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 http://mathforum.org/dr.math/
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, Lisa
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 http://mathforum.org/dr.math/
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