Help with math!

[Tanya167]

Hello. Very confused. I'm in an LPN program. Some of the math I get and some I'm comfused. Can someone do this problem? Teacher wanted us to try even though she did get to this yet.

client is to receive an IV infusion of 500 ml of D5W with 1000 mg of medication. The drop factor is 15 gtt/ml. The dosage of medication ordered is 4 mg/kg/hr. The client weighs 25 kg. Calculate the flow rate in drops per minute.

please help.

Thank you

[KrCmommy522, BSN, RN]

I would set this up with dimensional analysis. I find this formatting to be most helpful because it its easy to see what you do and dont need and cancel things out. And I say this because we haven't learn gtts/min in nursing school yet either, but with simple dimensional analysis I was able to figure it out.

15gtts/1ml x 500ml/1000mg x 4mg/1 kg x 25kg/1 hr x 1hr/60 min

try the next problem on your own and just post it here so we can help you. Also tell me what you don't understand about dimensional analysis.

I completely agree! That's why I tried to go with dimensional analysis in my first post. If anyone has ever seen my other posts helping with dosage calculations they know I love dimensional analysis! LoL. I'm glad when I was in nursing school our instructors didn't care which way we used to solve the problems - they taught us the different ways (dimensional analysis, ratio proportion, formula method) and we got to choose which one fit for us. I've always liked dimensional analysis because you follow it from what is ordered to what you need. It helped me know I did it right when I ended up with what I needed in the end!

Tanya167 - I know you said your instructor showed you the formula method, but do you have to use that to solve your problems, or can you use whatever way you'd like? If so, I highly suggest dimensional analysis. Like OsceanSN2019 said, tell us what you don't understand about dimensional analysis and we can help you understand it!

[bjwojcik]

Hi Osceans,

Not to be picky, but it might be a little confusing the way you set the problem up. There is no ratio of 25 kg/h. The 25 kg is one of the givens, and not part of a ratio. I believe the trick to handling the 4 mg/kg/h is to change it to 4 mg/kg*h.

-Brad

[Mavrick, BSN, RN]

12.5 gtts/min

Not at all helpful just doing the problem for someone and giving them the answer.

Read a few more of these "I need help with math" threads and discover how to not blurt out an answer before you understand the problem.

[KrCmommy522, BSN, RN]

bjwojcik said:

Hi Osceans,

Not to be picky, but it might be a little confusing the way you set the problem up. There is no ratio of 25 kg/h. The 25 kg is one of the givens, and not part of a ratio. I believe the trick to handling the 4 mg/kg/h is to change it to 4 mg/kg*h.

-Brad

I agree. Separating it like that seems confusing to me. I would just keep it all together as 4 mg/kg/hr with 4 mg in numerator of fraction and kg/hr in denominator of fraction.

First Problem:

Client is to receive an IV infusion of 500 ml of D5W with 1000 mg of medication. The drop factor is 15 gtt/ml. The dosage of medication ordered is 4 mg/kg/hr. The client weighs 25 kg. Calculate the flow rate in drops per minute.

Second Problem:

Client has an IV of 1,000 ml of D5W, infusing at the rate of 28 gtt/min. The drop factor is 10 gtt/ml. How many milliliter per hour is client receiving?

OP: This is how it would be set up for dimensional analysis - You can see that, in the first problem, I started off with the pts weight.

As I said in my first post, I always like to start off with what is all on it's own, like pts weight, in this case. Or, for example, you have a problem something like, the dr orders 50 mg and you have on hand 100 mg/mL, how many mL would you give.

I would start off with the order of 50 mg and go from there. You can only cancel out diagonally, so if you start off with 50 mg (in the numerator all on its own with nothing in denominator), then you need mg in the denominator of whatever fraction is second. In this example since what is on hand has mgs - 100 mg/mL - you don't need a conversion factor, you would just use what is on hand. You have 50 mg in numerator, so mg needs to be in the denominator of the fraction for what is on hand, so it would be mL/100 mg. So the problem would be 50 mg x mL/100 mg - You would cancel out the mg and be left with mL, which is what you need to know - how many mLs to give.

If it said dr orders 50 mcg and you have on hand 100 mg/mL, how many mL would you give. In this case, 50 mcg is all on its own, so I would start off with that. So, it would start off as 50 mcg x ?. Here, you would need a conversion factor - 1 mg = 1000 mcg (1 mg/1000 mcg). Again, you can only cancel out diagonally, so if you start off with 50 mcg (in the numerator all on its own with nothing in denominator), then you need mcg in the denominator of the conversion factor. So, with 50 mcg in the numerator of the first fraction, the second fraction needs mcg in the denominator. So, you look at your problem to see what has mcg in it that you can use. There isn't anything, so you need a conversion factor to change it to mg (which is what you have in your problem). So, you use the conversion factor 1 mg = 1000 mcg (1 mg/1000 mcg). The mcg needs to be in the denominator, so this is set up right. If you needed it in the numerator (1000 mcg/1 mg), you could do that too, because either way it equals 1 (whether its 1 mg/1000 mcg or 1000 mcg/1 mg, it equals 1). Now, you have cancelled out the mcg, so you are left with mg. You still don't have what you need, because the answer is asking for mL. So, you look at the problem to see what has mg in it so you can cancel out the mg that were in the conversion factor. What is on hand has mg and it has the mL that you need - 100 mg/mL. Since the conversion factor had mg in the numerator, so what you write the fraction of what is on hand, mg needs to be in the denominator, so you write it as mL/100 mg. So, in this case the problem would be set up as: 50 mcg x 1 mg/1000 mcg x mL/100 mg.

Hopefully this helps you understand dimensional analysis a little bit (I hope I didn't make it more confusing!!). It really is helpful to let you go from what is ordered going along the path to get to what you need (what is available).

[OsceanSN2018]

Hi Osceans,

Not to be picky, but it might be a little confusing the way you set the problem up. There is no ratio of 25 kg/h. The 25 kg is one of the givens, and not part of a ratio. I believe the trick to handling the 4 mg/kg/h is to change it to 4 mg/kg*h.

-Brad

I know there is no such ratio but considering dimensional analysis it works. It stills give the answer of 12.5 gtts/min.

[KrCmommy522, BSN, RN]

Not at all helpful just doing the problem for someone and giving them the answer.

Read a few more of these "I need help with math" threads and discover how to not blurt out an answer before you understand the problem.

Agreed! Try helping explain how to get to the answer, without giving the answer! It is more helpful to the person than just giving them the answer! That way, they learn how to answer it themselves and can use it in the future.

[bjwojcik]

Hi Tanya,

This problem has three parts: A rate that is given to you to start the problem, a rate that you are asked to solve for, and a couple of ratios which you will use to change the units of the starting rate into the units of the answer.

Step 1) List the starting rate and the units of the answer rate with an = in between. Both of these are in the problem.

Starting rate = units of the rate of the answer

Step 2) Write down the ratios 10 gtt/mL and 60 min/h. These are the tools you will used to change the units of the given into the units of the answer. You can flip these ratios upside down if needed.

Step 3) Fill in the ratios after the starting rate so the units that you don't want cancel out and you are left with mL/h.

Let me know if you need help.

Brad Wojcik, PharmD

[bjwojcik]

Just to let you know, if you have kg/h in the denominator, the hours do not cancel out. It is 4 mg/kg all over h. If you multiply top and bottom by 1/h you get 4 mg/k (1/h) all over h (1/h). At this point the denominator becomes 1 and you are left with 4 mg/kg*h.

-Brad

[bjwojcik]

Maybe this will explain it better.

4 mg.pdf

[KrCmommy522, BSN, RN]

bjwojcik said:

Just to let you know, if you have kg/h in the denominator, the hours do not cancel out. It is 4 mg/kg all over h. If you multiply top and bottom by 1/h you get 4 mg/k (1/h) all over h (1/h). At this point the denominator becomes 1 and you are left with 4 mg/kg*h.

-Brad

With dimensional analysis, you have to set it up so you cancel the units diagonally. So, you put the weight in the numerator (in proper format you would put 25 kg/1, but I just leave out the 1). Then, you need kg in the denominator, to cancel it out (so to say - you are just removing the units because they are the same). So you put 25 kg x 4 mg/kg/hr (with kg/hr in denominator), then you put the conversion factor of 1 hr/60 min. With kg/hr in the denominator, you need pts weight (kg) in numerator and hr from the conversion factor (1 hr/60 min) in the numerator - so you can cancel them diagonally. With dimensional analysis, if you put 4 mg/kg/hr with mg/kg in numerator and hr in denominator, then you would need the pts weight (25 kg) in the denominator, which would mean you would end up dividing 25, which wouldn't work.

The Way I Initially Set It Up:

Set Up with mg/kg in numerator and hr in denominator:

I'm not sure I understand your PDF. It says that 4 mg/kg over h is not the same as 4mg over kg/hr. But then it says 4 mg/kg over hr equals 4 mg over kg h? Please explain! I really want to understand what I'm missing! Thanks!

[chare]

[...]

I'm not sure I understand your PDF. It says that 4 mg/kg over h is not the same as 4mg over kg/hr. But then it says 4 mg/kg over hr equals 4 mg over kg h? Please explain! I really want to understand what I'm missing! Thanks!

This might help clarify.

https://allnurses.com/general-nursing-student/a-fyi-on-1149282.html

[bjwojcik]

On the second equation, you need to put 25 kg on top. If 25 kg were on top, it would cancel the kg in 4 mg/kg.

Take a look at the attachments.

-Brad

Dosage Calculations PDF-B.Wojcik.pdf

mg kg day.pdf