Most drug dosage calculation workbooks will show a variety of methods for working drug dosage problems, including formulas, ratio and proportion, and dimensional anaylsis.  You can use any of these methods as long as you get the correct answer and that your work is reasonable and supports the answer.  However, the only method illustrated in all example problems will be ratio and proportion.

Ratio and proportion shows the relationship between two items.  You can adjust the amount of one item as much as you want and as long as you make the same adjustment in the other item, you have maintained the proportional relationship they have.  If you have ever done any cooking where you "doubled the recipe", you know that as long as you doubled all ingredients you kept things in proportion and the recipe would be OK.  You could not, however, double some ingredients and not others. 

To further illustrate, using a non-dosage example, let's suppose you are making a favorite dish and the recipe calls for two apples and 1 1/2 teaspoons of sugar.  Let's suppose that you have three apples and you want to use them all.  How much sugar would you need?  

Setting up a ratio will help you solve this problem.  A ratio can be set up in a liner fashion or in a top to bottom fashion.  

Example of linear ratio:

2 apples: 1 1/2 tsp sugar :: 3 apples : X tsp sugar

I prefer the top to bottom ratio because I think it makes it easier compare the labels or units of measurement to assure you have the right components in the right places.

   2  apples       =      3 apples
1 1/2 tsp sugar        X tsp sugar

Notice that if you put apples on the top on the left, you must put apples on the top on the right.

You now solve for "X" by cross multiplying the top on left to the bottom on the right and the bottom on the left to the top of the right.

  2 x X = 1.5 x 3
     2 X = 4.5
 
  2X  = 4.5
   2       2

    X  = 2.25 

So if you use 2 1/4 tsp sugar with the 3 apples, you will keep the same proportion of sugar and apples and your receipe should be OK.

This is the same procedure we will use in all of the drug dosage problems with just a couple of exceptions.  The most common problems students make in calculations are (1) doing arithmatic without an appropriate set-up or (2) using ratio and proportion without putting in the labels.  Without the labels it is very easy to put the numbers on the right in the wrong place.  It can also make it difficult to know what you have when you have completed the calculation if you don't have the labels in place. 

I strongly, strongly, strongly encourage you to set up a ratio by setting up the left side and then putting the labels in on the right side first.  Once the labels are in place, then go back to your problem to see what numbers you need to "plug in" on the right.  If you just start doing arithmatic without setting things up, you will make mistakes!!!

Other common problems and how to avoid them
  1. Arithmatic errors:  Remember you cannot use a calculator on the first two drug dosage tests.  You need to practice basic arithmatic skills.  Errors are commonly made when the work is not nice and neat and lined up.  Another common arithmatic error is decimal errors. Review in the workbook how to divide and multiply decimals.
  2. Trying to work with big numbers:  Reduce the big numbers when possible.  Working with smaller numbers will reduce the chance of error.  Remember, however, you cannot reduce across an equation.  You can only reduce top to bottom numbers.
  3. Careless mistakes:  Pay attention to what you are doing.  Students will commonly mis-write numbers---problem says 1000 mg and they set up with 100 mg, etc.
  4. Use common sense.  Think about what you think an answer might possibly be before you start work.  This should then alert you to an error.  For example, suppose you have 75 mL in an IV that is infusing at 125 mL/hr and you are asked to determine how long it will take for the 75 mL to infuse.  75 is less than 125; therefore, your answer would have to be something less than one hour.  If your answer is more than an hour, you know you have made a mistake somewhere.  Or suppose you have to give 450 mg of a medication and you have 300 mg tablets.  450 is bigger than 300; therefore, your answer would have to be more than one tablet.  Or if you end up with an answer that sounds unreasonable, such as giving 20 tablets of something or giving 8000 mL of an IV, go back and check your work--you have made a mistake somewhere!
  5. Mislabeling answer:  When you set up a ratio and you have a label for the "X" of the ratio, then when you solve for X, look at the ratio for the answer label that goes with that X.  A common example of an error is a ratio that has "X hours" in the ratio and students solve for X and then label answer mL/hr instead of hours.  A wrong label to a correct numerical answer is a wrong answer and there is no partial credit!!
  6. With labels such as mg/kg or mcg/kg/min, students sometimes have difficulty with "when do I multiply and when do I divide" and also difficulty with final labels to such problems. Remember that the slash (/) represents "per" and it is per one of something if there is no other number there.  For example, 3 mg/kg means 3 milligrams per kilogram or 3 milligrams for every one kilogram. 3 mcg/kg/min would be 3 milligrams for every one kilogram for every one minute.  

To use a non-dosage example:  Suppose you go shopping and buy 3 dresses that cost $60 per dress.  How much did you spend?  You would automatically be able to do that in your head, knowing that you had to multiply the 3 by 60, and give me an answer of $180 or 180 dollars; you would not say 180 dollars per shirt.  Or you spent $250 for shirts that cost $50 per shirt.  How many shirts did you buy?  You automatically would divide $250 by $50 and give an answer of 5 shirts. 

The dose problems are just this simple.  You have 60 mg/kg; what is the dose for 3 kg?  To get rid of that "per" label and just know the total amount, we multiply by the 3.  You have 60 times 3 or 180 mg; not 180 mg/kg.  It cannot be 60 mg/kg and 180 mg/kg both.  So just like the dress example, we had a per unit problem (per dress in the dress problem and per kilogram in this problem) and we multiplied to get rid of the "per". 

You have 250 mcg.  What is the mcg/kg dose for a 50 kg patient?  Here we are needing to add in the "per" label, or we are "taking it down" to a smaller unit; therefore, we divide.  Just as we divided the $250 by $50 to get $5 per shirt ($5/shirt), we will divide the 250 mcg by 50 kilograms to get 5 mcg for every one kilogram or 5 mcg/kg.