Excerpt from Key to Ray's New Higher Arithmetic IN the preparation of the following pages, the chief aim has been to serve the teacher. Accordingly, through a great part of the work we have merely indicated the operations required, and have thus saved the space which would be demanded for the full statements of analysis, useful chiefly in recitation drill. The help afforded by a Key being of very little value under the fundamental rules, this work does not begin with the first exercises of the new higher arithmetic. In most cases, after a short study of an arithmetical problem, the operations themselves as indicated properly by signs, will suggest the reasoning on which the solu tion is based. In the solutions here given this has been kept in view, especially where the text-book 'has pre sented a formula. To the teacher and to the class, alike, it will be advantageous to have the blackboard work written in accordance with this plan; and, on this ao count, early in the Arithmetic, the subject of Arith metical Signs has been formally presented. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.