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Practice and exam technique

Practice: calculations

Compiled by the Sitonce editorial team from PTCB's own published outline, the federal regulations named below and US Bureau of Labor Statistics dataUpdated 3 min readFacts verified 5 September 2026
The short answer

Five calculations covering unit conversion, weight-based dosing, days supply, percentage strength and dilution, each worked step by step with the error behind every wrong option named.

Every one of these is dimensional analysis. Write the units, cancel them, read off what survives.

Five questions

Question 1

A patient is to take 2 teaspoons three times a day. How many mL per day?

  1. 15 mL
  2. 30 mL
  3. 10 mL
  4. 45 mL
Answer: B. One teaspoon is 5 mL, so 2 teaspoons is 10 mL. Three times a day is 30 mL. Option C is the single dose and option A is one teaspoon three times a day, which are the two ways of dropping a step.
Question 2

A 150 mL bottle is dispensed with a Sig of 5 mL three times a day. What is the days supply?

  1. 30 days
  2. 10 days
  3. 15 days
  4. 50 days
Answer: B. Fifteen mL a day into 150 mL is 10 days. Option A comes from dividing by the 5 mL dose rather than the 15 mL daily quantity, which is the standard error: quantity per dose times doses per day is the number you divide by.
Question 3

How many mg of active ingredient are in 500 mL of a 5 percent solution?

  1. 2,500 mg
  2. 25,000 mg
  3. 250 mg
  4. 50,000 mg
Answer: B. Five percent is 5 g in 100 mL, which is 50 mg per mL. Fifty times 500 is 25,000 mg, or 25 g. Option A is out by a factor of ten, which is what happens if you take 5 percent as 5 mg per mL rather than 50.
Question 4

You have 70 percent stock and need 500 mL of 35 percent. How much stock is required?

  1. 175 mL
  2. 250 mL
  3. 350 mL
  4. 500 mL
Answer: B. The amount of active does not change on dilution, so initial concentration times initial volume equals final concentration times final volume. Thirty-five times 500 divided by 70 is 250 mL of stock, made up to 500 mL with 250 mL of diluent. Note the question asked for the stock, not the diluent - here they happen to be equal, which will not usually be true.
Question 5

A patient weighs 176 pounds. The dose is 5 mg per kg. What is the total dose?

  1. 400 mg
  2. 880 mg
  3. 352 mg
  4. 80 mg
Answer: A. One hundred and seventy-six divided by 2.2 is 80 kg. Eighty times 5 is 400 mg. Option B multiplies by 5 without converting, and option D is the weight in kilograms mistaken for the answer. Both are single missed steps.
Every distractor here is one missed step

A dropped conversion, an inverted one, a decimal place, or the daily figure where a dose was wanted. None is random. That means a wrong answer usually tells you exactly which step you skipped, and it also means finding your answer among the options is not proof you are right.

The conversions behind all five

One teaspoon is 5 mL. One kilogram is 2.2 pounds. A percentage is grams per 100 mL, and multiplying by 10 gives mg per mL.

Three facts, five questions. Which is the argument for the daily drill.

Common questions

How do I calculate days supply?

Total quantity divided by quantity used per day - dose times frequency, not the dose alone.

How do I convert percentage to mg per mL?

Multiply by 10. A 5 percent solution is 50 mg per mL.

What is the dilution relationship?

Initial concentration times initial volume equals final concentration times final volume.

How do I convert pounds to kilograms?

Divide by 2.2.

Why are the wrong answers useful?

Each is one missed step, so your wrong answer usually identifies the step you skipped.

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