Hi, I'm Cathy with Level Up RN. In this video, I will be going through several examples of converting within the household system using two different methods, which include dimensional analysis and ratio and proportion. 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. In this video, I am going to work through a number of example problems that involve converting within the household system. And in order to be able to do these problems, you have to memorize these conversion factors over here on the side of my whiteboard. So definitely remember that one pound equals 16 ounces, one tablespoon equals three teaspoons, one cup equals eight fluid ounces, one pint equals two cups, one quart equals two pints, one gallon equals four quarts, and one foot equals 12 inches. So we are going to solve these example problems using dimensional analysis and ratio and proportion, and some of you may be like, "I can do some of this in my head," and that's great, but it's good to get familiar with these methods when the problems are really easy so that you know how to use those methods when the problems get harder.
Okay. So let's first solve this first example problem, which asks us to convert 2.4 pounds into ounces using dimensional analysis. So 2.4 pounds. We write down the current units of measure. So that's 2.4 pounds. And then we're going to multiply it times the appropriate conversion factor, which is this first one here. So we're going to set it up so that 16 ounces is on top, and one pound is on bottom, so that way my pounds will cross off, and I'll be left with ounces. So if you multiply this out, you end up with 38.4 ounces, okay? Let's solve it now with ratio and proportion. So we're going to put our known ratio down first. So one pound equals 16 ounces. And we want to know, for 2.4 pounds, how many ounces is that? So the X is our unknown value. And I could have set this ratio up kind of flipped. So I could have said 16 ounces over one pound equals X ounces over 2.4 pounds. That would be fine too. That's the benefit of ratio and proportion is that you have that flexibility. With dimensional analysis, things have to be set up just so in order for it to be correct. So now we are going to do our cross multiplication. So X times 1 is just X, and then we have 16 times 2.4. And if we multiply this out, we end up with the same answer, which is 38.4 ounces.
Let's work through another example of converting within the household system. So we're going to do it using dimensional analysis and then ratio and proportion. So with this example problem, we want to convert nine teaspoons into tablespoons. So we're going to write down the current units of measure, which is nine teaspoons, multiply it times the appropriate conversion factor, which is going to be right here, right? One tablespoon equals three teaspoons. So I want to put my tablespoons on top, because that's what I'm looking for, and my teaspoons on bottom so that my units will cross off here. And then if I multiply this out, I end up with three tablespoons, okay? You might have been able to do that in your head, and that's cool. We're just working through it using these methods so you can get used to the methods. Okay. Let's do this with ratio and proportion. So we know that one tablespoon equals three teaspoons, and we want to know how many tablespoons are in nine teaspoons, okay? So X is our unknown value. So now we're going to cross-multiply here. So 9 times 1 is 9, and 3 times X is 3X. And then we're just going to solve for X. So X equals 9 divided by 3, and X equals 3. So we have 3 tablespoons here as well. Get the same answer.
All right. Let's go through our third example problem of converting within the household system. With this problem, we want to convert five-foot two inches into just inches. So we're actually going to do this kind of in two steps. So we first want to convert this five feet into inches. So we're going to solve this with dimensional analysis, as well as ratio and proportion. So using dimensional analysis, we want to write down what we currently have, what our current units of measure are, which is five feet, and then we're going to multiply times the appropriate conversion factor in order to get to inches. So this is the one we're going to use down here. So we have 12 inches is in one foot. So I write it like this so that my feet will cross off, and I am left with 60 inches. So that's how many inches are in five feet, but I also need to add in this other two inches. So 60 inches plus the 2 additional inches equals 62 inches. And that little symbol there is the same thing as inches. All right. Let's solve the same problem using ratio and proportion. So let's first write down the known ratio, the thing that we know to be true. 12 inches equals 1 foot. So that is the known ratio. And then on this side, we want to know how many inches are in 5 feet, and we're going to cross-multiply here. So 1 times X is just X. And then we have 12 times 5, and that equals 60. So again, that's how many inches are in 5 feet, but we are being asked how many inches are in 5 feet, 2 inches, so we need to add that additional 2 inches to get 62 inches. And that's how you would solve that problem, using dimensional analysis and ratio and proportion.
