In pharmacy practice a pharmacist occasionally needs to be reduce or enlarge formulas of a pharmaceutical preparation. Reducing a formula involves calculating the amount of each ingredient to be used to make a smaller amount than the original formula. While enlarging a formula involves calculating the amount of each ingredient to make a larger amount than the original formula.
Pharmaceutical preparations can be reduced or enlarged using ratio and proportion, dimensional analysis, and the factor method. While reducing or enlarging a formula it is essential to maintain the proportion of all ingredients.
Factor Method
Step 1: Determine factor by which to reduce or enlarge the formula.
Factor = (quantity of formula desired ÷ quantity of formula given)
Step 2: Multiply quantity of each ingredient by the factor.
For example, if a formula is provided for 1000 ml solution, but you wish to make 100 ml solution.
The factor in this case would be 0.1. A factor greater than one indicates the formula needs to be enlarged, a factor less than 1 indicates the formula needs to be reduced.
Ratio and Proportion Method
Ratio: the relative magnitude of two like quantities is a ratio, which is expressed as a fraction. Certain basic principles apply to the ratio, as they do to all fractions.
a. When the two terms of a ratio are multiplied or divided by the same number, the value of the ratio is unchanged.
b. Two ratios with the same value are equivalent. Equivalent ratios have equal cross products and equal reciprocal and if two ratios are equal, then their reciprocals are equal.
Proportion: the expression of the equality of two ratios is a proportion. The product of the extremes is equal to the product of the means for any proportion.
Examples
1. What quantities should be used to prepare 100 g of “Diaper paste” from the following formula?
Rx
Mineral oil = 6 parts
Nystatin powder = 1 part
Hydrocortisone powder = 2 parts
Zinc oxide ointment = 200 parts
Label: diaper paste, maximum 1 year expiration
Total number of parts = 200 + 2 + 1 + 6 = 209 parts
For each of the ingredients, the ratio is then set up, such as:
6 parts/ 209 parts = x g/ 100 g, with x = 2.87 g for mineral oil or
1 part/ 209 parts = y g/ 100 g, with y = 0.48 g for nystatin powder.
2. If 240 mL of a cough syrup contains 480 mg of dextromethorphan hydrobromide, then what mass of drug is contained in a child’s dose, 1 teaspoon (5 mL) of syrup?
240 ml/ 5 ml = 480 mg/ x mg
x = 10 mg
3. Using a vial containing 200,000 units of penicillin G potassium, how many milliliters of solvent should be added to the dry powder in preparing a solution having a concentration of 25,000 units/ ml?
25000 units = 1 ml
200000 units = x ml
x = 200000 units/ 25000 units
x = 8 ml
4. The label of dry powder package of Cefprozil for oral suspension directs the pharmacist to add 72 ml of purified water to prepare 100 ml of suspension. If the package contains 2.5 g of Cefprozil, how many milligrams of the drug would be contained in each teaspoonful dose of the constituted suspension?
2.5 g = 2500 mg
2500 mg/ x mg = 100 ml/ 5ml
x = 125 mg cefprozil
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