Hi, this is Cathy with Level Up RN. In this video, I will be going over dosage calculation problems that involve injectable medications. 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 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.
All right. So in this first example problem, we have an order for enoxaparin 40 milligrams subcutaneous injection once daily. And what we have available is enoxaparin 30 milligrams in 0.3 mls of solution, so this is our available concentration. And we want to know how many milliliters are injected with each dose, and we need to round to the nearest tenth. So definitely want to check our rounding when we're done calculating our answer. All right. So we can solve this problem using dimensional analysis, ratio and proportion, or the formula method. So let's start with dimensional analysis. So when I set up my equation with dimensional analysis, I start with what is ordered, and what's ordered is 40 milligrams. Then I check to see if I need to convert any units of measure. So my ordered dose is in milligrams, and what I have available is also in milligrams, so we're good to go there. I don't have to multiply times any conversion factor. Now I can multiply times the available concentration. And I'm going to make sure I put my milliliters on top and my milligrams on bottom. And that way, my milligrams will cross off. And when I multiply this out, I'll be left with milliliters. So if we multiply this out, we end up with 0.4 milliliters. And that's the answer you get when you multiply it out. It's already rounded to the nearest tenth, so we don't need to do any additional rounding.
All right. Let's go ahead and solve this same problem using ratio and proportion. Again, before you set your ratios, you've got to check your units of measure to make sure they're consistent. And they are in this case. So on one side of the equation, we have our known ratio, so that's our available concentration. And then on the other side of the equation, we have the ordered dose and the unknown quantity. So we don't know how many milliliters it will take to give our patient 40 milligrams. So now with ratio and proportion, we're going to cross multiply. So we have 30 times X equals 0.3 times 40. So I'm cross-multiplying there. 30X equals 12, X equals 12 divided by 30, and that equals 0.4 ml. And again, we're rounded to the nearest tenths, so we're good. And then the last method we could use to solve the same problem is the formula method. So with the formula method, we have desired over half times vehicle. And again, we need to make sure our desired and have doses are in the same units of measure, which they are. So we are desiring what is ordered is 40 milligrams. What we have is 30 milligrams in 0.3 mls of solution. That is the vehicle for getting the 30 milligrams. So milligrams cross off here, and if we multiply this out, we end up with 0.4 ml. So same answer. And that's how we would solve this. Each of those three ways gets you to the same answer. You just need to figure out which way makes the most sense to you.
I'm now going to work through our second example problem that involves an injectable medication. So this is an order for heparin. So what is ordered is 5,000 units of heparin, subcutaneous injection, Q8H, meaning every eight hours. And what is available to us is heparin 10,000 units per ml. So I don't want you guys to freak out when you see a different unit of measure that you're not used to. So you see a lot of milligrams and milliliters or grams or liters. Units, we're just going to handle it in the same exact way as we do with milligrams. We're going to set up our equations the same way, and we're going to solve it in the same way, so it's no big deal. So if you see things like milliequivalents or units or micrograms, not a big deal. We're going to solve it in the same way. Okay. So in this problem, we are being asked how many milliliters are injected with each dose and how many milliliters are injected per day. So we can solve part A of this problem using dimensional analysis, ratio and proportion, or the formula method. So let's first solve it with dimensional analysis. So we're going to start off by writing down what is ordered, which is 5,000 units, and make sure our units of measure are consistent across what's ordered and what's available, and it is. So we're going to multiply what's ordered, 5,000 units, by the available concentration. So I'm going to make sure I put my milliliters on top and my units on bottom such that my units will cross off, and I'm left with milliliters, which is what we are looking for. So with each dose, we are going to administer 0.5 ml.
All right. Let's do the same calculation with ratio and proportion. So we're going to set up our ratios. On one side of the equation, we're going to put our known ratio. So this is our available concentration. We know we have 10,000 units in a milliliter, and what is ordered is 5,000 units. And we don't know how many milliliters, so X is our unknown. Now we're going to cross-multiply here. So 10,000X equals 1 times 5,000, so 5,000. And then we're going to solve for X. So X equals 5,000 divided by 10,000, that equals 0.5 ml. And then we can solve this as well with the formula method. So with the formula method, we have desired over half times vehicle. So what we desire is basically what's ordered, so that's 5,000 units. What we have is this available concentration. So we have 10,000 units in 1 ml of solution. That's our vehicle. So desired over half times vehicle. So when you see vehicle, that's the form and amount that the medication comes in. All right. So our units cross off here. We multiply this out. Again, we end up with 0.5 ml. So 0.5 ml is administered with each dose. How much is administered per day? Well, we're giving heparin Q8H, so that's every eight hours, which means three times in a day, three times in a 24-hour period. So 0.5 times three equals 1.5 ml. That's how much we are giving each day.
