AlabamaPharmTech.com›Pharmacy Math Mastery›Lesson 5 of 6Core
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.
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)
% 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
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%
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.
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.
EasyRetail
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
MediumHospital
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
MediumHospital
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.
HardHospital
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
HardRetailNHA 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
HardRetail
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
Context
Easy
Retail
Proportion
Amoxicillin suspension: 500 mg/5 mL.
How many mg are in 7.5 mL?
Answer: 750 mg
500/5 = 100 mg/mL. 100 × 7.5 = 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?
Answer: 7.5 mL
375/250 × 5 = 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?
Answer: 7.5 mL
187.5/125 × 5 = 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?
Answer: 25 g
5 g/100 mL × 500 mL = 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?
Answer: 4.5 g
9/1000 × 500 = 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?
Answer: 6 mL
150/125 × 5 = 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?
Answer: 100 mL
20/40 × 200 = 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?
Answer: 600 mg
3 g/100 mL × 20 mL = 0.6 g = 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?
Answer: 0.9 g
0.9% w/v = 0.9 g per 100 mL. Definition of percent w/v.
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?
Answer: 5 g
5% w/v = 5 g per 100 mL.
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?
Answer: 1 g
1% w/w = 1 g per 100 g. Same definition as w/v but for solid/solid.
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?
Answer: 300 mg
2% = 2 g/100 mL = 2,000 mg/100 mL = 20 mg/mL. 20 × 15 = 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?
Answer: 25 g
10/100 × 250 = 25 g.
10/100 × 250 = 25 g.
Med
Hospital
Percent Strength
3% sodium chloride solution.
How many grams of NaCl in 500 mL?
Answer: 15 g
3/100 × 500 = 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?
Answer: 600 mg
2% w/w: 2 g/100 g × 30 g = 0.6 g = 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?
Answer: 200 mg
10 mg/mL × 20 mL = 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?
Answer: 1 g
10/100 × 10 = 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?
Answer: 250 mL
C1V1=C2V2: 0.9 × V1 = 0.45 × 500. V1 = 225/0.9 = 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?
Answer: 5 mL
C1V1=C2V2: 50×V1 = 5×100. V1 = 500/50 = 10 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?
Answer: 354 mL
99×V1 = 70×500. V1 = 35,000/99 = 353.5 → 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?
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.
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?
Answer: 125 mL
0.9×V1 = 0.45×250. V1 = 112.5/0.9 = 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?
Answer: 2.5 mL
40×V1 = 10×10. V1 = 100/40 = 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?
Answer: 7 mL
50×V1 = 7×50. V1 = 350/50 = 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?
Answer: 100 mL
1:10 means 1 part per 10 total = 10%. V1 = 1,000/10 = 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?
Answer: 25 mL
1000×V1 = 500×50. V1 = 25,000/1000 = 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?
Answer: 0.3 mL
0.3 mg ÷ 1 mg/mL = 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?
Answer: 10 mL
1 mg ÷ 0.1 mg/mL = 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.
Answer: 0.5%
1/200 × 100 = 0.5%. Ratio to percent: divide top by bottom, multiply by 100.
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?
Answer: 0.2 mL
1 mg ÷ 5 mg/mL = 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?
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.
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?
Answer: 354 mL
C1V1=C2V2: 95×V1 = 70×500. V1 = 35,000/95 = 368.4 → 368 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?
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.
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?
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.
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?
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.
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?
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.
Alligation: parts of 20% = (5-0) = 5. Parts of 0% = (20-5) = 15. Total = 20. Grams of 20%: (5/20) × 100 = 25 g.
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ⓘ This lesson has 36 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions.
ⓘ This lesson has 36 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions.
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Lesson 5 · Ratio, Proportion & Percent Strength · AlabamaPharmTech.com
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