🧮

Pharmacy Math Concepts Overview

Jul 3, 2025

Overview

This lecture series covers essential pharmacy technician math concepts, including basic math skills, ratios/proportions, conversions, day supply, concentrations, dilutions, allegations, IV flow rates, temperature conversions, and weight-based dosage calculations, with step-by-step methods and practical examples for the PTCB exam.

Basic Math Skills: Fractions, Decimals, and Percentages

  • A fraction represents a part of a whole: numerator (top) is the part, denominator (bottom) is the whole.
  • Equivalent fractions can be found by multiplying/dividing numerator and denominator by the same number.
  • Improper fractions have numerators greater than denominators and can be converted to mixed numbers.
  • To multiply fractions, multiply numerators and denominators, then reduce.
  • Decimals represent fractions based on 10; left of the decimal is whole, right is decimal fraction.
  • Line up decimal points when adding/subtracting decimals.
  • To write a decimal as a fraction, name it by its place value (e.g., 0.35 = 35/100).
  • Percentages represent numbers per 100; convert by moving decimal two places or adjusting the denominator.
  • Fraction, decimal, and percentage equivalents: 1/2 = 0.5 = 50%; 1/4 = 0.25 = 25%.

Ratios and Proportions

  • A ratio compares two numbers (e.g., 5:100 or 5/100).
  • A proportion shows two equal ratios or equivalent fractions.
  • Solve proportions by setting up equal fractions, cross-multiplying, and dividing to find an unknown.

Conversions

  • Conversions change one measurement unit to another (e.g., grams to milligrams).
  • Memorize key equivalents: 1g = 1000mg, 1kg = 2.2lb, 1L = 1000mL, 1tsp = 5mL, 1oz = 30mL.
  • Convert using fractions or proportions, canceling units as needed.

Day Supply Calculations

  • Day supply = total quantity dispensed ÷ amount used per day.
  • For solids: multiply dose per day by days; for liquids, inhalers, drops, or injectables, convert all quantities to matching units before dividing.
  • Insulin expires 28 days after opening regardless of remaining content.

Concentrations

  • Concentration = amount of drug ÷ total product volume/weight.
  • Express as drug strength (e.g., mg/mL), percentage (grams per 100mL or 100g), or ratio (e.g., 1:1000).
  • Use equivalent fractions, cross-multiply and divide to find unknowns.

Dilutions

  • Dilution increases volume, reducing concentration but not the amount of active ingredient.
  • Use formula: Q₁×C₁ = Q₂×C₂ (quantities/volumes and concentrations must match in units).
  • If three values known, solve for the fourth.

Allegation Calculations

  • Used to mix two concentrations to achieve a desired new concentration.
  • Ratio method: Subtract DC-LC and HC-DC to get parts, sum parts, use fractions to find volumes needed.
  • Tic-tac-toe method: Place HC, LC, DC in a grid, subtract diagonally, sum, and use similar fractions to allocate amounts.

IV Flow Rates

  • Flow rate = volume given per unit time (e.g., mL/hr or drops/min).
  • Drop factor (gtts/mL) depends on IV set (macro = fewer, micro = more drops/mL).
  • Use unit cancellation or proportions to solve for time, volume, or rate.

Temperature Conversions

  • Fahrenheit (F) and Celsius (C) scales; conversions require formula, not ratio:
    • C = (F - 32) ÷ 1.8
    • F = (C × 1.8) + 32

Weight-Based Dosage Calculations

  • Dosage often based on weight (mg/kg or mg/kg/day).
  • Convert pounds to kilograms: kg = lb ÷ 2.2.
  • Total dose = weight (kg) × dose (mg/kg); for divided doses, split by number given per day.

Key Terms & Definitions

  • Numerator — Top part of a fraction (the portion).
  • Denominator — Bottom part of a fraction (the whole).
  • Proportion — Two equivalent ratios or fractions.
  • Concentration — Amount of drug in a given total of product.
  • Dilution — Reducing concentration by adding more volume.
  • Allegation — Mixing two concentrations to get a new desired one.
  • IV Flow Rate — Volume of IV solution delivered per unit of time.
  • Drop Factor — Number of drops needed for 1 mL (gtts/mL).

Action Items / Next Steps

  • Memorize common conversion factors for weight, volume, and length.
  • Practice setting up and solving ratio, proportion, and concentration problems.
  • Review and apply formulas for temperature conversion and weight-based dosage.

Full transcript