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Administering Insulin

From: Lisa
Subject: Pharmacy tech math

If a doctor prescribes 30 units of insulin in 500 ml to be 
administered over 2 hours, how many drops per minute should be 
administered if the set is calibrated to deliver 20 drops per ml?

From: Doctor Rick
Subject: Re: Pharmacy tech math

Hi, Lisa.

This kind of problem is easy to get right if you keep the units with 
the numbers. The units can be "canceled" just like numeric factors in 
a fraction, and this shows you that you've done it right.

It looks to me as if the information about 30 units of insulin is 
irrelevant to the problem. All you're concerned about is the 500 ml 
of solution. The rate we want is 500 milliliters over two hours, 
which we can write as a fraction:

  500 ml
   2 hr

We know that there are 20 drops per milliliter, so that

  20 drops
  -------- = 1
    1 ml

since the numerator is the same amount as the denominator. If we 
multiply the rate by this fraction, we won't change the rate. We then 
have ml in the numerator and the denominator, so they will cancel:

  500 ml   20 drops   500*20 drops
  ------ * -------- = ------------ = 5000 drops/hr
   2 hr      1 ml        2*1 hr

We're not done yet, because we need to know the number of drops per 
MINUTE. But that's easy using another "unit multiplier". Since 1 hour 
= 60 minutes, we can write

  1 hour
  ------ = 1
  60 min

I chose to put the hour on top to cancel the hours in the bottom of 
our fraction, 5000 drops/hour, when we multiply:

  5000 drops   1 hour
  ---------- * ------ = 5000/60 drops/min = 83.333 drops/min
     1 hour    60 min

Since this could have important consequences for a patient's health, 
we'd better check the answer! We can work backward. Each minute, we 
deliver 83.333 drops. Since 20 drops make 1 ml, each drop contains 
1/20 ml, and 83.333 drops contain

  83.333 * 1/20 ml = 83.333 / 20 = 4.16665 ml

One hour is 60 minutes. In 60 minutes we get 60 times as much 
solution, or

  4.16665 ml * 60 = 249.999 ml

This is 250 ml with a small round-off error. In two hours, we get 
twice as much, or 500 ml. That's what we needed.

Does this help? What you're doing is important, so I want to be sure 
you learn it well! Someday you may be putting a drug into me.

- Doctor Rick, The Math Forum 

From: Lisa
Subject: Pharmacy tech math

Is there a site that I can use as a tool for these kinds of problems? 
The answer made sense to me, but other problems are more complicated. 

Thank you, 

From: Doctor Rick
Subject: Re: Pharmacy tech math

Hi, Lisa.

I'd rather have you learn how to do these problems than find a site 
that does them for you; a crutch won't prepare you well for the 
future. Helping you learn how is what Dr. Math is best at, and what 
no automated site could do well. I understand how you'd not want to 
overload us with questions, since we're human, but I'd like to help 
as much as possible.

We can help best if you can identify the types of problems that give 
you the most trouble, and show us your best effort at working them, 
so we can see how you are doing. Then we can tailor our help to your 
particular difficulties.

I hope to hear more from you!

- Doctor Rick, The Math Forum 
Associated Topics:
Middle School Measurement
Middle School Ratio and Proportion
Middle School Terms/Units of Measurement

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