Ex 1: IM Medication Dosage Calculation – Two Steps

You receive an order for 250 micrograms IM. The medication is available as one
milligram, per two milliliters. How many milliliters will you give the patient. To solve this problem we’re going to use a proportion. Which is formed by setting two rates or ratios equal to each other as
we see here. And as long as the units in a and c are the same. And the units of b and d are the same, then a times d will always equal b times c. So if we have one unknown. We can solve the unknown using this
equation here. Looking at the given information. We’ll start with a known rate of one milligram per two milliliters. So
we’ll have one milligram, Is to two milliliter. As, we have 250 micrograms. Is to any unknown number of milliliters, we’ll say x milliliters. But notice in this form we cannot cross multiply and solve for x. The reason for this is because looking
on the top we have different units Here we have milligrams and here we have micrograms. So we need to convert either milligrams to micrograms or micrograms to milligrams. To do this conversion we’ll go ahead and use the fact that 1,000 micrograms is equal to one milligram. So for this problem let’s go ahead and convert milligrams to micrograms. And again because one milligram is equal to 1,000 micrograms. We can substitute 1,000 micrograms, for this one milligram. This would give us the proportion 1,000
micrograms. Per two milliliters. Must equal 250 micrograms. To x milliliters. And notice how we have the same units
on top. And the same units on the bottom. So now we can cross multiply and solve
for x. When cross multiplying we’ll go and leave off the units. So we’ll have 1000 time x, that’s 1000x. Must equal, two times 250 that’s five hundred. Dividing both sides by 1000. So we have x equals, this would be 1/2 or 0.5. So you would give the patient 1/2 or 0.5 milliliters. I hope you found this helpful!