SOLVING DOSAGE AND CALCULATION PROBLEMS
In some health care settings, most drugs come from the pharmacy in the correct dose, ready to give to the patients. However, remember that you are the last check in the system and are responsible for making sure that the patient not only gets the right drug but also gets the right dose.  Always read each drug order carefully,  watching for decimal points and zeros.
            Sometimes a drug dose that you have on hand does not equal what you want to administer to the patient. You will need to calculate the correct drug dose from what you have on hand. The first thing you must do is write down all the information that you have and then label each number (that is, categorize each number as either have or want). For example, if you have Catepres (clonidine) 0.1 mg and you want to give 0.2 mg, first label all the information. Then you may proceed to plug the numbers into the following formulas and do the math. Finally, do the DIMS (does it makes sense?) test to see if the answer makes sense! You can use these formulas only when the drug dose that you have on hand is in the same measurement unit (for example, milligrams and milligrams) as the drug dose that you want to give.
 
Oral drugs
Formula 1. This formula works for drug calculations involving dry pills (tablets, capsules, caplets). If the drug order is for 440 mg of naproxen and you have tablets that each contain 220 mg of naproxen, how many tablets should you give? Here is the easy way to know: divide the number you want by the number you have.
 
 
                                            Want
                                           ---------- =Number of tablets to give!
                                            Have
 
                                     440 mg                                              44
                             So, ----------- =(chop off the end zeros) ---- = 2 tablets!
                                     220 mg                                              22
 
 
What happens if the dose of diazepam (Valium) you want is 15 mg and you have Valium 10-mg tablets? Use the formula:
 
                                                       15 mg        1
                                                       --------- = 1 --- tablets
                                                       10 mg        2
 
 
 
You can cut a tablet in half and give a half tablet only if the tablet is scored. A scored tablet is one that has a line etched into it marking the exact center. Cutting (or breaking) a tablet along the lines gives you two halves of equal known dosage. If you you or break a tablet that is not scored, the dose will not be correct, and you will have uneven halves. If tablets are not scored, call the pharmacy to see if the drug come either in a smaller strength or as a liquid.
            Other types of drugs that should not be cut or broken include capsules, long-acting or sustained-release capsules or tablets, and enteric-coated tablets. Cutting a capsule allows the powder or tiny beads inside to spill. Long-acting or sustain-release drugs are made so that small amounts of drug are release continuously throughout the day. Cutting this type of drug allows all of the drug to enters the patient’s system rapidly and may cause an overdose. Enteric-coated drugs are meant to dissolve and be absorb in the intestine rather than in the stomach. Cutting or crushing these drugs may not only cause stomach irritation, but the acid in the stomach may inactivate the drugs so they won’t work. Always look up any new drug or one you are not familiar with to see of there is any reason that it should not be cut.
 
Formula 2. This formula works for drug calculations involving oral liquids. These drugs may be called a suspension or an elixir (an old word for an alcohol-based liquid).


                                       Want
                                     ---------- x Liquid= Amount of liquid to give
                                       Have

If an order reads, “Give Benadryl (diphenhydramine) 50 mg” and the diphenhydramine kiquid comes in 25/5 mL, 5 mL is the amount of liquid in one dose that you have on hand. In this example:


                                         50 mg
                                        -----------x 5 mL= 2x5 mL= Give 10 mL
                                         25 mg

Be sure to label both the numerator and the denominator of the formula to double check that the two dosage measurements you are working with are the same.


Drugs given by injection
There are three major types of injectable drugs: intramuscular (IM), which is injected into a muscle; subcutaneous, which is injected into the fat below the skin; and intradermal (ID), which is injected just under the top part of the skin. All three types are parenteral forms of drug delivery that do not go through the gastrointestinal tract. These drugs may come in either single-dose containers (syringes, vials, or ampules) or multiple-dose bottles (vials).
            All injectable drugs are liquids, so they follow the same formula as formula 2 for liquid drugs. For example, the unit-dose syringe that you have contains meperidine (Demerol) 100 mg/mL, and you are ordered (want) to give 50 mg IM. How should you set up the problem? You would set it up the same way as for other liquid drugs.


                                   Want
                                  ---------- x Liquid= Amount to pull up into syringe
                                   Have


                                               50 mg                1
                                              --------- x 1 mL= -- = 0.5 mL IM
                                              100 mg               2




USING PROPORTIONS TO SOLVE FOR X
A fraction uses a division line (called a bar) or slash to describe a mathematic relationship between two numbers (for example, ½ or ½ ). A proportion describes an equal mathematic relationship between two sets  of numbers (for example, ½ = 2/4). If you look closely, you will see that, when you multiply diagonally across the equal sign, 1x4 equals 2x2! Another way of thinking of the proportion is that 1 is related to 2 in the same way as 2 is related to 4.
            You can use proportions to solve for X, the unknown, as an alternate approach to drug calculations, especially if you don’t want to memorize a formula. When you write a proportion as a set of fractions, be careful to label each piece of the equation. For example:
 
 
                                                      1 case          3 cases
                                                      ------------- = --------------
                                                     12 bottles     36 bottles
 
 
            Notice that in the fractions, both numerators identify the number of “cases” and both denominators identify the number of bottles. All fractional proportions must be set up this way for you to obtain the correct answer.
            What if a piece of the proportion is missing? This is what happens when the prescriber orders a drug strength that is different  from the one you have on hand. To figure out how many of the drug tablets you have on hand will be equal to the strength that is ordered, set up a proportion to solve for the missing piece.
            For example, an order reads “Give 500 mg of Primidone by mouth (orally)”, and you have on hand primidone 250 mg per one caplet. How many caplets will you have to give the patient to equal 500 mg? Set the problem up as:
 
 
                                                      250 mg        500 mg
                                                       ------------ = -------------
                                                       1 caplet      X caplets
           
 The X is what you need to give. By figuring out the “X” correctly, both sides of the proportion will be equal. You can cross out (“cancel”) the word “mg” in the proportion equation because they are both known numbers. That leaves you with the word “caplets” as the missing part of the proportion. Therefore you answer must be the number od caplets needed.
            Maybe you can do this in your head, but you need to understand how you get the 2 caplets. First, cross multiply to set up the equation 250 X = 500. An easy way to work the problem is to remember that any time you bring the number in front of the X (250 in this case) across the equals sign (or bring the 250 to the other side of the equals sign), it means divide.
 
 
                                                                 500
                                                 So, X = ---------- = 2 caplets
                                                                 250


            Solving liquid drug problems by proportion involves two steps, but they are relatively easy. First label what you have and what you want, as usual.  Then, set up the proportion. For example, you want to give diphenhydramine (Benadryl) 100 mg, and you have diphenhydramine 50 mg per mL. How would the proportion be set up?
            Step 1:
 
                                            50 mg      100 mg
                                            ---------- = ----------- (cancel the mg)
                                             1 mL        X mL
 
 
 
                                             100                                                    10
                   50 X = 100 or  ------ (chop the zeros); 5 X = 10 or ----- ; 10/5=2
                                              50                                                       5
 
 
            Step 2: Take the answer from step 1 and multiply that times the liquid dose that you have:
 
 
                                              (Liquid = 1mL): 2x1mL = 2 mL