Hi, this is Cathy with Level Up RN. In this video, I'll be going over several dosage calculation problems involving oral medications, specifically liquid medications. And I'll be solving these problems on my whiteboard using three different methods, including dimensional analysis, ratio and proportion, and the formula method. You can find all the information that I'll be covering in this video in our Level Up RN dosage calculation workbook. If you are in nursing school, then you know how important it is to master dosage calculations. And our workbook will help you do just that. In a nutshell, our workbook contains all the different types of dosage calculation problems that you are likely to encounter in nursing school. And we demonstrate how to solve each problem using multiple methods so you can pick the way that makes the most sense to you.
So in this example problem, we have an order for 240 milligrams of acetaminophen to be given q6h, so every six hours. And what we have available is acetaminophen 160 milligrams in 5 mL. So that's our concentration. And this is in a 473-milliliter bottle. And we're being asked, how many milliliters should we give per dose, rounding to the nearest tenth, how many milliliters should we administer per day, round to the nearest 10th, and how many full doses are in that bottle? Okay, so we can solve part A of this problem using dimensional analysis, ratio and proportion, or the formula method.
So let's first solve this with dimensional analysis. So with dimensional analysis, I start by putting down what is ordered, which is 240 milligrams. Then I check to see if I need to multiply this times any conversion factor. So if I look at what's available, it's in milligrams, and my order is in milligrams, so I'm good to go there. I don't need to multiply times any conversion factor. Next, I would just multiply times the concentration, making sure I'm putting the milliliters on top and the milligrams on the bottom such that my milligrams cross off, and I'm left with milliliters, which is what I was looking for. So if you multiply this out, you end up with 7.5 milliliters. And the instruction said to round this to the nearest tenth. My answer is actually already to the nearest tenth. So we're good to go as far as rounding.
Okay. Let's solve this same problem using ratio and proportion. So let's put ratio and proportion. We're going to start by putting our known ratio. So our known concentration is 160 milligrams in 5 mL. And we want 240 milligrams, and we don't know how many mL that will take. So that's our unknown value. Now I'm going to cross multiply here. So I'm going to end up with 160X equals 5 times 240. 160X equals 1,200. X equals 1,200 divided by 160, and that turns out to be 7.5 mL. So we cross multiplied, and then we solved for X. And we get the same number as we did with dimensional analysis. Then with the formula method, we have desired over have times vehicle. So we desire or want 240 milligrams. We have 160 milligrams in 5 mL of solution. So that 5 mL of solution is the vehicle to get that 160 milligrams. So our milligrams cross off, and if we multiply this out, again, we get 7.5 mL. So 7.5 mL is the answer to part A.
Part B asks us how many milliliters is the patient receiving per day. So per the order, the patient is getting this medication every six hours, which is four times in a day or 24-hour period. So we're going to take 7.5 mL times 4, and that equals 30 mL. And that's how much they would get per day. This tells us to round to the nearest tenth. This is already rounded appropriately. So if we'd had 30.56 or whatever, then we would need to round. But this is already a whole number, so it's rounded to the nearest tenth. And then our last problem here, part C, is, how many full doses are in the bottle? So our bottle has 473 milliliters. And with each dose, we are giving 7.5 milliliters. So if you divide this out, you get 63.07. We can't give 0.07 of a dose, right? So that's not a full dose. So really, we only have 63 full doses in our bottle. Okay? And that's the answer to part C.
Let's now work through a second liquid medication example problem. In this problem, our patient is receiving lactulose 30 milliliters TID, so three times a day, for hepatic encephalopathy. Lactulose 10 grams in 15 milliliters is available. So that's our medication concentration. And we're being asked how many grams is your patient receiving with each dose, and how many grams is your patient receiving per day? We need to round all our answers to the nearest whole number. So you can see that this problem is kind of the reverse of the problem we just went through. Previously, we were given a dose in milligrams, and we needed to calculate the milliliters to provide the patient. Here, we're being told the milliliters the patient is getting, and we need to calculate the gram. So it's kind of reverse. We can use dimensional analysis or ratio and proportion to solve part A of this problem. The formula method does not really apply here because we're kind of doing things in reverse.
So let's go ahead and solve part A using dimensional analysis. So the patient is receiving 30 milliliters with each dose. And to calculate how many grams they're getting with each dose, I need to multiply this times the available concentration. And I want to make sure my grams is on top and my milliliters are on the bottom. That way, my milliliters will cross off, and I'll be left with grams. So you got to be careful about how you set this up. So if I do this multiplication, I end up with 20 grams. So that's how we would solve it with dimensional analysis. Now, let's solve the same problem with ratio and proportion. So with ratio and proportion, I'm going to put my known ratio down. So that's my available concentration. And then I'm going to put my unknown value on the other side with the 30 milliliters the patient is receiving. So known concentration, how much the patient is actually receiving, and X is our unknown value. So now I can cross multiply here. So I have 15X, and then I have 10 times 30. So 15X equals 300. X equals 300 divided by 15, which equals 20 grams. So we get the same answer as we did up here. A few more steps. But if you like algebra and you want some flexibility on how you set up your ratios, this may be a better method for you.
Okay. Part B of this question is, how many grams is your patient receiving per day? So since the patient is getting this TID - that is three times a day - then we just need to take the 20 grams that they're getting per dose, multiply that times three, and that gets us to 60 grams. And that's how much the patient is receiving per day. So let's check our rounding. We were instructed to round our answers to the nearest whole number, which the answer came out to a whole number anyway. So we're good to go, 20 grams per dose, 60 grams per day.
