Fractions, Decimals, and Percentages
Table of Contents
Fractions
A fraction represents a part of a whole or a ratio between two numbers. It consists of two parts:- Numerator (top number): How many parts you have.
- Denominator (bottom number): How many equal parts the whole is divided into.
- ½ means 1 part out of 2 equal parts.
- ¾ means 3 parts out of 4 equal parts.
Where are fraction calculations used in Pharmacy?
- Used in dosage calculations (e.g., ½ tablet, ¼ mg).
- Required for compounding medications (mixing ingredients in fractional ratios).
- Essential for dilutions and concentrations (e.g., 1:1000 solutions).
Decimals
A decimal is another way to express fractions or parts of a whole.- Example: 0.5 = ½, 0.25 = ¼
- 3/4 = 3÷4 = 0.75
Where are fraction calculations used in Pharmacy?
- Dosing Calculations
- Injectable and Liquid Medications
- Compounding and Measurements
- Inventory and Pricing
Percentages
A percentage is a fraction out of 100.- Example: 25% = 25/100 = 0.25
- Decimal to Percent: Multiply by 100 (e.g., 0.8 = 80%)
- Percent to Decimal: Divide by 100 (e.g., 45% = 0.45)
- Example: 20% of 150 = 0.20 × 150 = 30
Where are percentage calculations used in Pharmacy?
- Strength of Solutions and Creams (Concentration)
- Dilutions
- Compounding Formulas
- Bioavailability or Efficacy Calculations
- Markup, Discounts, and Insurance Copays
- Inventory Shrinkage or Expiration Rates
Types of Fraction Calculations
Pharmacy fraction calculations are commonly tested in pharmacy exams, technician certifications, and practical settings.These questions assess your ability to accurately measure, convert, and calculate medication dosages. Here are the types of questions you might encounter:
Basic Fraction Operations
Addition, subtraction, multiplication, and division of fractions.- Example: What is ½ + ¼?
- Example: Multiply ⅔ × ⅜.
Converting Between Fractions and Decimals
Converting fractions to decimals and decimals to fractions for dosage calculations.- Fractions ↔ Decimals (for precise measurements)
- Fractions ↔ Percentages (for concentrations)
Dosage Calculations Involving Fractions
Determining the correct dose based on patient weight or concentration.Example: A drug is ¾ mg per kg.
What dose should a 60 kg patient receive?
1. Addition of Fractions (+)
Rule: Fractions must have the same denominator (bottom number). If not, find the Least Common Denominator (LCD).(The Least Common Denominator (LCD) is the smallest number that two or more denominators can divide into evenly (without a remainder). It’s basically the Least Common Multiple (LCM) of the denominators.)
A prescription requires mixing ½ tsp of Drug A and ¼ tsp of Drug B. What’s the total volume?
A prescription requires administering ⅔ mL of a liquid medication in the morning and ¼ mL in the evening. What is the total daily dose in mL?
2. Subtraction of Fractions (-)
Rule: Just like addition, fractions must have the same denominator (bottom number).If not, find the Least Common Denominator (LCD).
A ⅞ oz bottle of medication is used. If ⅜ oz is administered, how much remains?
A pharmacist prepares 5⁄6 of a liter of a solution. If 1⁄3 of a liter is used for a patient, how much solution is left?
3. Multiplication of Fractions (x)
Rule: Multiply numerators, then denominators. Simplify if possible.Remember: ❌ You don’t need an LCD (Least Common Denominator) for multiplication of fractions.
A patient needs to take ⅔ of a ½ tablet. How much of the whole tablet is that?
A pharmacist mixes ¾ mL of one drug with ⅖ of another solution. What is the total amount used from the second drug?
4. Division of Fractions (÷)
Rule: To divide fractions, multiply the first fraction by the reciprocal of the second.
Converting between Fractions and Decimals
Fraction to Decimal Conversion
- To convert a fraction to a decimal, divide the numerator by the denominator.
Decimal to Fraction Conversion
- Identify the place value of the last digit (tenths, hundredths, thousandths).
- Write the decimal as a fraction using that place value.
- Simplify the fraction if possible.
Converting between Fractions and Percentages
Fraction to Percentage Conversion
To convert a fraction to a percentage:
- Divide the numerator by the denominator to get the decimal equivalent.
- Multiply the decimal by 100 to get the percentage.
Quick Conversions Fraction to Percentage
| Fraction | Decimal | Percent |
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ¾ | 0.75 | 75% |
| ⅓ | 0.33 | 33% |
| ⅔ | 0.66 | 66% |
| 1/10 | 0.1 | 10% |
Percentage to Fraction Conversion
To convert a percentage to a fraction:- Write the percentage as a fraction by placing the percentage number over 100.
- Simplify the fraction if possible.
Quick Conversions Percentage to fraction
| Percentage | Fraction Form | Simplified |
| 25% | 25/100 | 1/4 |
| 75% | 75/100 | 3/4 |
| 10% | 10/100 | 1/10 |
| 12.50% | 12.5/100 | 1/8 |
Dosage Calculations Involving Fractions
Dosage calculations involving fractions are common in healthcare settings, especially when measuring medications.Here’s a step-by-step guide to solving them:
- Multiply the ordered dose by the available concentration (often a fraction).
- Use common denominators when adding/subtracting doses.
- Convert fractions to decimals (or vice versa) for easier math.
Fractional Dose Adjustments / Applications in Pharmacy operations
Fractional Dosage Based on Weight
Many medications (especially for pediatric or critically ill patients, geriatrics) are dosed per kilogram (kg) or pound (lb) of body weight. Since patient weights are often measured in fractions (e.g., 12.5 kg, 24¾ lb), dosage calculations may involve multiplying or dividing fractions.Key Formula:
Dose = Weight (kg or lb) × Dosage per unit weightExample 1: Simple Fractional Weight Calculation
- Physician Order: Give Amoxicillin 20 mg/kg/day in divided doses every 8 hours.
- Patient weight: 14½ kg
- Calculate the total daily dose (TDD).
Example 2: Fractional Dosage Per Pound
- Physician Order: Drug X ½ mg/lb twice daily.
- Patient weight: 22¾ lb
- Calculate each dose in mg.
Example 3: Adjusting a Dose Due to Renal Impairment
- Physician Order: Normal dose = 1.5 mg/kg, but reduced to ⅔ of the dose for renal impairment.
- Patient weight: 60⅓ kg
- Calculate the adjusted dose.
Liquid Medication Measurements with Fractions
Liquid medications often require measuring fractional doses, especially in pediatrics, geriatrics, and critical care.These calculations involve milliliters (mL), teaspoons (tsp), tablespoons (Tbsp), drops, or other volume units, involving fractions.
Key Concepts
Conversions Between Units:
- 1 teaspoon (tsp) = 5 mL
- 1 tablespoon (Tbsp) = 15 mL
- 1 ounce (oz) = 30 mL
Common Fractional Measurements:
- ½ tsp = 2.5 mL
- ¼ tsp = 1.25 mL
- ¾ tsp = 3.75 mL
- 1½ tsp = 7.5 mL
Example 1: Calculating mL from mg with Fractional Concentration
- Physician Order: Amoxicillin 187.5 mg PO every 8 hours.
- Available: 250 mg/5 mL suspension.
- Question: How many mL should be administered per dose?
Example 2: Measuring a Small Fractional Dose (Pediatrics)
- Physician Order: Digoxin 62.5 mcg PO daily.
- Available: 0.05 mg/mL elixir.
- Question: How many mL should be given?
Example 3: Complex Fractional Dose (Weight-Based Liquid Medication)
- Physician Order: Ibuprofen 7.5 mg/kg for a child weighing 10¼ kg.
- Available: 100 mg/5 mL suspension.
- Question: How many mL should be given?
Example 4: Fractional Measurement in Drops (gtts)
- Physician Order: Administer ⅜ tsp of a liquid medication.
- Available: A dropper that delivers 20 gtt/mL.
- Question: How many drops (gtts) should be given?
Example 5: Measuring a Fractional Teaspoon Dose
- Physician Order: Acetaminophen 1¼ tsp every 6 hours.
- Available: 160 mg/5 mL suspension.
- Question: How many mL should be given per dose?
Fractional IV Drip Rate Calculations
Fractional IV Drip Rate IV drip rate calculations determine how many drops per minute (gtt/min) a patient should receive based on the prescribed infusion rate (mL/hr or mL/min) and the drop factor (gtt/mL) of the IV tubing.Sometimes, these calculations involve fractions due to:
- Fractional infusion rates (e.g., 62.5 mL/hr)
- Drop factors with fractions (e.g., 10, 15, 20, or 60 gtt/mL)
- Time adjustments (e.g., infusing over 4.5 hours)
Example 1: Fractional Infusion Rate
- Physician Order: Infuse 125.5 mL/hr using IV tubing with a drop factor of 15 gtt/mL.
Example 2: Fractional Time Calculation
- Physician Order: Infuse 250 mL over 3.5 hours with a drop factor of 20 gtt/mL.
Example 3: Pediatric Fractional Dose
- Physician Order: Infuse 37.5 mL/hr for a child using microdrip tubing (60 gtt/mL).
DIY (Do It Yourself) Questions
Fractional IV Drip Rate Questions
Q 1: A patient needs 250 mL of IV fluid over 2.5 hours. The IV tubing delivers 20 drops/mL. What is the drip rate in gtt/min?
Answer: ______
Q 2: An IV order calls for 500 mL over 3¾ hours. The drop factor is 15 gtt/mL. Calculate the drip rate in gtt/min.
Answer:______
Liquid Medication Measurements with Fractions Questions
Q 3: A prescription calls for ¾ teaspoon of medication. How many mL should be dispensed?
Answer:______
Q 4: A pediatric patient is prescribed 1½ tablespoons of a cough syrup. How many mL is this?
Answer:______
Fractional Dosage Based on Weight Questions
Q 5:
-
Physician Order: 5 mg/kg of Drug A
-
Patient weight: 22 lb
-
Available: 50 mg/mL
-
How many mL should be given?
Answer:______
Q 6: A 33 lb child needs 2.5 mg/kg of Drug B. How many mg is the dose?
Answer:______
Fraction to Decimal Conversion Practice Questions
Q 7: A pharmacist measures ⅛ tsp of a concentrated solution. What is this volume in decimal form?
Answer: ________
Q 8: A dose of ⅗ mL is required for a pediatric patient. What is this in decimal form?
Answer: ________
Decimal to Fraction Conversion Practice Questions
Q 9: A label reads “Take 0.75 tsp daily.” What is this in fraction form?
Answer: ________
Q 10: A pharmacist prepares 0.2 grams of a powdered drug. What is this in fraction form?
Answer: ________
Fraction to Percentage Conversion Practice Questions
Q 11: A prescription calls for a ¼ strength solution. What is the concentration as a percentage?
Answer: ________
Q 12: If a topical cream contains ⅖ of active drug, what percentage of the cream is active?
Answer: ________
Percentage to Fraction Conversion Practice Questions
Q 13: A medication label states “Solution contains 80% alcohol.” Express this concentration as a fraction.
Answer: ________
Q 14: A cream is labeled as containing 12.5% hydrocortisone. What is the fractional equivalent?
Answer: ________
