Simplifying Ratios

Pre-Algebra · Axiom Academy

Reduce the ratio 12 : 18 to simplest form by dividing both parts by their greatest common factor. Simplify the ratio 12 : 18 — that is, rewrite it with the smallest whole numbers possible while keeping the same relationship. Nice work — you simplified a ratio using the GCF method. The recipe: List the factors of both numbers in the ratio. Find the common factors that appear in both lists, and take the largest — that's the GCF. Divide both parts of the ratio by the GCF. Result: 12 : 18 = 2 : 3 , and a ratio is in simplest form when its two numbers share no factor other than 1. The same move powers proportions, scaling recipes, and unit conversions — anywhere you need the smallest equivalent ratio.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.