--- title: "Lesson 5 — Ratio, Proportion & Percent Strength | AlabamaPharmTech.com" description: "Ratio, proportion, and percent strength calculations for compounding and concentration problems. Interactive pharmacy math with practice and quiz." lang: en json-ld: | { "@context": "https://schema.org", "@type": "LearningResource", "name": "Ratio, Proportion & Percent Strength", "description": "Ratio, proportion, and percent strength calculations for compounding and concentration problems. Interactive pharmacy math with practice and quiz.", "url": "https://www.alabamapharmtech.com/lessons/lesson5-ratio-proportion-percent.html", "inLanguage": "en", "learningResourceType": "Interactive lesson", "educationalLevel": "Beginner", "isPartOf": { "@type": "Course", "name": "Pharmacy Math Mastery", "url": "https://www.alabamapharmtech.com/pharmacy-math-practice" }, "provider": { "@type": "Organization", "name": "AlabamaPharmTech", "url": "https://www.alabamapharmtech.com" } } --- AlabamaPharmTech .com An Allied Health Academy company Pharmacy Math Mastery ALBOP-Approved · PTCB & NHA Prep Overall progress 71% Lessons 1 Math Foundations 25 min · Complete ✓ 2 Dimensional Analysis 30 min · Complete ✓ 3 Day Supply Calculations 40 min · Complete ✓ 4 Dosage Conversions 35 min · Complete ✓ 5 Ratio, Proportion & Percent 35 min · In progress 6 Sig Interpretation 30 min Final exam ★ Bringing It All Together Cumulative · All 6 lessons AlabamaPharmTech.com › Pharmacy Math Mastery › Lesson 5 of 6 Core # Lesson 5: Ratio, Proportion & Percent Strength Calculate percent concentrations, set up dilutions, interpret ratio strengths, and mix solutions — with special coverage of alligation for NHA ExCPT students. [Back to Course](/pharmacy-math-practice) [Back to Dashboard](/modules) Overview Examples Practice 36 Quiz Three methods — each solves a different problem type Proportion: X / known = wanted / known  |  Percent: g per 100 mL  |  Dilution: C&sub1;V&sub1; = C&sub2;V&sub2; Cross-multiply works for simple ratios. C1V1=C2V2 works for all dilutions. Percent strength has ONE definition: grams per 100 mL (or g per 100 g). That's it. Percent strength — the #1 tested concept **% w/v** = grams of solute per 100 mL of solution **% w/w** = grams per 100 g (creams, ointments) 1% = 1 g/100 mL = **10 mg/mL** 2% = 2 g/100 mL = 20 mg/mL 0.9% NS = 0.9 g/100 mL = 9 mg/mL Most common error: treating 1% as 1 mg (wrong by 1,000x) Dilution — C₁V₁ = C₂V₂ C&sub1; = starting concentration V&sub1; = starting volume (what you need to find) C&sub2; = desired concentration V&sub2; = desired final volume Example: Make 100 mL of D5W from D50W: 50 × V1 = 5 × 100 → V1 = **10 mL** Ratio strength 1:1,000 = 1 g per 1,000 mL = **1 mg/mL** 1:10,000 = 1 g per 10,000 mL = **0.1 mg/mL** Epinephrine 1:1,000 = anaphylaxis dose (IM) Epinephrine 1:10,000 = cardiac arrest (IV) Convert ratio to %: 1/1,000 × 100 = 0.1% Cross-multiply / proportion If A/B = C/D, then A×D = B×C Example: 250 mg/5 mL — how many mL for 375 mg? 250/5 = 375/x → 250x = 1,875 → x = **7.5 mL** Works for any two equivalent ratios. **⚠ Alligation (NHA/ExCPT only):** Alligation was removed from the 2026 PTCB exam. This lesson includes 6 alligation questions for students taking the NHA ExCPT or working in compounding. If you are PTCB-focused, use your study time on percent strength and dilution instead. Questions are labeled \[NHA ExCPT only\] throughout. **★ PTCB tip:** Percent strength and dilution (C1V1=C2V2) are the most PTCB-tested topics in this lesson. Expect 2–4 questions combining percent strength with dose calculation. Ratio strength (epinephrine concentrations) appears in safety/patient care questions. Practice recognizing percent as g/100 mL until it is automatic. Six worked examples — from basic percent strength definition through advanced dilution calculations. Easy Retail Normal saline 0.9% NaCl. Patient asks: "How much salt is actually in this?" How many mg of NaCl are in 100 mL of 0.9% NS? Percent w/v definition: 0.9% = 0.9 g per 100 mL Convert to mg: 0.9 g × 1,000 = 900 mg per 100 mL ✓ 900 mg (0.9 g) of NaCl per 100 mL — this is why NS tastes salty Medium Hospital Prepare 100 mL of D5W from D50W (50% dextrose) and sterile water. How many mL of D50W do you need? (C₁V₁ = C₂V₂) Set up C₁V₁ = C₂V₂: 50% × V&sub1; = 5% × 100 mL Solve for V₁: V&sub1; = (5 × 100) / 50 = 10 mL Add SWFI to make total 100 mL: 100 − 10 = 90 mL SWFI ✓ 10 mL D50W + 90 mL SWFI = 100 mL of D5W Medium Hospital Epinephrine 1:1,000 used for anaphylaxis. Dose: 0.3 mg IM. How many mL? 1:1,000 = 1 g per 1,000 mL = 1 mg/mL: 0.3 mg ÷ 1 mg/mL = 0.3 mL ✓ Draw up 0.3 mL from the 1:1,000 vial for anaphylaxis IM injection **Critical distinction:** 1:1,000 (1 mg/mL) is IM for anaphylaxis. 1:10,000 (0.1 mg/mL) is IV for cardiac arrest. Using the wrong concentration gives a 10x dose error. Hard Hospital Prepare 250 mL of 0.45% NaCl using 0.9% NaCl and SWFI. How many mL of 0.9% NaCl? C₁V₁ = C₂V₂: 0.9 × V&sub1; = 0.45 × 250 Solve: V&sub1; = 112.5 / 0.9 = 125 mL ✓ 125 mL of 0.9% NS + 125 mL SWFI = 250 mL of 0.45% NS Hard Retail NHA ExCPT only \[NHA ExCPT — not on 2026 PTCB\] Mix 2.5% and 0.5% hydrocortisone cream to make 60 g of 1% cream. How many grams of 2.5% cream? (Alligation method) Alligation grid: 2.5%     ↘     (1-0.5) = 0.5 parts of 2.5%       1% (target) 0.5%     ↗     (2.5-1) = 1.5 parts of 0.5% Total parts: 0.5 + 1.5 = 2 parts Grams of 2.5%: (0.5/2) × 60 = 15 g ✓ 15 g of 2.5% + 45 g of 0.5% = 60 g of 1% hydrocortisone Hard Retail Lidocaine 3% solution. Need to know mg content for a local anesthetic procedure using 20 mL. How many mg of lidocaine in 20 mL of 3% solution? 3% = 3 g per 100 mL = 30 mg/mL: 30 mg/mL × 20 mL = 600 mg ✓ 600 mg lidocaine. Maximum safe dose for a 70 kg adult: ~350 mg — verify with prescriber before preparing. Difficulty Easy Medium Hard Context Retail Hospital Patient Easy Retail Proportion Amoxicillin suspension: 500 mg/5 mL. How many mg are in 7.5 mL? Check Show solution **Answer: 750 mg** 500/5 = 100 mg/mL. 100 × 7.5 = **750 mg**. Easy Retail Proportion Suspension: 250 mg/5 mL. Need to measure 375 mg. How many mL contain 375 mg? Check Show solution **Answer: 7.5 mL** 375/250 × 5 = **7.5 mL**. Easy Retail Proportion Cefdinir 125 mg/5 mL suspension. How many mL contain 187.5 mg? Check Show solution **Answer: 7.5 mL** 187.5/125 × 5 = **7.5 mL**. Med Hospital Proportion D5W = 5 g dextrose per 100 mL. How many grams of dextrose in a 500 mL bag? Check Show solution **Answer: 25 g** 5 g/100 mL × 500 mL = **25 g**. Med Hospital Proportion Normal saline: 9 g NaCl per 1,000 mL. How many grams of NaCl in 500 mL? Check Show solution **Answer: 4.5 g** 9/1000 × 500 = **4.5 g**. Med Retail Proportion Phenytoin oral suspension: 125 mg/5 mL. How many mL for a 150 mg dose? Check Show solution **Answer: 6 mL** 150/125 × 5 = **6 mL**. Hard Hospital Proportion KCl: 40 mEq in 200 mL. Order: 20 mEq IV. How many mL to draw up? Check Show solution **Answer: 100 mL** 20/40 × 200 = **100 mL**. Hard Retail Proportion Lidocaine 3% solution (3 g per 100 mL). How many mg of lidocaine in 20 mL? Check Show solution **Answer: 600 mg** 3 g/100 mL × 20 mL = 0.6 g = **600 mg**. Easy Retail Percent Strength Normal saline = 0.9% w/v solution. How many grams of NaCl are in 100 mL? Check Show solution **Answer: 0.9 g** 0.9% w/v = **0.9 g per 100 mL**. Definition of percent w/v. Easy Retail Percent Strength D5W = 5% w/v dextrose solution. How many grams of dextrose per 100 mL? Check Show solution **Answer: 5 g** 5% w/v = **5 g per 100 mL**. Easy Retail Percent Strength Hydrocortisone 1% w/w cream. How many grams of active ingredient per 100 g of cream? Check Show solution **Answer: 1 g** 1% w/w = **1 g per 100 g**. Same definition as w/v but for solid/solid. Med Retail Percent Strength Acetic acid 2% w/v otic solution. How many mg of acetic acid are in 15 mL? Check Show solution **Answer: 300 mg** 2% = 2 g/100 mL = 2,000 mg/100 mL = 20 mg/mL. 20 × 15 = **300 mg**. Med Hospital Percent Strength D10W = 10 g dextrose per 100 mL. How many grams of dextrose in a 250 mL bag? Check Show solution **Answer: 25 g** 10/100 × 250 = **25 g**. Med Hospital Percent Strength 3% sodium chloride solution. How many grams of NaCl in 500 mL? Check Show solution **Answer: 15 g** 3/100 × 500 = **15 g**. Med Retail Percent Strength Erythromycin 2% topical gel, 30 g tube. How many mg of erythromycin in the tube? Check Show solution **Answer: 600 mg** 2% w/w: 2 g/100 g × 30 g = 0.6 g = **600 mg**. Hard Retail Percent Strength Lidocaine 1% injection = 10 mg/mL. How many mg of lidocaine in a 20 mL vial? Check Show solution **Answer: 200 mg** 10 mg/mL × 20 mL = **200 mg**. Hard Hospital Percent Strength Calcium gluconate 10% w/v in a 10 mL vial. How many grams of calcium gluconate in the vial? Check Show solution **Answer: 1 g** 10/100 × 10 = **1 g**. Hard Hospital Percent Strength Prepare 500 mL of 0.45% NaCl from 0.9% NaCl and SWFI. How many mL of 0.9% NaCl do you need? Check Show solution **Answer: 250 mL** C1V1=C2V2: 0.9 × V1 = 0.45 × 500. V1 = 225/0.9 = **250 mL**. Med Hospital Dilution (C₁V₁=C₂V₂) Prepare 100 mL of D5W (5%) from D50W (50% dextrose) and SWFI. How many mL of D50W are needed? Check Show solution **Answer: 5 mL** C1V1=C2V2: 50×V1 = 5×100. V1 = 500/50 = **10 mL**. Med Hospital Dilution (C₁V₁=C₂V₂) Prepare 500 mL of 70% isopropyl alcohol from 99% stock. How many mL of 99% stock are needed? Check Show solution **Answer: 354 mL** 99×V1 = 70×500. V1 = 35,000/99 = 353.5 → **354 mL**. Med Hospital Dilution (C₁V₁=C₂V₂) 20 mEq KCl (from a 40 mEq/20 mL vial) added to 1,000 mL NS. What is the final KCl content? How many mEq of KCl are in the final bag? Check Show solution **Answer: 20 mEq/1,020 mL** 10 mL of KCl added to 1,000 mL NS = 1,010 mL (approx 1,020 mL total). KCl content: **20 mEq in approximately 1,020 mL**. Note: actual final volume differs slightly. Hard Hospital Dilution (C₁V₁=C₂V₂) Prepare 250 mL of 0.45% NaCl using 0.9% NaCl and SWFI. How many mL of 0.9% NaCl to use? Check Show solution **Answer: 125 mL** 0.9×V1 = 0.45×250. V1 = 112.5/0.9 = **125 mL**. Hard Hospital Dilution (C₁V₁=C₂V₂) Gentamicin 40 mg/mL vial. Need 10 mg/mL solution in 10 mL total volume. How many mL of gentamicin to add? Check Show solution **Answer: 2.5 mL** 40×V1 = 10×10. V1 = 100/40 = **2.5 mL**. Hard Hospital Dilution (C₁V₁=C₂V₂) Acyclovir 500 mg/10 mL concentrate (= 50 mg/mL). Prepare 7 mg/mL solution in 50 mL. How many mL of concentrate to add? Check Show solution **Answer: 7 mL** 50×V1 = 7×50. V1 = 350/50 = **7 mL**. Hard Retail Dilution (C₁V₁=C₂V₂) Prepare 1:10 bleach solution (1 part bleach to 10 parts total). How many mL of bleach for 1,000 mL total? Check Show solution **Answer: 100 mL** 1:10 means 1 part per 10 total = 10%. V1 = 1,000/10 = **100 mL**. Hard Hospital Dilution (C₁V₁=C₂V₂) Heparin 1,000 units/mL. Prepare 500 units/mL solution with NS. Final volume: 50 mL. How many mL of heparin to add? Check Show solution **Answer: 25 mL** 1000×V1 = 500×50. V1 = 25,000/1000 = **25 mL**. Med Hospital Ratio Strength Epinephrine 1:1,000 = 1 g/1,000 mL = 1 mg/mL. Dose: 0.3 mg IM. How many mL? Check Show solution **Answer: 0.3 mL** 0.3 mg ÷ 1 mg/mL = **0.3 mL**. Med Hospital Ratio Strength Epinephrine 1:10,000 = 0.1 mg/mL (cardiac arrest concentration). Dose: 1 mg IV. How many mL? Check Show solution **Answer: 10 mL** 1 mg ÷ 0.1 mg/mL = **10 mL**. Hard Hospital Ratio Strength A 1:200 solution. Express 1:200 as a percent strength. Check Show solution **Answer: 0.5%** 1/200 × 100 = **0.5%**. Ratio to percent: divide top by bottom, multiply by 100. Hard Retail Ratio Strength Atropine 1:200 solution = 5 mg/mL (1 g per 200 mL). Dose: 1 mg. How many mL? Check Show solution **Answer: 0.2 mL** 1 mg ÷ 5 mg/mL = **0.2 mL**. Med Retail Alligation (NHA/ExCPT) \[NHA ExCPT — not on 2026 PTCB\] Mix 5% and 1% lidocaine to make 100 mL of 2% solution. How many mL of 5% lidocaine are needed? Check Show solution **Answer: 25 mL** Alligation: parts of 5% = (2-1) = 1. Parts of 1% = (5-2) = 3. Total parts = 4. Volume of 5%: (1/4) × 100 = **25 mL**. Med Retail Alligation (NHA/ExCPT) \[NHA ExCPT — not on 2026 PTCB\] Mix 95% ethanol and SWFI to make 500 mL of 70% ethanol. How many mL of 95% ethanol are needed? Check Show solution **Answer: 354 mL** C1V1=C2V2: 95×V1 = 70×500. V1 = 35,000/95 = 368.4 → **368 mL**. Hard Retail Alligation (NHA/ExCPT) \[NHA ExCPT — not on 2026 PTCB\] Mix 2.5% and 0.5% hydrocortisone cream to make 60 g of 1% cream. How many grams of 2.5% cream are needed? Check Show solution **Answer: 15 g** Alligation: parts of 2.5% = (1-0.5) = 0.5. Parts of 0.5% = (2.5-1) = 1.5. Total = 2. Grams of 2.5%: (0.5/2) × 60 = **15 g**. Hard Hospital Alligation (NHA/ExCPT) \[NHA ExCPT — not on 2026 PTCB\] Mix D50W (50%) and D5W (5%) to make 500 mL of D10W (10%). How many mL of D50W are needed? Check Show solution **Answer: 56 mL** Alligation: parts of D50W = (10-5) = 5. Parts of D5W = (50-10) = 40. Total = 45. Volume D50W: (5/45) × 500 = 55.6 → **56 mL**. Hard Hospital Alligation (NHA/ExCPT) \[NHA ExCPT — not on 2026 PTCB\] Mix 3% and 0.9% NaCl to make 1,000 mL of 2% NaCl. How many mL of 3% NaCl are needed? Check Show solution **Answer: 524 mL** Alligation: parts of 3% = (2-0.9) = 1.1. Parts of 0.9% = (3-2) = 1. Total = 2.1. Volume: (1.1/2.1) × 1,000 = 523.8 → **524 mL**. Hard Retail Alligation (NHA/ExCPT) \[NHA ExCPT — not on 2026 PTCB\] Mix 20% zinc oxide ointment and petrolatum (0%) to make 100 g of 5% zinc oxide. How many grams of 20% ointment are needed? Check Show solution **Answer: 25 g** Alligation: parts of 20% = (5-0) = 5. Parts of 0% = (20-5) = 15. Total = 20. Grams of 20%: (5/20) × 100 = **25 g**. **How this quiz works:** Pick your question count and difficulty, then start. After answering, click _Reveal explanation_ to see the full step-by-step solution — answers never show automatically. Score and type breakdown appear at the end. ⓘ This lesson has 36 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions. How many questions? 102030 Question difficulty Random mixEasy onlyMedium onlyHard only Options Randomize question order Shuffle every time you start Timed mode 45-second countdown per question Number of sets Each set draws a fresh pool − 1 + 10 Questions 1 Sets 10 Total ~10 min Est. time ▶  Start quiz — Ratio, Proportion & Percent Strength Question 1 of 10 0 correct · 0 skipped \--% Score Quiz complete! Lesson 5 · Ratio, Proportion & Percent Strength · AlabamaPharmTech.com \-- Correct \-- Wrong \-- Skipped \-- Time Performance by question type \--% Overall accuracy \-- Weakest area Miss rate by question type Retry missed + skipped Next set New quiz Answer review — every question this session [Home](/) [Back to Dashboard](/modules) Previous [Back to Course](/pharmacy-math-practice) Lesson 5 of 6 Next lesson