Ratio and proportion

Ratio and proportion dosage calculation practice

Practise setting up and solving proportions for dosage calculations. Every question supplies the strength and the dose it needs, and each answer shows the setup as well as the number.

New to the method? Read Medication Calculation Methods Explained

8 practice questions

Write your setup down before checking. Each answer shows the reasoning and the mistake students make most often, because a wrong setup is more useful to understand than a wrong number.

Foundation

A liquid is labelled 250 mg in 5 mL, and 500 mg is prescribed. Set up the proportion.

Show the setup, answer and why

Set up the proportion

250 mg / 5 mL = 500 mg / x mL

Answer: The known strength on one side, the prescribed dose over the unknown volume on the other.

A proportion states that two ratios are equal. The known pair comes from the label; the unknown pair pairs the prescribed dose with the volume you are solving for. Milligrams stay above millilitres on both sides.

A common wrong answer — 250 mg / 5 mL = x mL / 500 mg

The units are flipped on the right-hand side. Both ratios have to be written the same way round, or cross-multiplying compares milligrams with millilitres.

Beginner

A liquid is labelled 250 mg in 5 mL. What volume contains 500 mg?

Show the setup, answer and why

Set up the proportion

250 / 5 = 500 / x

Answer: 10 mL

Cross-multiplying gives 250x = 500 × 5 = 2500, so x = 2500 ÷ 250 = 10 mL. Sense check: 500 mg is twice 250 mg, so the volume should be twice 5 mL.

A common wrong answer — 2.5 mL

This solves the proportion upside down. The required dose is larger than the strength on the label, so the volume has to be larger than 5 mL, not smaller.

Beginner

A liquid is labelled 100 mg in 4 mL. What volume contains 75 mg?

Show the setup, answer and why

Set up the proportion

100 / 4 = 75 / x

Answer: 3 mL

100x = 75 × 4 = 300, so x = 3 mL. Sense check: 75 mg is three quarters of 100 mg, and 3 mL is three quarters of 4 mL.

A common wrong answer — 5.33 mL

This divides 4 by 75 and multiplies by 100 — the proportion inverted. A dose smaller than the labelled strength must give a volume smaller than the labelled volume.

Intermediate

A liquid is labelled 0.5 g in 10 mL. What volume contains 200 mg?

Show the setup, answer and why

Set up the proportion

500 mg / 10 mL = 200 mg / x mL

Answer: 4 mL

Convert first so both sides use the same unit: 0.5 g = 500 mg. Then 500x = 200 × 10 = 2000, so x = 4 mL.

A common wrong answer — 4000 mL

This sets up 0.5 / 10 = 200 / x without converting, so grams are being compared with milligrams. A proportion is only valid when both ratios use the same units.

Intermediate

A liquid is labelled 120 mg in 5 mL. A dose of 180 mg is prescribed. What volume is needed?

Show the setup, answer and why

Set up the proportion

120 / 5 = 180 / x

Answer: 7.5 mL

120x = 180 × 5 = 900, so x = 7.5 mL. Sense check: 180 mg is one and a half times 120 mg, and 7.5 mL is one and a half times 5 mL.

A common wrong answer — 8 mL

This rounds 7.5 to a whole number. Nothing in the question asked for rounding, and a measurable volume of 7.5 mL is perfectly ordinary.

Advanced

A liquid is labelled 250 mg in 5 mL. A supplied order is 15 mg/kg for a patient who weighs 40 kg. What volume is needed?

Show the setup, answer and why

Set up the proportion

Dose: 15 × 40 = 600 mg. Then 250 / 5 = 600 / x

Answer: 12 mL

The proportion cannot start until the dose exists. Once it does, 250x = 600 × 5 = 3000, so x = 12 mL.

A common wrong answer — Setting up 250 / 5 = 15 / x

This puts the per-kilogram figure into the proportion instead of the calculated dose. 15 mg/kg is a rate, not an amount, until it has been multiplied by the weight.

Advanced

A liquid is labelled 200 mg in 5 mL. A dose of 300 mg is prescribed, and the question also states the patient weighs 62 kg and the last dose was 6 hours ago. What volume is needed?

Show the setup, answer and why

Set up the proportion

200 / 5 = 300 / x

Answer: 7.5 mL

200x = 300 × 5 = 1500, so x = 7.5 mL. The weight and the timing are context: the prescription is a flat dose, so neither enters the proportion.

A common wrong answer — Multiplying the dose by 62 first

A supplied weight invites a per-kilogram calculation even when the prescription is not written that way. Deciding what the question asks before reading the numbers prevents it.

Advanced

A liquid is labelled 80 mg in 2 mL. What volume contains 340 mg, to one decimal place?

Show the setup, answer and why

Set up the proportion

80 / 2 = 340 / x

Answer: 8.5 mL

80x = 340 × 2 = 680, so x = 8.5 mL. Sense check: 340 mg is a little over four times 80 mg, and 8.5 mL is a little over four times 2 mL.

A common wrong answer — 4.25 mL

This divides 340 by 80 and stops, giving the number of label-strengths rather than the volume. The result still has to be multiplied by the 2 mL those 80 mg occupy.

Where to go next

Medication Calculation Methods Explained

The formula method, ratio and proportion, and dimensional analysis compared on one worked example.

Dimensional analysis practice

The same problems approached by cancelling units instead of cross-multiplying.

mg → mL lesson

The lesson behind most of these questions, with four levels of practice.

mg to mL Calculator

Check a dose-to-volume answer once you have worked it out yourself.

8 practice questions

Write your setup down before checking. Each answer shows the reasoning and the mistake students make most often, because a wrong setup is more useful to understand than a wrong number.

Foundation

A liquid is labelled 250 mg in 5 mL, and 500 mg is prescribed. Set up the proportion.

Show the setup, answer and why

Set up the proportion

250 mg / 5 mL = 500 mg / x mL

Answer: The known strength on one side, the prescribed dose over the unknown volume on the other.

A common wrong answer — 250 mg / 5 mL = x mL / 500 mg

The units are flipped on the right-hand side. Both ratios have to be written the same way round, or cross-multiplying compares milligrams with millilitres.

Beginner

A liquid is labelled 250 mg in 5 mL. What volume contains 500 mg?

Show the setup, answer and why

Set up the proportion

250 / 5 = 500 / x

Answer: 10 mL

Cross-multiplying gives 250x = 500 × 5 = 2500, so x = 2500 ÷ 250 = 10 mL. Sense check: 500 mg is twice 250 mg, so the volume should be twice 5 mL.

A common wrong answer — 2.5 mL

This solves the proportion upside down. The required dose is larger than the strength on the label, so the volume has to be larger than 5 mL, not smaller.

Beginner

A liquid is labelled 100 mg in 4 mL. What volume contains 75 mg?

Show the setup, answer and why

Set up the proportion

100 / 4 = 75 / x

Answer: 3 mL

100x = 75 × 4 = 300, so x = 3 mL. Sense check: 75 mg is three quarters of 100 mg, and 3 mL is three quarters of 4 mL.

A common wrong answer — 5.33 mL

This divides 4 by 75 and multiplies by 100 — the proportion inverted. A dose smaller than the labelled strength must give a volume smaller than the labelled volume.

Intermediate

A liquid is labelled 0.5 g in 10 mL. What volume contains 200 mg?

Show the setup, answer and why

Set up the proportion

500 mg / 10 mL = 200 mg / x mL

Answer: 4 mL

Convert first so both sides use the same unit: 0.5 g = 500 mg. Then 500x = 200 × 10 = 2000, so x = 4 mL.

A common wrong answer — 4000 mL

This sets up 0.5 / 10 = 200 / x without converting, so grams are being compared with milligrams. A proportion is only valid when both ratios use the same units.

Intermediate

A liquid is labelled 120 mg in 5 mL. A dose of 180 mg is prescribed. What volume is needed?

Show the setup, answer and why

Set up the proportion

120 / 5 = 180 / x

Answer: 7.5 mL

120x = 180 × 5 = 900, so x = 7.5 mL. Sense check: 180 mg is one and a half times 120 mg, and 7.5 mL is one and a half times 5 mL.

A common wrong answer — 8 mL

This rounds 7.5 to a whole number. Nothing in the question asked for rounding, and a measurable volume of 7.5 mL is perfectly ordinary.

Advanced

A liquid is labelled 250 mg in 5 mL. A supplied order is 15 mg/kg for a patient who weighs 40 kg. What volume is needed?

Show the setup, answer and why

Set up the proportion

Dose: 15 × 40 = 600 mg. Then 250 / 5 = 600 / x

Answer: 12 mL

The proportion cannot start until the dose exists. Once it does, 250x = 600 × 5 = 3000, so x = 12 mL.

A common wrong answer — Setting up 250 / 5 = 15 / x

This puts the per-kilogram figure into the proportion instead of the calculated dose. 15 mg/kg is a rate, not an amount, until it has been multiplied by the weight.

Advanced

A liquid is labelled 200 mg in 5 mL. A dose of 300 mg is prescribed, and the question also states the patient weighs 62 kg and the last dose was 6 hours ago. What volume is needed?

Show the setup, answer and why

Set up the proportion

200 / 5 = 300 / x

Answer: 7.5 mL

200x = 300 × 5 = 1500, so x = 7.5 mL. The weight and the timing are context: the prescription is a flat dose, so neither enters the proportion.

A common wrong answer — Multiplying the dose by 62 first

A supplied weight invites a per-kilogram calculation even when the prescription is not written that way. Deciding what the question asks before reading the numbers prevents it.

Advanced

A liquid is labelled 80 mg in 2 mL. What volume contains 340 mg, to one decimal place?

Show the setup, answer and why

Set up the proportion

80 / 2 = 340 / x

Answer: 8.5 mL

80x = 340 × 2 = 680, so x = 8.5 mL. Sense check: 340 mg is a little over four times 80 mg, and 8.5 mL is a little over four times 2 mL.

A common wrong answer — 4.25 mL

This divides 340 by 80 and stops, giving the number of label-strengths rather than the volume. The result still has to be multiplied by the 2 mL those 80 mg occupy.