DUBBS' COMPLETE MENTAL ARITHMETIC A VOLUME OF CAREFULLY GRADED EXERCISES CINCINNATI 1893 615090 REFERENCES. "DUBBS' ARITHMETICAL PROBLEMS." W. H. MORGAN, JOHN B. PEASLEE, Superintendent Cincinnati Schools. G. A. CARNAHAN, Prin. First Intermediate School, Cincinnati. MRS. G. MCCLINTOCK, MRS. JENNIE B. JOHNSON, Prin. Brownell School, Cleveland. A. B. JOHNSON, Clerk Hamilton Co., O., Board of Examiners. COPYRIGHT, 1893, BY E. L. DUBBS & CO. Electrotyped, Printed and Bound by C. J. KREHBIEL & CO., 248-250 Walnut St., Cincinnati, O. OF PREFACE. F all the branches now taught in our schools, Mental Arithmetic is perhaps the most important, inasmuch as it develops and strengthens the reasoning faculties more rapidly and thoroughly than the study of any other branch, while at the same time it insures the exact use of language. And as a knowledge of arithmetic is the basis of all future attainment in mathematical studies, it is evident that the instruction given upon this subject should be exhaustive and complete, and the student made master of every detail throughout all of its various departments. The art of reasoning from known to unknown-from part to whole, and vice versa-is not only useful, but attractive; and the learner, when once fairly upon the highway of rational method to a valuable end, will readily pass from one success to another-finding pleasurable recreation rather than mystery and difficulty in his endeavors to attain higher proficiency in the mathematics beyond. Education has become a matter of paramount importance, and the venerable pastime of "doing sums" without a why for rule, or a reason for explanation—or, in analysis,—“ darkening counsel by words without knowledge" to the confusion of mind and abuse of language; -all this is rapidly giving place to improved text-books, |