𝐿 NOTE: Again the setup is really simple. Start with that simple unit (hr) and then look at your rate which has hours in it (and the mL you need). Make the hr cancel and you’re done.
- 37. Order: Infuse 50 mL of solution in 15 min Drop factor: 15 gtt/mL Wanted: infusion rate (manual IV) in gtt/mL ANSWER: 50 gtt/min 50 𝑚𝐿 15 𝑚𝑖𝑛 × 15 𝑔𝑡𝑡 𝑚𝐿 = 50 𝑔𝑡𝑡 1 𝑚𝑖𝑛 = 50 𝑔𝑡𝑡/𝑚𝑖𝑛 Problem: After 5 min there are 40 mL left in the IV bag. Wanted: Adjusted flow rate so that the drug is finished infusing on time. ANSWER: 60 gtt/mL 40 𝑚𝐿 10 𝑚𝑖𝑛 × 15 𝑔𝑡𝑡 𝑚𝐿 = 60 𝑔𝑡𝑡 1 𝑚𝑖𝑛 = 60 𝑔𝑡𝑡/𝑚𝑖𝑛 NOTE: We start with mL on the top, because that is a volume and we want a volume (gtt) on top in our answer. We only need to cancel mL. For the adjusted flow rate problem, we of course have to SUBTRACT 15 – 5 = 10 min remaining to put in the given (now) 40 mL.
- 38. Order: For wound care – 1 ½ oz of ¾ strength wound care solution applied each hr for 24 hr. Available: full strength solution (“medication”) Wanted: volume of medication and volume of normal saline to prepare enough ANSWER: 810 mL of medication and 270 mL of normal saline Calculate total volume needed: 24 𝑑𝑜𝑠𝑒𝑠 × 1.5 𝑜𝑧 𝑑𝑜𝑠𝑒 × 30 𝑚𝐿 1 𝑜𝑧 = 1080 𝑚𝐿 Calculate the volume of medication needed: 3 4 × 1080 𝑚𝐿 = 810 𝑚𝐿 Calculate the volume of normal saline needed: 1080 mL − 810 mL = 270 mL NOTE: Start with the simple unit (doses), then use the oz per dose, then convert oz to mL (memorize that conversion). The strength of the solution is best done as a separate calculation (the ¾ or .75 does not have units). Finally, add or subtract needs to be done separately from unit cancellation: unit cancellation is only multiply and divide.
- 39. REVIEW: IMPORTANCE OF CORRECT CALCULATOR OPERATION EXAMPLE: 74.8 𝑙𝑏 × 1 𝑘𝑔 2.2 𝑙𝑏 × 1.5 𝑚𝑔 1 𝑘𝑔 × 2 𝑚𝐿 125 𝑚𝑔 = .816 = .82 𝑚𝐿 DO: 74.8 X 1 ÷ 2.2 X 1.5 ÷ 1 X 2 ÷ 125 = .816 or 74.8 ÷ 2.2 X 1.5 X 2 ÷ 125 OR 74.8 X 1 X 1.5 X 2 ÷ 2.2 ÷ 1 ÷ 125 or 74.8 X 1.5 X 2 ÷ 2.2 ÷ 125 DO NOT DO: 74.8 X 1 X 1.5 X 2 ÷ 2.2 X 1 X 125 = 8500 or 74.8 X 1.5 X 2 ÷ 2.2 X 125 = 8500 Unless you use PARENTHESES: 74.8 X 1 X 1.5 X 2 ÷ (2.2 X 1 X 125) = .816 or 74.8 X 1.5 X 2 ÷ (2.2 X 125) = .816 REMEMBER: It is fine to use ÷ two or more times in a row. Just be sure any number on top gets X and any number on the bottom gets ÷ .
- 40. WRAP UP • Memorize formulas – not recommended. • Proportion – OK, but on more complicated problems (IV) may take 2 or 3 separate ones. • Unit cancellation – you can’t go wrong. o However: always check to see if the unit (uncancelled) that you end up with is the unit of the wanted answer – otherwise you stopped too soon! o Always look toward the units of the answer: what is on top of the answer will have to be somewhere on top of the set-up (and not cancel), and what is on the bottom of the answer will have to be somewhere on the bottom of the set-up (and not cancel). o If a number has a single unit only – that is, it is simply a whole number with a unit, no fraction involved (like lb or whatever), it is understood to be on the top. You may write it over a 1 if that helps you. o It helps to start with a simple unit number if possible, but sometimes you have to start with a “complex” unit which is a ratio (“rate”) or “per expression.” For example: 50 mL 15 min . Just be sure what you want on the top of your answer is on the top of the ratio. Try it! I did an hour practice test in 45 min, and I found myself using ALL unit cancellation. I got, oops, 90%, but that was from 3 simple errors. One I stopped to soon (check the units when you’re done!). One I put .75 instead of 0.75. And one was a rounding error (up instead of down). GO FOR IT! PRACTICE! ALL THE BEST IN YOUR NURSING CAREER!