rat_reckon

This root sits on a fascinating Roman idea: that thinking and counting are the same act. It comes from Latin rērī ('to reckon, calculate, think'), whose past participle is ratus ('reckoned, calculated, fixed, valid'), and from its noun ratiō ('a reckoning, an account, and therefore reason'). To a Roman, a ratiō was both a column of figures and a line of reasoning — logic was a kind of bookkeeping.

That double life splits the family into two branches that still feel related.

The counting branch. ratiō gives us ratio (the proportion of one quantity to another), and from the same root come rate (a measured amount per unit — speed, price, frequency), rating (a measured score), ration and rationing (a calculated, fixed allowance — your share, worked out by arithmetic). All of these are about measuring and allotting by number.

The reasoning branch. The very same ratiō also means 'reason,' giving us reason (cause, justification, and the faculty of logical thought), reasoning (the process of thinking it through), and reasonable (in line with reason — fair, sensible, not excessive). The adjective rational ('governed by reason') keeps the Latin form intact, and the grand, bookish ratiocination literally means 'the working-out of a reckoning' — step-by-step logical thought.

Bridging both branches is ratify: rat- ('reckoned, fixed, made valid') + a hidden -fic-/-fac- ('to make') = 'to make valid.' To ratify a treaty is to give it official, settled validity by formal reckoning — the moment a calculation becomes binding. Its noun is ratification.

The unifying thread of the whole family: take something — a quantity, a claim, an argument — and settle it by reckoning. Whether the reckoning is arithmetic (ratio, ration) or logical (reason, rational) or legal (ratify), it is the same Roman habit of treating reason as a careful account.