Understanding ratio and proportion is crucial to solving various mathematical problems in pharmacy. A Ratio is a mathematical comparison of two numbers or quantities, often expressed as a fraction, division, or with a colon (:). Ratios are used to describe the relationship or proportion between the two quantities. In a ratio, the order of the numbers matters because it indicates which quantity is being compared to the other. Ratio and proportion are used in various fields, such as mathematics, science, finance, and everyday life, to compare quantities, express relationships, and solve various types of problems. They provide a way to describe relative sizes or proportions between two or more values.
Ratios are typically represented using one of the following expressions
As a fraction → a/b
Using a colon → a:b
Using the word “to” → a to b
As a decimal → a/b (if expressed as a fraction and then simplified)
In a ratio a:b
“a” is called the “antecedent” or “numerator,” representing the first quantity.
“b” is called the “consequent” or “denominator,” representing the second quantity.
Similarly, ratio and proportion are fundamental mathematical concepts in pharmacy that play a crucial role in various aspects of pharmaceutical calculations, including dose calculations, finding concentrations, and formulating compounds. These concepts enable the accurate determination of medication dosages, guide the preparation of mixtures, and contribute to ensuring patient safety.
Here are some applications of ratio and proportions in pharmacy calculations.
Calculating Doses
Note that with Approach B, it appears that the numerator did not originate from the denominator due to the difference in description. In a fraction, it is commonly understood that the numerator characterizes the denominator, and the denominator represents the whole. For example, in the fraction ¾, three represents three out of the four parts in the whole, which is divided into four parts. In terms of proportionality, this fraction signifies a relationship where the numerator is related to the denominator based on the expressed proportion. If another relationship is formed with similar characteristics to the first one, and if any of the values in the second relationship are unknown, proportionality allows for the easy solving of the unknown value.
Determining Concentration
Note that the expressions of proportions assume that the drug is distributed uniformly within the liquid, resulting in a homogeneous product where the drug is evenly distributed throughout the entire system. Therefore, if 1 mL contains 2.5 mg of the drug by proportion, then 2 mL will contain 5 mg of the drug, and so on. This concept has a wide range of applications. Another example is when you know the final concentration you require, but you need to determine how much of the raw materials or stock drugs you need to mix and in what proportion to achieve the desired concentration.
Adjusting Formula Quantities
Again, this is a perfect illustration of ratio and proportion. If you would like to test it, simply follow these steps. The master formula produces 100 capsules. If you use 30 g of Clindamycin in the formula, it means each capsule will contain 30 g/100 capsules = 0.3 g or 300 mg/capsule. If you were to perform the same operation with the new formula, the amount of Clindamycin per capsule should also be 300 mg/capsule.
Summary
Students must grasp the fundamental concepts of ratio and proportion as these mathematical principles are the bedrock of accurate medication dosing, compounding, and pharmaceutical calculations. Understanding ratio and proportion is essential because it empowers students to calculate precise medication doses tailored to individual patient needs, ensuring both safety and efficacy.
In pharmacy practice, ratios and proportions play a pivotal role in various scenarios. They enable students to determine the appropriate dosage of medications based on factors like patient weight, ensuring that patients receive the correct therapeutic doses. Additionally, these concepts aid in compounding medications and adjusting formula quantities, crucial skills for pharmacy professionals.
Moreover, ratio and proportion are central to pharmacy calculations, helping students find concentrations, dilute solutions, and prepare compounded medications accurately. With these skills, pharmacy students can confidently navigate the complexities of pharmaceutical practice, reduce the risk of medication errors, and provide high-quality patient care. In an evolving healthcare landscape, a solid understanding of ratio and proportion is indispensable for aspiring pharmacists to excel in their roles, safeguard patient well-being, and contribute to the advancement of pharmaceutical science and practice.
References
Ansel, H. C., & Stoklosa, M. J. (2016). Pharmaceutical Calculations (15th ed.). Wolters Kluwer Health, Lippincott Williams & Wilkins.
Ballington, D. A., & Fulcher, R. L. (2014). Pharmacy Calculations for Pharmacy Technicians. Paradigm Education Solution.
Troy, D. B., & Beringer, P. (Eds.). (2006). Remington: The Science and Practice of Pharmacy (21st ed). Lippincott Williams & Wilkins, Philadelphia.
Author: Dwight L. Baker (BPharm, MBA, MPH, Dip.Ed.)
Published: 2023- Sept- 20, Last updated 2024- Jan- 12