Pharmaceutical calculations

Principles of pharmacy (lec1)

Pharmaceutical calculations
is the area of study that applies the basic principles of mathematics to the preparation and safe and effective use of pharmaceuticals.

Common fractions are portions of a whole, expressed at 1?3, 7?8, and so forth. They are used only rarely in pharmacy calculations nowadays.

Examples:
If the adult dose of a medication is 2 teaspoonsful (tsp.), calculate the dose for a child if it is 1?4 of the adult dose.

If a child’s dose of a cough syrup is 3?4 teaspoonful and represents 1?4 of the adult dose, calculate the corresponding adult dose.

NOTE: When common fractions appear in a calculations problem, it is often best to convert them to decimal fractions before solving.


A decimal fraction is a fraction with a denominator of 10 or any power of 10 and is expressed decimally rather than as a common fraction. Thus,1/10 is expressed as 0.10 and 45/100 as 0.45. It is important to include the zero before the decimal point. This draws attention to the decimal point and helps eliminate potential errors. Decimal fractions often are used in pharmaceutical calculations.
To convert a common fraction to a decimal fraction, divide the denominator into the numerator.


The term percent and its corresponding sign, %, mean ‘‘in a hundred.’’ So, 50 percent (50%) means 50 parts in each one hundred of the same item.

The relative magnitude of two quantities is called their ratio. Since a ratio relates the relative value of two numbers, it resembles a common fraction except in the way in which it is presented. Whereas a fraction is presented as, for example, 1?2, a ratio is presented as 1:2 and is not read as ‘‘one half,’’ but rather as ‘‘one is to two.’’


When two ratios have the same value, they are equivalent.
e.g., 2?4 = 4?8,
2 * 8 (or 16) = 4 * 4 (or 16).


A proportion is the expression of the equality of two ratios. It may be written in any one of three standard forms:



Examples:
If 3 tablets contain 975 milligrams of aspirin, how many milligrams should be contained in 12 tablets?

If 3 tablets contain 975 milligrams of aspirin, how many tablets should contain 3900 milligrams?
If 12 tablets contain 3900 milligrams of aspirin, how many milligrams should 3 tablets contain?

• Dimensional Analysis
In solving problems by dimensional analysis, the student unfamiliar with the process should consider the following steps:
Step 1. Identify the given quantity and its unit of measurement.
Step 2. Identify the wanted unit of the answer.
Step 3. Establish the unit path (to go from the given quantity and unit to the arithmetic answer in the wanted unit), and identify the conversion factors needed.
Step 4. Set up the ratios in the unit path such that cancellation of units of measurement in the numerators and denominators will retain only the desired unit of the answer.
Step 5. Perform the computation by multiplying the numerators, multiplying the denominators, and dividing the product of the numerators by the product of the denominators.


How many fluidounces ( fl. oz.) are there in 2.5 liters (L)?
Step 1. The given quantity is 2.5 L.
Step 2. The wanted unit for the answer is fluidounces.
Step 3. The conversion factors needed are those that will take us from liters to fluidounces.
As the student will later learn, these conversion factors are:
1 liter _ 1000 mL (to convert the given 2.5 L to milliliters), and
1 fluidounce _ 29.57 mL (to convert milliliters to fluidounces)
Step 4. The unit path setup: