Ratio, Proportion & Unitary Method

A ratio compares two quantities of the same kind by division — 'how many times' one is of the other — and is written a : b, read 'a to b'. The two quantities must be in the same unit before you compare (30 minutes to 1 hour is 30 : 60, not 30 : 1). A ratio has no unit of its own and is normally given in simplest form by dividing both terms by their HCF. Order matters: 2 : 3 is not the same as 3 : 2. A proportion states that two ratios are equal, a : b :: c : d, and its defining test is that the product of the extremes (a, d) equals the product of the means (b, c) — this cross-product rule is the engine of most ratio problems. The unitary method underlies all of it: find the value of one unit first, then scale up to however many you need. PEDAGOGY: the upper-primary curriculum builds ratio out of children's intuitive sense of 'sharing' and 'for every', so good teaching starts concrete (3 spoons of sugar for every 5 cups of milk) before the colon notation. COMMON MISCONCEPTIONS: children compare quantities in different units without converting; they treat 2 : 3 and 3 : 2 as the same; and they add to a ratio instead of multiplying — thinking 1 : 2 becomes 2 : 3 when 'one more of each' is added. HOW TESTED: dividing a quantity in a given ratio, finding the missing term of a proportion, and a pedagogy item on why a child's same-unit error happens.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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