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PTCB calculations · focused study pack

Stop losing the units halfway through.

Work through 24 original, openly solved calculation examples. See the setup, the tempting mistake, and a check that catches it. Try two complete examples below before deciding.

One relationship at a time

For learners who can follow a formula but get stuck choosing the units or setting up the relationship. Each example states its assumptions and shows the solution; this is a teaching supplement, not a scored test.

  1. Metric conversions and decimalsChoose the direction from the units, not from a memorized instruction to move a decimal.
  2. Quantities and tablet countsKeep a mass, a count per use and a total count separate. All tablet descriptions below are fictional training materials.
  3. mg/mL and label-ratio arithmeticRead the complete ratio on a fictional label. A mass per 5 mL is not a mass per 1 mL.
  4. Days-supply arithmetic with stated assumptionsBuild the daily use first, then divide the available quantity by it. A classroom result is not an insurance-billing or clinical rule.
  5. Percent strength and ideal dilutionName the denominator first. These are paper-only mixture models, not instructions for making or changing a medicine.
  6. Mixed multi-step error checksTrace the entire chain and reverse-check the proposed result. A plausible-looking number is not enough.
Read two complete examples first

PDF + condensed phone reference

PTCB Calculations Study Pack

$19.00 USD · one-time

  • 24 worked examples across six topics, four per topic.
  • Printable PDF with selectable text and source links.
  • A condensed PNG reference for your phone—not all 24 solutions.
  • Setups, units, common mistakes, and reasonableness checks.

A separate purchase. Not included with practice access or the $2.99 quick sheet; neither is included here. No subscription or promise of future editions.

Full refund requests within seven calendar days, including after download. Refunded or disputed purchases lose download access.

For personal study only. Not a complete PTCE course, pass guarantee, official exam aid, or instructions for preparing or administering medication.

Free preview · 2 of 24 examples

See whether the explanations help you.

Read the scenario and write your setup before opening the solution. These examples are intentionally unscored and separate from our protected practice-question bank.

Grams to milligrams without guessing

A fictional training label lists 0.375 g of an inert marker. Express that same mass in milligrams.

Find: Mass in mg

  • This is a unit conversion of one unchanged mass, not a medicine amount.
  • The conversion factor 1 g = 1000 mg is exact.
Show the setup, solution, and error check

Setup: Start with 0.375 g. Put grams under milligrams in the conversion factor so the starting g will cancel.

Units: g × (mg/g) = mg

  1. Write 0.375 g × (1000 mg / 1 g).
  2. Cancel g, then multiply 0.375 × 1000 = 375.
  3. Keep the requested unit: 375 mg. The mass did not change; its numerical value did.

0.375 g = 375 mg.

Tempting mistake: Dividing by 1000 gives 0.000375, which goes in the wrong direction. A milligram is a smaller unit, so more of those units are needed to express the same mass.

Check: 0.375 g is between 0.3 g and 0.4 g, so the answer must be between 300 mg and 400 mg. Also, 375 mg ÷ 1000 = 0.375 g.

Find volume from a mass-per-volume label

A fictional training liquid contains 150 mg of inert marker in every 5 mL. Find the volume that represents 225 mg of marker.

Find: Volume in mL

  • The classroom liquid is uniform, so the stated ratio applies to every portion.
  • The target is supplied only for arithmetic. It is not a real medicine amount or a preparation instruction.
Show the setup, solution, and error check

Setup: Multiply the target mass by 5 mL / 150 mg. Put the label's mass in the denominator so mg cancels.

Units: mg × (mL/mg) = mL

  1. Write 225 mg × (5 mL / 150 mg).
  2. Calculate the numerator: 225 × 5 = 1125.
  3. Divide 1125 by 150 to obtain 7.5 mL. Alternatively, the label is 30 mg/mL and 225 ÷ 30 = 7.5 mL.

The fictional target corresponds to 7.5 mL.

Tempting mistake: Using 150 mg/mL ignores the label's 5 mL denominator and produces 1.5 mL. Read the amount and its associated volume together.

Check: 225 mg is 1.5 times 150 mg, so the volume should be 1.5 times 5 mL: 7.5 mL. Multiplying 7.5 mL by 30 mg/mL returns 225 mg.

Download the free two-example PDFOpen the free sample phone image

What was checked—and what this does not claim

Edition v2026-09-26. Original examples with independent AI content review on 2026-09-26; not human, instructor, or official-provider review. The exam outline establishes topical relevance, not endorsement or complete coverage. Mathematical assumptions are stated within each example.

  • PTCE Content Outline, effective January 6, 2026

    PDF page 2, objective 4.1; effective date on page 1. Objective 4.1 includes calculation-related topics relevant to this selected-skills pack. It does not certify this product, its coverage or its examples.

  • Metric (SI) Prefixes

    Prefixes table, milli and micro rows; Common metric prefixes and the relationship with their place values, introductory paragraph. Milli means 10^-3 and micro means 10^-6. A leading zero makes values below one easier to read. All quantities in our examples are newly chosen.

  • SI Units - Volume

    Common Units of Volume table, row 1000 mL = 1 L; opening unit-symbol bullets. One liter equals 1000 milliliters. The pack uses L and mL consistently.

  • NIST Guide to the SI, Chapter 7

    Sections 7.1, 7.2, 7.10.2 and 7.11. A value includes its unit; equations distinguish quantities from bare numbers. For a dimensionless fraction, percent represents a factor of 0.01. This source is not used to claim that a mass/volume strength is a dimensionless mass fraction.

  • NIST Guide to the SI, Chapter 8

    Section 8.6.5 note 1, mass concentration; section 8.6.10, mass fraction. Mass concentration uses component mass divided by mixture volume; mass fraction uses component mass divided by mixture mass. These different denominators must not be interchanged.

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