I'm sorry I didn't see your post until today and couldn't respond to it until now. I started chemotherapy yesterday and have been a bit incapacitated. I will show you how each of the problems is solved by dimensional analysis (DA for short). DA is also called the factor label method, so named because you include labels along with the number on each of the terms. You create equations, usually based upon the drug formula of
dose desired divided by dose on hand and work from there keeping in mind that you must follow the order of operations of numbers. Often you end up with a string of fractions. Fractions are also ratios. You can manipulate the numerators and denominators of ratios (fractions) when performing these calculations as long as you are keeping the relationships (dose desired or dose on hand) together in the same fraction. You do this manipulation in order to cancel out the labels that are duplicated in numerators and denominators. With DA you want to set up problems so that you are ultimately left with the desired label(s) on the final answer.
Order (dose desired): 50 mg IV every 6 hours.
Supply (dose on hand): 50 mg in 50 mL
What will be the rate of infusion of the medication if infused over 15 minutes?
You need to know that IV infusion rates are expressed at mL/hour or cc's per hour. That information is not given to you in the problem--it is assumed that you know this. That will mean that your figures to plug into the dose desired divided by dose on hand formula now become 50 mg/15 minutes (a ratio which can be expressed as a fraction) divided by 50 mg/50 mL. This is a complex fraction (a fraction with a fraction in the numerator and a fraction in a denominator). Also, you want to end up with a final answer that has the label of "mL" in the numerator and "hour" in the denominator (mL/hour)50 mg/15 minutes (dose desired) / 50 mg/50 mL (dose on hand)
To clear the fraction out of the denominator you have to multiply the numerator and denominator of the complex fraction by the reciprocal of the fraction in the denominator. The reciprocal is 50 mL/50 mg.50 mg/15 minutes / 50 mg/50 mL X 50 mL/50 mg/50 mL/50 mg
which leaves you with this equation:50 mg/15 minutes x 50 mL/50 mg
This equation if multiplied out leaves you with 50 mL/25 minutes which is still not the correct answer because you must determine the rate in terms of an "hour". So, you must apply a conversion factor to change the minutes to hours.50 mg/15 minutes x 50 mL/50 mg x 60 minutes/1 hour = 200 mL/hour
To infuse this dose of medication as ordered you would set the 50 mL of solution to infuse at 200 mL per hour. It will complete its infusion of the 50 mL in 15 minutes.
Order (dose desired): Nitrostat grain 1/400 sublingually PRN
Supply (dose on hand): tablets of 0.3 mg (grain 1/200)
What do you administer to the patient?
This is a simple problem that involves some complex math. The fact that you were told the mg equivalent of the dose on hand is a red herring.
1 grain/400 (dose desired)/1 grain/200 (dose on hand)
Another complex fraction! Multiply the numerator and denominator by the reciprocal of the fraction in the denominator.
1 grain/400/1 grain/200 x 200/1 grain/200/1 grain
that gives you
1 grain/400 x 200/1 grain = 1/2
The answer is that you would give 1/2 of a tablet. In actual practice you should question a calculation that gives you 3/4 of a tablet. It is very difficult to break a tablet into a 3/4 tablet dose. Nitroglycerine tablets are very small. It is going to be hard to break one tablet into a half.
You can see other problems worked out by DA on the Dosage Calculations thread which is a sticky in the Nursing Student Assistance Forum (
http://allnurses.com/forums/f205/dosage-calculations-88867.html).
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