Ratio and proportion

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Chapter: Pharmaceutical Drugs and Dosage: Pharmacy math and statistics

Ratio represents a quantitative relationship between two quantities.

Ratio and proportion

Ratio represents a quantitative relationship between two quantities. It can be expressed as a fraction (e.g., ½, ¼, and so on) or as a ratio (e.g., 1:2, 1:4, and so on).

A proportion represents the equality of two ratios. Thus,


The equality of two ratios can be checked by cross multiplying the numerator of the first with the denominator of the second. For example,

1/2 = 2/4 but 1/2 ≠ 2/6


1× 4 = 2 × 2 but 1× 6 2 × 2

Proportions are commonly utilized to find an unknown quantity or variable when three other related quantities or variables are known. For example,

If x/4 = 2/9 , then x = (2 × 4)/9 = 8/9

In these calculations, caution must be exercised to ensure that the numera-tors and denominators have the same units on both sides of the proportion. For example, if the pharmacist wishes to substitute 100-mg strength tablets with 200-mg strength tablets for a patient who was prescribed four tablets of 100-mg strength, then the number of tablets of 200-mg strength can be calculated as:

A good practice in carrying out these calculations is to always label the units in the proportions.

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