Simplifying Ratios

A ratio is in simplest form when its terms are whole numbers with no common factor other than \(1\), so \(45:75\) simplifies to \(3:5\). In NSW Year 8 maths this subtopic takes simplifying further than Year 7, with larger numbers and more terms (NESA outcome MA4‑RAT‑C‑01).

You will divide every term by the highest common factor, simplify ratios with three or four terms, clear decimals, fractions and mixed numerals first, and change amounts to the same unit before writing the ratio, so \(40\text{c} : \$2 = 1:5\). Ratios with pronumerals, money, drink recipes and canteen sales all appear, along with comparing one part to the whole. It is part of Year 8 Rates and Ratios.