# Dosage Calculation: Ratio and Proportion (Nursing)

by Rhonda Lawes

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00:00 Hi. Welcome to our dosage calculation series. Now, don't get uptight about the math.

00:06 I know usually people don't like it but I promise you learn these simple rules with us and you'll become a pro in no time.

00:14 See, understanding ratio and proportion, this is the concept that you need to learn; it's the first step in understanding how to solve for x or unknown numbers.

00:23 What we use when we're trying to figure out how to give a dosage of medication that's different than what we have available.

00:31 Okay, so first let's start with what is a ratio? A ratio is a number that just describes a relationship between two numbers.

00:40 Now, you'll see up there, schnauzers, because that is my favorite breed.

00:45 My own puppy is called Harley.

00:48 So, I wanted something friendly to introduce this concept to you.

00:51 So, let's just look at what's the ratio of tennis balls, Harley's favorite, to Schnauzers.

00:58 So, we look at this, we have how many tennis balls? 3. How many Harleys? 4.

01:05 So, the ratio is 3 tennis balls to 4 Schnauzers or 3:4.

01:13 Now, I know this isn't medication but I thought it'd be a lot more fun to learn about ratios with something that's a little more interesting than dealing with medications.

01:21 So, we've got a ratio of 3:4 or 3/4. Looks like a fraction combination, so you've got 3/4, also means, 3 divided by 4 when we start talking about the ratio.

01:35 So, it's all about the relationship. 3 of this item to 4 of that item or 3:4.

01:43 Now, sometimes you'll see us use this, you see this semi-colon in between there.

01:49 So, each one of these three ways is just saying the same thing.

01:54 So, one way it's expressed in graphics with 3 tennis balls, four Schnauzers, or the number 3/4 like a fraction, or 3:4.

02:07 All three examples are saying the same thing.

02:11 Now, the number on the top in the fraction is called the numerator.

02:14 The number on the bottom is called the denominator.

02:18 So, in our example, 3 is the numerator and 4 is the denominator.

02:23 Alright, this is just some of the lingo that we use when talking about fractions.

02:27 So, it's the same thing as 3:4.

02:32 It all represents three on the top, whether it's over a fraction or if it's on the left side of the semi-colon, that is the numerator.

02:41 So, if I'm gonna take a fraction and write it as a proportion, I'll take the top number, write it first, then a semi-colon and the second number.

02:50 So, look at the fraction, 3/4.

02:54 The numerator is the number on the left, the denominator is the number on the right.

02:59 Okay, now, if any of you need the time to pause a video, you just do that when you need to, if you need to catch your breath or kinda think through these concepts on your own.

03:08 Now, medications in solutions are also described using ratios.

03:13 That's one of the reasons we want you to understand it.

03:16 So, you may see something like epinephrine 1:10,000.

03:20 So, that means there's one-part medication, the epinephrine, in 10,000 parts of a solution.

03:28 So, it's a good idea if you have a frame of reference for this.

03:31 This becomes particularly problematic when we have the same medication use for a pediatric population that we do for an adult population like the example of heparin.

03:43 I don't know if you're familiar with the episode that happened with a famous actor, the Quaid family.

03:49 They had adopted twins, and the twins were accidentally given a solution that was so intense that was meant for adults, not for infants.

04:00 Now luckily, these babies survived.

04:02 But the Quaids did a really good job in pursuing the company to change the labeling so it'd be very difficult to mix up the adult strength or solution with the pediatric or neonatal strength.

04:16 So, it matters that you pay attention.

04:19 1:10,000 means there's one-part medication to 10,000 parts solution.

04:26 So, let's look at it from a different perspective.

04:28 We talked about that example with the heparin and the new babies.

04:31 I wanna think about something of food.

04:34 So, would you rather drink bitter vinegar? I mean really intensely bitter vinegar, at a ratio or proportion of 1:10, or 1:10,000, right? That answer's pretty obvious.

04:49 1:10,000 is several times less potent than 1:10.

04:54 So, if it tastes terrible, I think you'd wanna take the what? 1:10,000.

04:59 Now, the same applies to medication, and back to the example we talked about, was something quoted in adult ratio miggt be 1:10 and that's okay in an adult body.

05:09 But it needs to be something like 1:10,000 for a neonate.

05:14 So, that's why it's critically important that nurses understand ratio and proportions.

05:20 Now, proportion means that two ratios are fractions, are equal.

05:25 So, 3:4 equals 6:8.

05:28 Now, if we write those out as fractions: 3/4, right, numerator is on the left.

05:33 3/4, the denominator, equals, 6/8.

05:38 Now, if this statement is true, then this proportion or these fractions are equal that's what we're looking for.

05:47 And that's a key point in setting up the correct dosage of medication.

05:51 Now, first, I need to introduce you to a math term, it's not a big deal.

05:55 But we just call it means and extremes.

05:57 I want you to understand the theory behind why we do the math that we do.

06:02 So, these numbers are the means, they're in the middle. That's how I remember them.

06:07 If I've written 3 to 4 equals 6 to 8, the means are in the middle.

06:12 Now, the extremes are on the extreme outside. So that's the way my brain remembers it.

06:18 Means are in the middle and the extremes are on the outside.

06:23 So, when you're cross-multiplying, you're gonna multiply the top left which is the numerator.

06:30 We've got the left numerator and the bottom right which is the denominator.

06:36 So, you see the numbers in that kind of pinkish color, they're LN and RD.

06:41 And when we're cross-multiplying to check to see if these are actually proportion and equal.

06:46 You multiply the top left numerator by the bottom right denominator.

06:52 The next step is you multiply the bottom left number, the denominator, and top right numerator.

06:59 Now, we call it cross-multiply, because if you follow that it makes like an X, so that's why it gets the term cross-multiply.

07:09 We've highlighted those in the special colors so you can see which ones we're gonna multiply against each other.

07:14 So, again, if you need a second just to pause a video and think about it, you feel free to do that when you want to.

07:20 So, in proportions, the product of the means always equals the product of the extremes.

07:28 That means these two sets are proportional or equal.

07:33 So, I just wanna hit that one more time.

07:35 The product of the means always equals the product of the extremes.

07:39 Why does that matter? That helps you make sure you're giving the correct dosage to your patient.

07:46 Because this is the first step of us figuring out how to solve for X.

07:50 That means if the physician has ordered one dosage of medication and I have it available in another range, this is how I do the math to figure out what's the appropriate dosage to withdraw from the vile, or the amount of tablet to give or liquid, etc.

08:07 So, just stay with us. I promise this will make sense as we continue to go through it.

08:12 So, we've got the right, we'll just show you another way. Left numerator, right denominator.

08:18 Left denominator, right numerator.

08:20 We just spelled that out for you so you could see how we do the cross-multiplication.

08:24 So, in order for it to be an equal proportion, we're gonna actually have to do the math.

08:29 Now, if you need a minute, you can just do this in your head, we did this with simple numbers.

08:33 But if you wanna double check on a calculator, that's fine.

08:36 Grab your cellphone, and multiply along with us.

08:39 But 3 times 8 equals 4 times 6, if this is an equal proportion, right? This is how we can tell if those fractions are equal. Well, 3 times 8 is 24.

08:51 4 times 6 is 24. So, yes, we can say this is an equal proportion.

The lecture Dosage Calculation: Ratio and Proportion (Nursing) by Rhonda Lawes is from the course Dosage Calculation (Nursing).

### Included Quiz Questions

1. 1:10
2. 1:100
3. 1:1000
4. 1:10,000
1. 8:10
2. 6:8
3. 10:15
4. 12:20
1. 4 and 6
2. 3 and 8
3. 3 and 6
4. 4 and 8
1. 3 with 8 and 4 with 6
2. 3 with 6 and 4 with 8
3. 3 with 4 and 6 with 8
4. 3 with 6 and 8

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