PTCB Quiz Prep

How to Use Ratio and Proportion

Updated

Ratio and proportion is the workhorse of pharmacy math. It is not one calculation among many: it is the underlying method that solves conversions, liquid doses, tablet counts, and concentration problems, and it sits inside almost every other formula in this series. Learn to set it up reliably and a large share of the calculation questions on the exam become mechanical. Practise it in context on the PTCB math practice test once you have worked the examples below.

a / b = c / d

a × d = b × c

What a proportion actually says

A ratio compares two quantities: 250 mg to 5 mL, one tablet to 10 mg, 60 minutes to 1 hour. A proportion states that two such ratios are equal. In practice you almost always know one complete ratio, which is the strength printed on the bottle, and three quarters of a second one, which is the dose the prescriber wants. The missing quarter is x.

The setup is where accuracy lives. Write the known ratio on the left and the wanted ratio on the right, keeping the same unit in the same position on both sides. If milligrams are on top on the left, milligrams must be on top on the right. Get that alignment right and the arithmetic cannot mislead you.

Solving it

Once the proportion is written, cross multiply: multiply each numerator by the opposite denominator. That turns the fractions into a single equation with x in it. Divide both sides by whatever number is multiplying x, and the answer is left. Finish by asking whether the size of the answer makes sense: if a dose is twice the strength on the bottle, the volume should be about twice as much, not half.

Worked example: a liquid dose

How many millilitres deliver 400 mg?

A suspension is labelled 250 mg/5 mL. The prescriber orders 400 mg per dose. How many millilitres should be given?

  1. Step 1. Write the known ratio: 250 mg / 5 mL.
  2. Step 2. Write the wanted ratio with the same units in the same positions: 400 mg / x mL.
  3. Step 3. Set them equal: 250 / 5 = 400 / x.
  4. Step 4. Cross multiply: 250 × x = 5 × 400, so 250x = 2,000.
  5. Step 5. Divide both sides by 250: x = 2,000 ÷ 250 = 8 mL.

Answer: 8 mL

The trap: Writing the second ratio upside down as x mL / 400 mg. The units must sit in the same positions on both sides, or cross multiplying produces the reciprocal of the right answer.

Worked example: how many tablets

The method does not change when the units are tablets rather than millilitres.

How many 25 mcg tablets make a 0.1 mg dose?

A prescription calls for 0.1 mg of a drug. The pharmacy stocks 25 mcg tablets. How many tablets are needed per dose?

  1. Step 1. Make the units match before setting up. 0.1 mg = 100 mcg, because 1 mg = 1,000 mcg.
  2. Step 2. Write the known ratio: 25 mcg / 1 tablet.
  3. Step 3. Write the wanted ratio: 100 mcg / x tablets.
  4. Step 4. Set them equal and cross multiply: 25x = 100.
  5. Step 5. Divide by 25: x = 4 tablets.

Answer: 4 tablets

The trap: Setting up 0.1 against 25 without converting first. Mixing milligrams and micrograms in one proportion gives an answer 1,000 times out.

Worked example: working backwards to a strength

x does not have to be the volume. Sometimes you know the volume and need the amount of drug it contains.

How much drug is in 12 mL?

An oral solution contains 80 mg in every 15 mL. How many milligrams are in a 12 mL dose?

  1. Step 1. Write the known ratio: 80 mg / 15 mL.
  2. Step 2. Write the wanted ratio: x mg / 12 mL.
  3. Step 3. Set them equal: 80 / 15 = x / 12.
  4. Step 4. Cross multiply: 15x = 80 × 12 = 960.
  5. Step 5. Divide by 15: x = 64 mg.

Answer: 64 mg

The trap: Reaching for a formula. This is the same single proportion as the earlier examples, just with the unknown in a different position.

The most common mistake

Nearly every wrong answer here comes from a setup problem rather than an arithmetic one: either the two ratios are written with their units in opposite positions, or two different units are compared without converting first. Write the units beside every number, check that the same unit sits in the same place on both sides of the equals sign, and only then cross multiply. If the answer comes out wildly larger or smaller than the numbers you started with, the setup is inverted.

Try it

  1. A solution is 125 mg/5 mL. How many millilitres contain 300 mg?
  2. Tablets are 0.5 mg each. How many tablets provide a 2.5 mg dose?
  3. An injection contains 40 mg/mL. How many milligrams are in 0.6 mL?
  4. A syrup is 100 mg/15 mL. How many millilitres deliver 250 mg?
Show answers
  1. 125 / 5 = 300 / x, so 125x = 1,500 and x = 12 mL.
  2. 0.5 / 1 = 2.5 / x, so 0.5x = 2.5 and x = 5 tablets.
  3. 40 / 1 = x / 0.6, so x = 24 mg.
  4. 100 / 15 = 250 / x, so 100x = 3,750 and x = 37.5 mL.

Frequently asked questions

What is a proportion in pharmacy math?

A proportion is a statement that two ratios are equal. In the pharmacy it usually reads as known strength equals needed strength: if 250 mg sits in 5 mL, then 400 mg sits in x mL. Setting the two ratios equal and solving for x answers a large share of every calculation on the exam.

How do you cross multiply?

Write the proportion as a/b = c/d, then multiply each numerator by the opposite denominator so that a times d equals b times c. Divide both sides by whatever is attached to x, and x is left alone. The arithmetic is the easy part; the setup is what needs care.

How do you know the proportion is set up correctly?

The units have to match across the equation. Milligrams sit above milligrams and millilitres sit above millilitres on both sides. If milligrams appear on top of one side and millilitres on top of the other, the setup is inverted and the answer will be wrong even though the arithmetic is right.

What is the difference between ratio and proportion and dimensional analysis?

They reach the same answer by different routes. A proportion sets two equal ratios side by side and solves for the missing term. Dimensional analysis chains conversion factors together so unwanted units cancel out. Proportion is usually faster for a single conversion, while dimensional analysis handles multi-step problems more cleanly.

Can proportions be used for anything other than liquids?

Yes. The method works for tablets, ointment strengths, IV concentrations, days supply, and business calculations. Any time you know a relationship between two quantities and need a third, a proportion will solve it.

Practise this

Once proportions are automatic, the rest of the series is mostly applying them in context: weight-based dosing uses a proportion for the final volume step, and days supply uses one to turn a quantity into a number of days. Work a mixed set on the pharmacy math practice test, then head back to the pharmacy math hub for the other formulas.

PTCB Quiz Prep is an independent study resource, not affiliated with the Pharmacy Technician Certification Board.

The rest of the pharmacy math series

Each calculation below is worked start to finish with the same method, so once one clicks the others read faster. The full set sits on the pharmacy math guide.

  • Days Supply: how long a dispensed quantity lasts, including the drops, insulin and inhaler cases that trip people up.
  • Conversions: metric, household to metric, temperature, and the Roman numerals that still appear on prescriptions.
  • Concentrations and Dilutions: percentage strength (w/v, w/w, v/v), ratio strength, and the C1 x V1 = C2 x V2 dilution equation.
  • Alligation: the tic-tac-toe method for mixing two strengths to reach a target, and turning parts into quantities.
  • IV Flow Rates: flow rate in mL/hr, drip rate in gtt/min using the drop factor, and infusion time.
  • Weight-Based Dosing: pounds to kilograms, mg/kg per dose against mg/kg per day, and checking a dose against its maximum.
  • Body Surface Area: the Mosteller formula in metric and imperial units, and the mg/m2 dosing that depends on it.