In order that a student may pursue the study of Arithmetical Analysis successfully, there are a few things, in a preliminary way, he must know. Among the most important of which are the following: (1) He must be able to divide a number or quantity into parts in the ratio of whole numbers. (2) He must be able to divide a number or quantity into parts in the ratio of several fractions. (3) He must be able, if he have, of one number say equal to of another," to express these numbers in common terms. Number (1) above may be illustrated by the following problem and its accompanying solution. (a) Divide 520 into three parts which shall be to one another as 2, 3, and 5. SOLUTION. Represent the first portion by 2 parts, the second by 3 parts, and the third by 5 parts. Then will the number be represented by 2 parts + 3 parts + 5 parts = 10 parts. ... 10 parts 520, 2 parts = 104, 3 parts 5 parts = 210. .. The parts are 104, 156 and 210. After one or two detailed solutions like the above, have pupils contract solutions, leading them to see that each part will be such a fraction of the number to be divided, as its proportional part is of the sum of all the proportional parts. In the above, the first part would be of 520, the second, and the third. This important process should be thoroughly mastered. II. Number (2) may be illustrated by the following problem. 8=8×$4=$32, B's share. The expression of one or more quantities in common terms, in problems like this one, is a very difficult, and also a very important thing to be able to do. After pupils have thoroughly mastered simple exercises like the above, problems like the following might be equals of your age, how old am given: If of my age + 8 years I, the sum of our ages being 45 years? Keep your exercises graded to the increasing strength of your class. IV - (4) THE EQUATION The equation belongs to arithmetic as well as to Algebra. Every formal comparison between two quantities leads to it; all our reasoning in arithmetic involves it; we could not think to any purpose in arithmetic without the equation. Hence the importance of thoroughly mastering the equation in all its various forms. This can be accomplished best by arranging a series of interesting problems whose solutions will produce equations involving all the The equivalent of Algebraic transposition is required in almost. every exercise of mental arithmetic, and it should be effected in this way: Pointing to the first equation in the above solution, say " is the sum of two quantities; and if from the sum of two quantities, we should take away one of them, the remainder would be the other." Therefore of A's age = 16 years. Or, say "If equals be subtracted from equals, results will be equal; therefore of A's age 16 years." As an illustration, a pair of balance scales might be drawn on the board, placing of A's age in one scale pan, and A's age + 16 years in the other. Then to preserve the balance, if of A's age be taken. from one scale pan, we must also remove of A's age from the other; thus showing that of A's age = 16 years, as before. THE OHIO EDUCATIONAL MONTHLY. PUBLISHED AT COLUMBUS, OHIO. O. T. CORSON, EDITOR. MARGARET W. SUTHERLAND, ASSOCIATE EDITOR. SUBSCRIPTION RATES. PER YEAR IN ADVANCE, $1.50. In clubs of four or more, $1.25 each. Single Number, except August, 15 cents. August Number, 25 cents. All club subscriptions not paid within three months, $1.50. MONEY should be sent by express, draft, money order or registered letter. Make all remittances payable to O. T. CORSON. THE MONTHLY is mailed the first week of each month. Any subscriber failing to receive a copy by the tenth should give notice promptly, and another will be sent. Any person wishing his address changed must send notice not later than the twenty-fifth of the month, and must give both the old and the new address. Notice will be given to each subscriber of the time his subscription expires. July 7-12, 1898. A FEW Prime requisites of a good high school commencement: 1. Prompt beginning. 2. Brief prayer with at least an indirect reference to the class and the exercises. (Foreign missions. can be omitted and made a special order for the next missionary meet. ing.) 3. Music furnished by representatives of the school, if possible. (If furnished by an orchestra, a sol emn agreement should be entered into that not quite all the time should be taken up by it. A little is needed for the other exercises.) 4. Brief exercises by the graduates with no attempt at oratory. 5. Little eloquence and much common sense and brevity in presenting diplomas. We are indebted to Prof. J. V. Denney, O. S. U., for a very interesting account of the recent meeting of the North Central Association of Colleges and Secondary Schools. The editor without Prof. Denney's knowledge or consent desires to add to what he has so well said that one of the most important and helpful papers read at the meeting was the one by Prof. Denney himself. It was most favorably commented upon by all present. WITH this number we close the O. T. R. C. Department for the present year. We feel sure that the articles published in this department have been helpful to our readers, and it is our present intention to open it up again with the October number. The Board of Control meets in Columbus, Saturday, May 14, to receive the annual report of the State Secretary, adopt books for the coming year and attend to any other business which may properly come up for consideration. The Reading Circle is a great power for good in Ohio and is worthy the support of every teacher and friend of education in the State. Let us all continue to stand by the O. T. R. C NORTH CENTRAL ASSOCIATION OF BY PROF. J. V. DENNEY, O. S. U. The third annual meeting of this association, which includes representatives of the leading colleges and secondary schools of the twelve North Central States, was held at the Chicago Auditorium, April 1 and 2. Dr. Canfield, president of the association during the last year, opened the program with a characteristic address on broad lines, reviewing the progress of the schools and emphasizing the public side of education. He showed that the conception of education, as a necessity for all classes of people, and as a matter of public concern, is com |