In this review, I’m going to show you how to solve dosage calculations using the ratio and proportion method. In my dosage calculations videos, I have used various methods like dimensional analysis and the desired over have formula method, but today we’re going to concentrate on the ratio and proportion method.
With this method, you’re going to set up an equation with ratios and solve for a particular part of the ratio that you don’t know. In the end, once you calculate your answer, these ratios will be equal and proportionate to each other.
Ratios are often expressed as fractions. We want to combine a known ratio and an unknown ratio, and this information will come from your problem.
For your known ratio, you create it by putting the dosage you have on hand over the volume you have on hand. This should be equal to the dose ordered, which is the dose that the provider has ordered, over X, which is what you’re solving for. This should be the amount to give.
There are some things I want you to remember about ratio and proportion that you must ensure before you solve the problems. First, make sure that the units of measurement are in the same order and match before cross-multiplying, as that’s how you solve these problems. For instance, if you have milligrams for the top unit of measurement for the known ratio but grams for the top unit of measurement for the unknown ratio, you must do some converting BEFORE you cross-multiply. See problem 2 for an example like this.
Ratio and Proportion Dosage Calculation Practice Problem Examples
Problem 1
Let me solve this problem so you can see what I mean. Our problem states:
The provider orders 25 milligrams (mg) by mouth twice daily (BID). You’re supplied with 50 milligrams (mg) per tablet. How many tablets per dose will you administer? (this is what we’re trying to figure out, which will be our X, the tablets)
Let’s first create our known ratio: the dosage we have on hand is 50 milligrams (mg), and the volume we have is one tablet. So it’s 50 mg over 1 tablet.
Next, create the unknown ratio: Remember, the known ratio should be equal to the unknown ratio in the end. Therefore, to set up the unknown ratio, write the dose ordered, which was 25 mg, and and put it over X (this is what we don’t know yet…the tablets per dose).
Next, cross-multiply: Before I cross-multiply, let’s check somethings first:
Are the unit measurements in the same order? They are. Do their units match? They do. So now I can cross-multiply.
50 times X equals 50x, and 25 times 1 equals 25. To get X by itself, divide 50 on both sides to cancel it out. Bring down your X and the equal sign, which gives us 0.5 tablets. That’s our answer, but let’s verify it to ensure it’s correct by plugging 0.5 into this equation and check the ratios. When you times 50 by 0.5, you get 25, and when you do 1 times 25, you get 25. Are these numbers equal? They are, so this is correct.
Problem 2
Now let’s tackle a problem that requires an extra step.
The provider orders 2 grams (g) intramuscular (IM) for one dose, and you’re supplied with a 1,000 milligram (mg) per 2 ml vial. The vial states that for every 2 ml you draw up, there are 1,000 milligrams, but we need to give 2 grams. (Note the units of measurement are different). How many milliliters per dose will you administer?
Let’s set up our ratios. First, the known ratio: We have 1,000 milligrams (mg), so place that over the volume, which is 2 milliliters (mL). Our unknown ratio is the dose ordered: The provider ordered 2 grams (g), and we’re solving for X, which is milliliters (mL) per dose.
Check if we can cross-multiply: The order is the same, but the units don’t match as we have milligrams and grams.
Thus, we need to convert using the metric table. We’ll convert 1,000 milligrams to grams. 1,000 milligrams equals 1 gram, which you must memorize from the metric table.
Replace 1,000 milligrams with 1 gram for the known ratio part, and now the units match. Cross-multiply: 1 times X equals 1X, and 2 times 2 equals 4. To isolate X, divide by 1, which leaves us with 4 milliliters. That’s our answer, but let’s double-check. Rewrite and cross-multiply: 4 times 1 equals 4, and 2 times 2 equals 4. They are equal, so the problem is correct.
That concludes this review. You may be interested in dosage calculation problems.