Dosage Calculation: Solving for X – Ratio and Proportion (Nursing)

00:00 Hi, welcome to our video series on dosage calculation.

00:04 Now hopefully we're making this a friendlier topic for you because no matter how you feel about math, I promise if you'd just hang with us, we'll show you the most important concepts that you need to know to figure safe and effective medication dosages.

00:19 Now on this one, we're gonna take the next step in ratio and proportion and we're gonna talk about how to solve for x.

00:26 Now x just means the unknown. Let me tell you what I mean.

00:29 So when 3 of the 4 numbers of a ratio are known, x can be just used as a placeholder.

00:36 So you know there's our familiar format right, 3:4.

00:40 That would look as a fraction like 3/4, with the numerator being 3 on the left, 4 being the denominator that would be the number on the bottom.

00:48 So when we use x as a placeholder, it can help us figure out what that 4th number is.

00:55 Now I'm gonna talk about the theory behind it just enough to make it understandable.

00:59 Don't worry, I have some of the same math phobia as you do.

01:03 That's why I'm confident our video series can really help you.

01:07 So let's talk about a clinical application.

01:10 The reason we would use this is because the dosage that the physician has ordered is slightly different than what we have available.

01:18 So that's why we solve for x. It's not just us being mean one to go through math problems.

01:23 This is very practical in a clinical setting.

01:27 Often times, a physician will order something and what we have available is a different strength, a different dosage.

01:33 So we have to figure out how to make these two things align because we know when our proportion that's equal, right? Okay, so we're back to the means and extremes.

01:45 We've talked about these before in other video series but remember how I remember.

01:50 The means are in the middle so the means are the two numbers in the middle and the extremes are the ones on either end.

01:58 So in proportion, the product of the means always equals the product of the extremes.

02:05 Now you see how we've laid that out their for you.

02:08 This was the previous numbers that we saw on the slide.

02:11 3:4, we're trying to figure out does it equal 6:8.

02:15 So we turned that ratio into what looks like a fraction.

02:20 3/4 equals 6/8, that's what we're trying to see.

02:25 So in this, you cross multiply.

02:27 You take the ratio, you make it into a fraction and we put those two together then we cross multiply.

02:34 So this would be 3 times 8, does it equal 4 times 6? So that's how we make the formula for that.

02:42 You see that on the bottom of the screen.

02:43 3 times 8, does it equal 4 times 6 is what we're trying to figure out.

02:48 Well since 3 times 8 and 4 times 6 is 24, these are equal and in proportion.

02:56 Now, let's try it with x. Trust me, if you could just follow that last part, you got it.

03:03 So if at any point, it seems to be going like ugh you need a break, you need a breather, or you need to listen to that one more time, feel free to pause the video, rewind and re-watch what you need to. Maybe just take some notes.

03:16 Whatever works best for your brain is you're walking through it with us is the best way for you to learn.

03:22 Remember, we know that you are the expert at recognizing what's the appropriate pace for you for that day and how you're feeling in your brain.

03:32 So let's do it with x.

03:33 You're gonna multiply, remember, the extremes and the means, that's what you're doing. So when we have something that's 3:4 equals 6 to what? Now, we're trying to solve it.

03:44 Okay, I know you already know the answer but we did that on purpose because we want you to be able to see how all those pieces fit together.

03:52 So you multiply the extremes and then the means.

03:55 Remember, that involves cross multiplication. So for one of these, we have the x.

04:02 So when you multiply, you cross multiply.

04:05 Remember, this way and this way, just to match the colors as we have on the slide.

04:08 You always wanna end up with the x on the left. It just keeps things tidier.

04:13 So keep in mind, multiply, that's the cross multiply when you see it in that format and that mean we're multiplying extremes and the means.

04:21 You're gonna put the number in front of the x on the side.

04:25 So 3 times x equals 4 times 6. That gives us 3x equals 24.

04:32 Okay. Now, we need to get rid of that number in front of the x because we need it be just x by itself. So that's how we solve for x.

04:42 Now it's pretty simple how you do that.

04:44 Whatever number is in front of that x, you just divide both sides by.

04:50 We have to keep everything equal so you divide each side of the equation by the number that's in front of the x.

04:56 So 3x divided by 3 is going to equal, right, 1. And then you divide 24 by 3.

05:04 Okay, so we come up with x equals 8.

05:09 X equals the remaining number as long as you do it in step 3 or you divide both sides by the number that's in front of the x.

05:20 Okay, I promise it's really that straightforward.

05:23 Now I always have someone check my math when I'm doing dosage calc.

05:27 I recommend you do that in practice too, just another safe card method for keeping our patients safe.

05:34 Now even after you find x, we're gonna go back up and plug the number of x in just to double check our work.

05:41 So remember, after that 4 step, you would go back up to the equation.

05:45 Now we know that x equals 8, go back and plug it back in to the formula.

05:50 3 times 8 equals 24, 4 times 6 equals 24.

05:55 Yes, we have a proportion, we have the right answer and we have a safe medication dosage as ordered by the physician.

06:03 So don't forget to always check your work.

06:06 Go back and plug in the value for x into the original formula to make sure everything lines out.

06:14 You can never be too careful when we're doing dosage calc for our patient.