Common Registration Assessment, Part 1
Direct proportion and cross-multiplication
Practise scaling quantities with ratios and cross-multiplication, with three original worked questions.
Published 9 October 2026. Independent revision material, not GPhC questions, not for patient care.
Many calculation questions are direct proportion: if one quantity doubles, so does the other. A ratio table or cross-multiplication gets the answer without a formula.
The examples are fictional. Write the known pair on one line and the pair with the unknown on the next, keeping the units aligned.
The method
- Write the known pair, for example 5 mg in 2 mL.
- Write the second pair with a gap for the unknown.
- Cross-multiply, then divide.
- Keep the same unit on both sides.
- Check the answer is larger if the other quantity grew.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
A fictional solution holds 5 mg in 2 mL. What volume holds 7.5 mg?
Show the answer
Answer: 3 mL
Working: 7.5 ÷ 5 = 1.5. 1.5 × 2 = 3 mL.
Question 2
A fictional pack of 15 tablets costs £3.60. What do 40 tablets cost?
Show the answer
Answer: £9.60
Working: £3.60 ÷ 15 = £0.24 per tablet. 0.24 × 40 = £9.60.
Question 3
A fictional cream has 18 g of active in 450 g. How much active is in 125 g?
Show the answer
Answer: 5 g
Working: 18 ÷ 450 = 0.04. 0.04 × 125 = 5 g.
Same unit both sides
Convert before you set up the ratio. A mismatched unit is the commonest slip.
Where marks are lost
- Putting the unknown over the wrong quantity.
- Mixing units, such as mg on one side and g on the other.
- Not checking the result is sensible.
Frequently asked questions
What is cross-multiplication?
If a/b = c/d, then a × d = b × c. Solve for the missing term.
Can I use unit rates instead?
Yes. Finding the amount per one unit first is the same method.
Sources
- The Pharmaceutical Journal, medication maths: dilutions
- The Pharmaceutical Journal, medication maths: quantities to supply and using provided formulae
- GPhC, 2026 assessment specification and permitted items
The questions above are original and use fictional drugs. PreRegExamPrep is not affiliated with or endorsed by the General Pharmaceutical Council.
Practise until the method is automatic
Try 15 free questions with worked answers. No sign-up required.
More calculation topics
- Dose by weight calculations for the GPhC assessment
- Volume to give: liquid medicine calculations
- Percentage strength calculations: w/v, w/w and ratios
- Dilution calculations with C1V1 = C2V2
- Infusion rate calculations in mL per hour
- Drip rate calculations: drops per minute
- Body surface area calculations
- Creatinine clearance (Cockcroft-Gault) calculations
- Moles and millimoles calculations
- Displacement volume calculations for reconstitution
- Quantity to supply calculations
- Using a provided formula in calculations
- Dose information from packaging and labels
- Diluting a stock to a lower strength
- Medicine cost and switch calculations
- Rounding rules in calculations
- Enteral feed rate calculations
- Electrolyte content over time
- Infusion dose per kg per hour
- Rounding doses to measurable volumes
- Relative risk and relative risk reduction
- Absolute risk reduction and number needed to treat
- Odds ratio and confidence intervals
- Relative versus absolute risk reduction
- Loading dose and volume of distribution
- Top-up doses from measured drug levels
- Salt correction factors
- Mass and molar drug concentrations
- Half-life and falling drug levels
- Steady-state concentration and infusion rate
- Bioavailability and equivalent oral doses
- Oral maintenance dose and dosing interval
- Elimination rate constant and half-life
- Accumulation towards steady state
- Ratio strengths and one in X
- Serial dilution factors
- Mixing solutions of different strengths
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
- Unit conversions for mass and volume
- Units and units per mL
- Reconstituting powders and final concentration
- Millimoles and milliequivalents
- Infusion time and volume remaining
- Days supply from pack sizes
- Percentage w/v and w/w conversions
- Ideal and adjusted body weight from formulae
- Diluting creams and ointments by weight
- Scaling a formula to a batch size
- Age-band doses from a provided table
- Tablet fractions and split doses
- Stones, pounds, inches and metric conversions
- Micrograms per minute from mg per hour
- Percentage change and mark-up
- Molar solutions and mass per volume
- Osmolarity from component concentrations
- Scientific notation and very small quantities
- Stock use and reorder quantities
See also the formula sheet, the eight sample questions and the approved calculator page.