Ratios, Proportions & Rates

Ratios compare quantities

A ratio a:b compares two quantities of the same kind. You can scale both parts by the same non-zero number without changing the comparison.

Unit rates and speed

A rate compares different kinds of quantities (km per hour, price per kg). A unit rate uses a denominator of 1 — that is usually the number you want for decisions.

• Unit price: total cost ÷ quantity.
• Speed = distance ÷ time; time = distance ÷ speed; distance = speed × time.
• Scale drawings: map distance / real distance = constant scale factor.

Worked example — mixture

Paint is mixed 3:2 (blue:white). For 15 litres of mix, parts = 3+2 = 5. Blue = (3/5)×15 = 9 L; white = 6 L.