Simplifying Ratios

Simplifying a ratio means rewriting it with the smallest whole numbers that keep the same comparison, so \(18:24\) becomes \(3:4\). In NSW Year 7 maths this builds directly on finding common factors (NESA outcome MA4‑RAT‑C‑01).

You will divide every term by the highest common factor, simplify ratios with three terms, clear decimals and fractions first, and change measurements to the same unit before comparing, so \(30\text{ cm} : 1\text{ m} = 3:10\). Recipes, paint mixes and concrete all rely on simplified ratios. This subtopic is part of Year 7 Ratios, Rates and Time.