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Treat the units as unknowns in algebra and manipulate them using the laws of indices.

eg a volume of cm³ of a substance spread over an area of cm² (say 5 cm³ spread over an area of 10 cm²) gives an answer in cm³ ÷ cm² = cm^(3-2) = cm^1 = cm (5 cm³ ÷ 10 cm² = 0.5 cm of depth).

eg density is mass over volume, thus the units of density can be kg/m³ (where mass is in kg and volume is in m³), g/cm³ (where mass is in g and volume is in cm³), etc.

eg speed = distance/time → distance = speed × time; if speed is mph (miles/hour) and time is in hours then distance = speed × time = miles/hour × hour = (miles×hour)/hour = miles {as the hours cancel}.

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