Learning Lab

In the hospital environment you will need to calculate the required volume of liquid solution by mental calculation and by using simple proportionality.

By proportionality I mean if one thing is doubled so is the other.

If one quantity is reduced by a quarter then the other is reduced by a quarter as well.

Your drug in solution form is a quantity of liquid so if you want more or less of the drug you need proportionally more or less of the liquid.

Let's look at some of the labels that may appear on a vial of drug solution.

Here, we have a label for Oxytocin and we have in this vial 10 units and in this vial it is in a solution of 1 ml of liquid. The doctor has ordered 6 units out of the 10, so we need a fraction of 6 over 10.

We only need 0.6 of the vial or 60% of the vial, or 6/10ths of the vial if you like. So 6/10ths of one ml is 0.6 ml.

Here, we have another drug and in this vial we have 300 mg of drug and it is in a solution of 15 mls. The quantity that you see below is actually a simplified version the same fraction, but I suspect that the vial that the label is on here actually has 15 ml in it. 300 over 15 is proportionally the same as 20 over 1, the fraction has just been simplified for you.

So, this time, the doctor has ordered 200 mg of the drug. We will not need the whole vial, or all of the amount, and this time 200/300 is a fraction of two-thirds, so we need two-thirds of the bottle. Two-thirds of the 15 ml is equal to 10 ml. We will need 10 ml of solution.

Here, we have another drug, and this time we have 100 mg of the drug and it is dissolved in 5ml of liquid. Once again, we have another reduction that 20 mg per ml is a reduced form of that fraction, but as we can see from this label, near the bottom, this is actually a 5ml bottle.

So, the doctor this time the doctor has order 50 mg out of the 100 mg. So 50/100 mg is a fraction of 1/2. We will only need half of the bottle, and half of the bottle this time means half of the 5 mls which is 2.5 mls.

Last but not least, we have another drug label. This time, we have a Caffeine Citrate Injection and we have 60 mgs of this medication, which is dissolved in 3 ml of the liquid. Again, we have the 20 mg/1 ml as a simplification of that fraction. So the doctor this time has ordered 80 milligrams. That means we will be needing more than the one vial because the vial has only 3 ml in it and we will need 80 over 60. So 80 over 60 is more than 1, that is equivalent 4 over 3 and that is equal to one and one-third. We will need one and one-third of this medication. 4/3 and 3 ml is 4 milligrams. If we cancel the threes there, we will need 4 ml of the liquid.