Hi, welcome to our video series on dosage calculation.
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.
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.
Now x just means the unknown. Let me tell you what I mean.
So when 3 of the 4 numbers of a ratio are known, x can be just used as a placeholder.
So you know there's our familiar format right, 3:4.
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.
So when we use x as a placeholder, it can help us figure out what that 4th number is.
Now I'm gonna talk about the theory behind it just enough to make it understandable.
Don't worry, I have some of the same math phobia as you do.
That's why I'm confident our video series can really help you.
So let's talk about a clinical application.
The reason we would use this is because the dosage that the physician has ordered
is slightly different than what we have available.
So that's why we solve for x. It's not just us being mean one to go through math problems.
This is very practical in a clinical setting.
Often times, a physician will order something
and what we have available is a different strength, a different dosage.
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.
We've talked about these before in other video series but remember how I remember.
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.
So in proportion, the product of the means always equals the product of the extremes.
Now you see how we've laid that out their for you.
This was the previous numbers that we saw on the slide.
3:4, we're trying to figure out does it equal 6:8.
So we turned that ratio into what looks like a fraction.
3/4 equals 6/8, that's what we're trying to see.
So in this, you cross multiply.
You take the ratio, you make it into a fraction and we put those two together then we cross multiply.
So this would be 3 times 8, does it equal 4 times 6? So that's how we make the formula for that.
You see that on the bottom of the screen.
3 times 8, does it equal 4 times 6 is what we're trying to figure out.
Well since 3 times 8 and 4 times 6 is 24, these are equal and in proportion.
Now, let's try it with x. Trust me, if you could just follow that last part, you got it.
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.
Whatever works best for your brain is you're walking through it with us is the best way for you to learn.
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.
So let's do it with x.
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.
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.
So you multiply the extremes and then the means.
Remember, that involves cross multiplication. So for one of these, we have the x.
So when you multiply, you cross multiply.
Remember, this way and this way, just to match the colors as we have on the slide.
You always wanna end up with the x on the left. It just keeps things tidier.
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.
You're gonna put the number in front of the x on the side.
So 3 times x equals 4 times 6. That gives us 3x equals 24.
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.
Now it's pretty simple how you do that.
Whatever number is in front of that x, you just divide both sides by.
We have to keep everything equal so you divide each side of the equation
by the number that's in front of the x.
So 3x divided by 3 is going to equal, right, 1. And then you divide 24 by 3.
Okay, so we come up with x equals 8.
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.
Okay, I promise it's really that straightforward.
Now I always have someone check my math when I'm doing dosage calc.
I recommend you do that in practice too, just another safe card method for keeping our patients safe.
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.
So remember, after that 4 step, you would go back up to the equation.
Now we know that x equals 8, go back and plug it back in to the formula.
3 times 8 equals 24, 4 times 6 equals 24.
Yes, we have a proportion, we have the right answer
and we have a safe medication dosage as ordered by the physician.
So don't forget to always check your work.
Go back and plug in the value for x into the original formula to make sure everything lines out.
You can never be too careful when we're doing dosage calc for our patient.