Dosage Calculation: Liquids – Ratio and Proportion (Nursing)

00:00 Now on liquid medications.

00:01 We talked about those a little bit but let's talk about -- you've got 100 mg of CoughNot in 1 mL of syrup.

00:10 Yeah, that's pretty cool name for a drug. You know, we just made that up for fun.

00:13 But you have 100 mg in 1 mL. We've made the relationship.

00:19 We've expressed it as a fraction. 100 mg as a denominator in 1 mL.

00:26 Now the order reads 225 mg every 12 hours.

00:32 Okay, so now we have to figure out, what we have on hand is the known ratio.

00:37 We need to figure out how do we give this patient 225 mg every 12 hours or q12 hours.

00:47 Okay, so how many milliliters of CoughNot would you give? If you wanna try it on your own based on what we've already studied.

00:54 Pause the video, and do the math and then join back up with us.

00:58 If not, we're gonna move forward to how you would set this up for a liquid medication.

01:03 Remember, we're gonna identify the known ratio, that's the medication that we have on hand and then the unknown ratio, that's the ordered medication.

01:12 You're gonna set up the proportion, cross multiply and solve and then check your answer by plugging the result into the unknown ratio just to double check and make sure it's correct.

01:23 So let's get it set up. We have 100 mg in 1 mL.

01:27 We know that we want 225 mg and we want to figure out how many milliliters that is.

01:34 Now it's always important that your units match, that they align.

01:38 The problem on the left is mg over mL. On the right side, it's mg over mL.

01:46 Proportion won't work unless you have those the same on both sides so the units need to match, numerator and denominator on the left and right sides of the equation.

01:58 So you multiply the extremes and then the means.

02:01 We always put x on the left side of the equation to keep things in order.

02:05 Now we have 100x equals 225.

02:10 So we divide each side by the number that's in front of x, divide that by 100, you've got 225 divided by 100. That will give us x equals 2.25 mL.

02:25 Okay, ask yourself, "Hey, is that reasonable?" If I had a liquid medication, can I draw up 2.25 mL? Yeah, of course I can. Now I'm not gonna do it in a 30 mL medicine cup.

02:40 I'm gonna draw that up in a syringe that allows me to measure 0.25 mL but not ready to do that yet because my last step is really the most important.

02:51 Check your work by replacing x with the number and go back through the entire equation again.

02:57 It won't take long and it's critically important to patient safety.

03:02 So go back in and plug x into the equation. Do the math again.

03:07 100 times 2.25 equals 225 times 1? Absolutely. Both sides of the equation equal 225. There you go.

03:20 You've done it. That's how you figure the correct dosage.

03:24 2.25 mL is the correct dose and we know that it's appropriate for liquid medication.

03:29 I could easily draw that up in a syringe and get exactly that dosage for my patient.

03:35 So the guidelines for ratio and proportion.

03:39 You know now how to take the words, figure out the relationship, turn that into a fraction to show us what it is.

03:47 The have side is the known ratio to what you have available.

03:52 So we've got that highlighted in green for you. We talked about known versus the unknown.

03:58 The known is the rate and amount and the dosage of medication that you have available.

04:04 On the opposite side is the unknown. This is what the physician has ordered.

04:09 It's an unknown ratio because we're trying to figure out what the dosage of this particular medication will be.

04:16 So you take the unknown and the known, you put those together in the appropriate order, that's gonna help us discover what the safe dosage is.

04:26 So to prevent errors, make sure the units match.

04:29 I know we touched on this before but I wanted to slow down here and make sure you caught that because the units have to match and be in the same sequence.

04:40 So they have to match. Note we have milligrams to milligrams, mLs to mLs.

04:45 They need to be in same sequence or order.

04:48 Meaning, milligrams are both in the numerator or on the top.

04:52 Milliliters are both on the bottom or in the denominator.

04:56 So that's really important. Don't get going too quickly and miss that step.

05:01 Sometimes, you will have to translate milligrams into grams before you can get everything to line up or vice versa.

05:09 And we can show you how to do that but just be very aware this is an important step, you don't want to miss for patient safety.