Help with math

dudette10, MSN, RN · Oct 18, 2010

1. Doctors order: 1000 ml D5W IV with 40 mEq KCL to infuse at 2 mEq/hr. Calculate rate of flow in ml/h.
2. Doctors order: Lidocaine 2 g IV in 500 mL D5W at 2mg/min. Calculate rate of flow in ml/h.

If you don't use dimensional analysis to do it all in one shot, you can use a two-step proportion method to figure out the dilution first and the rate second. I did it both ways and came up with the same answer for both problems.

I hope that gets you started.

bananimal · Oct 18, 2010

That gets me started with the 2nd one.. But I feel like the way I do it is so complicated and unnecessary, I wish I could grasp DA! The formula I'm familiar with is mcg/min to ml/h... so I would do:

2000mcg/1000 x 60 mins = 120mg/h

then, 120/2000mg x 500 ml = 30 ml/h.

Did you get 30 ml/h?

And for the first one, I am all screwed up because I have no idea how to incorporate mEq into that formula........ AHHHH > :(

Music in My Heart · Oct 18, 2010

That gets me started with the 2nd one.. But I feel like the way I do it is so complicated and unnecessary, I wish I could grasp DA! The formula I'm familiar with is mcg/min to ml/h... so I would do:
2000mcg/1000 x 60 mins = 120mg/h
then, 120/2000mg x 500 ml = 30 ml/h.
Did you get 30 ml/h?
And for the first one, I am all screwed up because I have no idea how to incorporate mEq into that formula........ AHHHH >

To begin with, you should never, NEVER have unitless numbers in your quations.

Look at your first line... the dimensional arithmetic on the left yields mcg x min, not mg/hr.

Begin by writing out the problem as stated: Lidocaine 2 g IV in 500 mL D5W at 2mg/min. Calculate rate of flow in ml/h.

Now look at what they've given you... they're saying that each 500 mL D5 has 2 g of Lidocaine.

How many mg of Lidocaine is that in 500 mL? (2,000 mg)

How many mg of Lidocaine in 250 mL? Well, half the volume means half the drug, right? (1,000 mg)

How many mg of Lido in 100 mL? One-fifth of the solution has one-fifth of the drug (400 mg).

You should be able to follow this reasoning all the way until you figure out how much solution contains 2 mg of Lidocaine and then simply convert the rate from a "per-minute" rate to a "per-hour" rate.

To solve it rigorously, begin by writing the flow as given: (2 mg Lido/minute)

Then multiply by the concentration of Lido as given in a fashion so as to cancel out units: (500 mL solution / 2,000 mg Lido)

Now convert your flow rate from mL/min to mL/hr (x mL/min X [60 min / 1 hr]).

dudette10, MSN, RN · Oct 18, 2010

Did you get 30 ml/h?

Yep, I did. However, I have absolutely no idea how you got the numbers you did for your equation. I'm afraid that if you do it that way again, it might not work on another problem, and your answer will be wrong.

The proper way to figure this out with a two step proportion method would be this:

Dilution:

2000 mg/500 ml = 2 mg/x ml

answer for dilution: 2mg/0.5 ml

Then...

Rate:

0.5 ml/1 min = x ml/60 min

answer for rate: 30 ml/hr.

As music in my heart stated, always use the labels on your equations. Keep the solute volume/solution volume together in your proportions. In this one, you can say it out loud to know what it is: "There are 2000 mg in 500 ml of solution, and I want to know 2 mg are in x ml of solution."

In the rate part of the problem, you want to infuse 2 mg per minute, which is the same as 0.5 ml per minute, but you need to figure out how many ml in one hour. "I need to infuse 0.5 ml in one minute; how many ml do I infuse in 60 min?"

***********Your first problem is actually somewhat easier than the second. I did it in one proportion, and then the rate is staring at you in the face, and I didn't even have to set up a second proportion.

bananimal · Oct 18, 2010

yep, i did. however, i have absolutely no idea how you got the numbers you did for your equation. i'm afraid that if you do it that way again, it might not work on another problem, and your answer will be wrong.
yes, this is what i worry about. i figure out my math by set formulas (example: gtt/min = volume x drop factor divided by minutes) rather than da.. and it is definitely not convenient to do this because the second i can't plug numbers into a formula i know, i have no idea what i'm doing. the particular equation i went by i got from nursing calculators, specifically the mcg/min to ml/h equation-- because it was the only thing i could find relating to this problem (or so i thought).
the proper way to figure this out with a two step proportion method would be this:
dilution:
2000 mg/500 ml = 2 mg/x ml
answer for dilution: 2mg/0.5 ml
then...
rate:
0.5 ml/1 min = x ml/60 min
answer for rate: 30 ml/hr.
as music in my heart stated, always use the labels on your equations. keep the solute volume/solution volume together in your proportions. in this one, you can say it out loud to know what it is: "there are 2000 mg in 500 ml of solution, and i want to know 2 mg are in x ml of solution."
in the rate part of the problem, you want to infuse 2 mg per minute, which is the same as 0.5 ml per minute, but you need to figure out how many ml in one hour. "i need to infuse 0.5 ml in one minute; how many ml do i infuse in 60 min?"
thank you, this helps a lot.
***********your first problem is actually somewhat easier than the second. i did it in one proportion, and then the rate is staring at you in the face, and i didn't even have to set up a second proportion.
i'll have to look at it again tomorrow when i attempt the rest of the ones i couldn't get today, i know i am making it harder than it is in my weird way of trying to figure math out for myself..

before school began we had to take an online dosage calc course which you could decide which way you wanted to learn; ratio/proportion or dimensional analysis and i picked ratio/proportion and i understood it so well and passed the course with an a+.. then i get into school and they want us to do dimensional analysis, and for some reason i can't figure it out and everyone else can. i think i might benefit from just taking that course over. i don't know. i need to get this settled quickly because i don't want any of this to translate into med errors. :crying2: thanks for your help and patience so far :)

pippylockstocking · Oct 19, 2010

This is the only way I know how to solve the math problems. Im not sure if it's the "dimensional analysis" thing... but this is how I learned to do them.

You always use this equation: Desired / Have on hand X Quantity = Dose

#1 Plug in your numbers accordingly...

2 mEq/Hr X 1000 mL =

40 mEq

you can reduce the top and bottom by diving by 2 and cancelling out "mEq"

so now you have

1 Hr X 1000 mL =

20

mutiply accross the top and the bottom

you get 1 Hr X 1000 mL =

20

you can't reduce here so now you get

1000 mL/Hr

20

complete your problem by dividing again

Answer = 50 mL/Hr

Does this answer seem appropriate? Yes, a rate of 50 mL/hr is a common rate for infusions containing higher doses of KCL. Too fast would be dangerous.

# 2 Use the same formula of D x Q =

H

2 mg / min X 500 mL =

2000 mg

reduce the fraction by 2, and cancell out "mg"

so you have

1 min X 500 mL =

1000

complete the multiplication above the fraction first...

500 mL / min

1000

reduce the fraction to

1 mL/min

2

the problem asked you to change the dosing to mL/Hr so you need to convert minutes to an hour

so you multiply by 60

1 mL/min X 60

2

Answer = 30 mL/Hr

I hope this was helpful. Sorry if I was late getting to you. Perhaps someone else already answered you. But this is a good method to learn too :))

pippylockstocking · Oct 19, 2010

I just read some of the other responses and they have me really confused.

I always stick to D X Q = dose

H

It works like a charm EVERY time!