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Read a Medication Maths Question
Separate what the patient needs, what you have available, and what the question wants you to find before calculating.
MedMaths Learn pathway
Medication Maths Essentials
Build the essential maths and thinking skills used in medication practice every day. Work through short, focused lessons and build confidence step by step.
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Read a Medication Maths Question
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Work through Medication Maths Essentials
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Unit Conversions
Grams, milligrams, micrograms, liters, milliliters, kilograms, pounds, hours and minutes.
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Medication Labels & Concentrations
Read what is in a bottle, vial or ampoule and understand how much medication is present in a stated volume.
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Decimals, Fractions & Rounding
Understand values such as 0.5 and 0.25, connect common fractions to decimals, use safer decimal notation, and round only when required.
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Medication Administration Rights & Safety Checks
Use six simple medication checks around the maths: patient, medicine, dose, time, route and documentation.
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Lesson summaries
What each Medication Maths Essentials lesson teaches
A short recap of every lesson in this stage: the key idea, a worked example and the mistake students make most often. Open any lesson for the full step-by-step teaching and its four levels of practice.
Read a Medication Maths QuestionMost medication questions contain three different kinds of number: what the patient has been prescribed, what the available product contains, and sometimes a figure such as weight or time that changes the calculation. Sorting the numbers into those groups before calculating is what makes the rest of the maths straightforward, because it tells you which value belongs where.
Most medication questions contain three different kinds of number: what the patient has been prescribed, what the available product contains, and sometimes a figure such as weight or time that changes the calculation. Sorting the numbers into those groups before calculating is what makes the rest of the maths straightforward, because it tells you which value belongs where.
Worked example
A question states: the prescribed dose is 750 mg. The available liquid is labelled 250 mg in 5 mL. The patient weighs 68 kg. What volume is needed?
- 1Prescribed: 750 mg — this is what has to be given.
- 2Available: 250 mg in 5 mL — this describes the product, not the patient.
- 3Weight: 68 kg — nothing in this question uses weight, so it is not needed.
- 4Final answer unit: mL, because the question asks for a volume.
Three numbers are supplied; only two of them belong in the calculation.
Common mistake
Using every number the question offers. A supplied weight only matters when the prescription is written per kilogram — otherwise it is context, not an input.
Name what you are being asked to find, and in what unit, before you touch the arithmetic.
Unit ConversionsA conversion expresses the same amount using a different unit — the quantity does not change, only the way it is written. Within the metric families used in medication maths, each step is a factor of 1000: grams to milligrams, milligrams to micrograms, litres to millilitres. Hours to minutes is a factor of 60.
A conversion expresses the same amount using a different unit — the quantity does not change, only the way it is written. Within the metric families used in medication maths, each step is a factor of 1000: grams to milligrams, milligrams to micrograms, litres to millilitres. Hours to minutes is a factor of 60.
Formula
1 g = 1000 mg · 1 mg = 1000 micrograms · 1 L = 1000 mL · 1 hour = 60 minutes
Moving to a smaller unit multiplies; moving to a larger unit divides.
Worked example
A prescription is written as 1.2 g. The available product is labelled in milligrams.
- 1Grams to milligrams is a move to a smaller unit, so multiply.
- 21.2 × 1000 = 1200
- 3Check by reversing: 1200 ÷ 1000 = 1.2 g.
1.2 g = 1200 mg
Common mistake
Dividing when you should multiply. The direction is easy to confirm: a smaller unit always produces a larger number, so 1.2 g becoming 1200 mg makes sense while 0.0012 does not.
Convert first so both values share a unit, then reverse the conversion to check it.
Medication Labels & ConcentrationsA label usually tells you two separate things: the total amount in the container, and the concentration — how much medicine sits in each stated volume. A vial marked 500 mg in 10 mL contains 500 mg altogether, at a concentration of 50 mg in every 1 mL. Confusing the total with the concentration is one of the most common sources of a wrong volume.
A label usually tells you two separate things: the total amount in the container, and the concentration — how much medicine sits in each stated volume. A vial marked 500 mg in 10 mL contains 500 mg altogether, at a concentration of 50 mg in every 1 mL. Confusing the total with the concentration is one of the most common sources of a wrong volume.
Formula
concentration = total amount ÷ total volume
Worked example
A vial is labelled 500 mg in 10 mL.
- 1Total amount in the vial: 500 mg.
- 2Total volume in the vial: 10 mL.
- 3500 ÷ 10 = 50
The concentration is 50 mg/mL — every 1 mL contains 50 mg.
Common mistake
Reading '500 mg in 10 mL' as though 500 mg were the strength of each millilitre. The number on the front of the label is a total until you divide it by the volume.
Work out what one millilitre contains before you calculate the volume to give.
Decimals, Fractions & RoundingThe places after a decimal point are tenths, hundredths and thousandths, so each step right divides the value by ten. That is why 0.5 is ten times larger than 0.05 — a difference that is easy to miss when reading quickly. Rounding is a separate decision from calculating, and it belongs at the end of the working, not in the middle.
The places after a decimal point are tenths, hundredths and thousandths, so each step right divides the value by ten. That is why 0.5 is ten times larger than 0.05 — a difference that is easy to miss when reading quickly. Rounding is a separate decision from calculating, and it belongs at the end of the working, not in the middle.
Worked example
A calculation produces 1.666666… mL and the question asks for one decimal place.
- 1Keep the full value while calculating — do not round early.
- 2One decimal place means the nearest tenth.
- 3The digit in the hundredths place is 6, so the tenths digit rounds up from 6 to 7.
1.7 mL, rounded only at the final step
Common mistake
Rounding an intermediate value and carrying the rounded number forward. Each early round introduces a small error that grows through the remaining steps.
Write a zero before a decimal below one, avoid an unnecessary trailing zero, and round once — at the end.
Medication Administration Rights & Safety ChecksThe administration rights — patient, medicine, dose, time, route and documentation — are the checks that sit around a calculation. They matter to medication maths because a perfectly correct number can still be the wrong number to act on if it was calculated from the wrong label, for the wrong patient, or for a different route than the one prescribed.
The administration rights — patient, medicine, dose, time, route and documentation — are the checks that sit around a calculation. They matter to medication maths because a perfectly correct number can still be the wrong number to act on if it was calculated from the wrong label, for the wrong patient, or for a different route than the one prescribed.
Worked example
A volume has been calculated correctly from a label reading 100 mg in 2 mL, but the prescription specifies a different route than the product is labelled for.
- 1The arithmetic is checked and correct.
- 2The product in hand does not match the prescribed route.
- 3The calculation is not the thing that resolves this — the mismatch is.
Correct arithmetic does not make an administration decision safe on its own.
Common mistake
Treating a checked calculation as a completed check. The maths confirms a number; it says nothing about whether that number should be given.
A correct answer is one input to a decision, not the decision — local policy and clinical judgement still apply.