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newSchoolWorks.com › VoTechWorks › Health & Personal Services › Pharmacy Technician › Pharmacy Calculations and Order Entry › Lesson 12
HLT-PHAR41-03 · Lesson 12 · 17 clock hours · practice

Calculations competency lab

Objective. Pass a timed calculations exam covering every problem type in the course.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed pharmacist or by a certification or approval body. It is a study draft and may contain errors. Do not use it to make decisions about any patient or medication. Always follow your instructor, your supervising professional, and current official references and regulations.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

Calculations Competency Lab: Preparing for Your Final Exam

This lab brings together every calculation type you have practiced throughout the course. Your goal is to demonstrate mastery by scoring at least 90% on a timed calculations exam. This reading reviews the most important problem types, reminds you of the formulas you need, and shows you how to check your own work before moving on.

Why Accuracy Matters

Calculation errors in pharmacy can cause serious patient harm. A dose that is ten times too high or too low can be life-threatening. As a pharmacy technician, you are a critical checkpoint before medication reaches the patient. Pharmacists verify your work, but a clean, correct calculation gives the pharmacist the best chance of catching any error—and your goal is to have none.

Problem Types Covered on the Exam

1. Ratio and Proportion

Use this method whenever you know a relationship between two quantities and need to find an unknown. Set up your proportion so that matching units are in the same position on each side, cross-multiply, then divide.

Example relationship: 250 mg per 5 mL. How many mL for 375 mg?

2. Dimensional Analysis (Factor-Label Method)

Write the starting value with its unit, then multiply by conversion fractions that cancel unwanted units one at a time until only the desired unit remains. This method is especially useful for multi-step conversions.

3. Percent Strength and Concentration

Percent weight-in-volume (w/v) means grams of solute per 100 mL of solution. A 1% solution contains 1 g per 100 mL. Percent weight-in-weight (w/w) means grams of solute per 100 g of product.

4. Alligation

Use alligation when you must mix two products of different strengths to reach a desired intermediate strength. Place the desired strength in the center of a tic-tac-toe grid, the higher strength upper left, and the lower strength lower left. Subtract diagonally to find the number of parts of each.

5. Days Supply

Divide the total quantity dispensed by the amount used per day. Always confirm whether the sig uses metric or household units and convert as needed.

6. Powder Volume

When a powder for reconstitution is dissolved, the powder itself adds volume. Final volume minus powder volume equals the diluent volume you must add.

7. Pediatric and Weight-Based Dosing

Convert the patient's weight to kilograms if given in pounds (divide by 2.2). Multiply the weight in kg by the dose in mg/kg to find the total dose.

8. IV Flow Rate

To find drops per minute: (Volume in mL × Drop factor in gtt/mL) ÷ Time in minutes.

To find mL per hour for an infusion pump: Volume in mL ÷ Time in hours.

9. Business Math: Markup and Discount

Selling price = cost + markup. Markup rate = markup ÷ cost × 100. Discount = original price × discount rate.

10. Roman Numerals and Sig Code Conversions

Review common abbreviations (sig codes) and Roman numerals I through XXX.

Exam Strategy: Error Analysis

Before the final exam, practice finding your own errors. When you miss a problem during review, ask:

Keeping a personal error log—writing down each mistake and why you made it—is one of the most effective study tools available.

Unit Conversions You Must Know

Timed Practice Tips

During the timed practice session, simulate real exam conditions: no notes, a basic calculator (if your program allows one), and a set time limit. Work at a steady pace. If a problem stumps you, mark it and move forward—returning to hard problems after finishing easier ones preserves your score on questions you know.

Show all work in a clear, organized column. Even if you make an arithmetic slip, a well-organized setup may reveal the error before you write your final answer.

The 90% Standard

A score of 90% on the calculations exam means you answered at least 9 out of every 10 questions correctly. This benchmark reflects the accuracy expected of a working pharmacy technician. If you do not reach 90% on your first attempt, review the categories where you lost points, complete targeted practice, and retake the exam. Persistent, deliberate practice on weak areas is the fastest path to passing.

Key terms8

Ratio and proportionA method of solving for an unknown quantity by setting two equivalent fractions equal to each other and cross-multiplying.
Dimensional analysisA calculation method that uses a chain of conversion fractions to cancel unwanted units until only the desired unit remains.
Percent weight-in-volume (w/v)A concentration expression meaning the number of grams of solute dissolved in every 100 mL of solution.
AlligationA mathematical method used to determine the proportions of two products of different strengths needed to prepare a product of an intermediate desired strength.
Days supplyThe number of days a dispensed quantity of medication will last a patient based on the prescribed directions for use.
Powder volumeThe volume that a dry powder contributes to the final solution after reconstitution; calculated as final volume minus the volume of diluent added.
Drop factorThe number of drops per milliliter that an IV administration set is calibrated to deliver, expressed as gtt/mL.
Weight-based dosingCalculating a medication dose by multiplying the patient's weight in kilograms by the prescribed dose per kilogram.

Worked examples4

1. A prescription calls for amoxicillin 400 mg. The suspension on hand is labeled 250 mg/5 mL. How many milliliters should be dispensed per dose?
  1. Set up a proportion with matching units in matching positions: 250 mg / 5 mL = 400 mg / x mL
  2. Cross-multiply: 250 × x = 400 × 5, which gives 250x = 2,000
  3. Divide both sides by 250: x = 2,000 ÷ 250
  4. x = 8 mL
Answer: 8 mL per dose
2. A physician orders an IV infusion of 500 mL of normal saline to run over 4 hours. The administration set has a drop factor of 15 gtt/mL. What is the flow rate in drops per minute?
  1. Convert the infusion time to minutes: 4 hours × 60 minutes/hour = 240 minutes
  2. Apply the flow rate formula: (Volume in mL × Drop factor) ÷ Time in minutes
  3. (500 mL × 15 gtt/mL) ÷ 240 minutes = 7,500 ÷ 240
  4. 7,500 ÷ 240 = 31.25, rounded to 31 gtt/min
Answer: 31 gtt/min
3. A technician needs to prepare 200 mL of a 3% solution by mixing a 10% stock solution with sterile water (0%). How many milliliters of the 10% solution and how many milliliters of sterile water are needed?
  1. Set up the alligation grid: place 10 (higher strength) upper left, 0 (lower strength, sterile water) lower left, and 3 (desired strength) in the center
  2. Subtract diagonally: 3 − 0 = 3 parts of the 10% solution; 10 − 3 = 7 parts of sterile water
  3. Total parts = 3 + 7 = 10 parts
  4. Volume of 10% solution: (3/10) × 200 mL = 60 mL; volume of sterile water: (7/10) × 200 mL = 140 mL
Answer: 60 mL of 10% solution and 140 mL of sterile water
4. A child weighs 44 pounds. The physician orders 10 mg/kg/day of a medication to be given in two equal doses. What is the dose per administration in milligrams?
  1. Convert weight to kilograms: 44 lb ÷ 2.2 = 20 kg
  2. Calculate the total daily dose: 20 kg × 10 mg/kg = 200 mg/day
  3. Divide the daily dose into two equal doses: 200 mg ÷ 2 = 100 mg per dose
  4. Each administration is 100 mg
Answer: 100 mg per dose

The math in this lesson2

Learners solve timed dose problems such as 250 mg/5 mL = 400 mg/x for 8 mL.
7.RP.2N-Q.1
Brush up in the math halls at newSchoolWorks.com:
In class: Mixed timed practice · Error analysis · Final calculations exam
Materials: Calculation workbook, calculators
Check: Calculations exam ≥ 90%

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Order Entry and Processing
1. A prescription reads: 'Metformin 500 mg tablets, take ii tablets BID.' A 30-day supply is dispensed. How many tablets should be in the bottle?
Order Entry and Processing
2. A pharmacist asks a technician to prepare 1 liter of a 0.9% sodium chloride solution using pure sodium chloride powder. How many grams of sodium chloride are needed?
Order Entry and Processing
3. A patient is to receive 1,200 mL of D5W over 8 hours via an infusion pump. What rate in mL/hr should the technician program?
Order Entry and Processing
4. A vial of powdered antibiotic states that adding 9.3 mL of sterile water will yield 10 mL of final solution. What is the powder volume?
Order Entry and Processing
5. A technician uses alligation to mix a 20% solution with sterile water (0%) to make 500 mL of a 4% solution. How many milliliters of the 20% solution are needed?
Patient Safety and Quality Assurance
6. Which of the following is the correct conversion for a patient's weight of 66 pounds into kilograms?
Order Entry and Processing
7. A prescription is written for amoxicillin 250 mg/5 mL suspension. The sig reads: 'Take 1 teaspoonful three times daily for 10 days.' What total volume in milliliters should be dispensed?
Patient Safety and Quality Assurance
8. A technician calculates a final answer of 0.025 mg for a single dose. The pharmacist notes the order reads 25 mcg. Which statement best describes the situation?
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