THE ILLUSTRATIVE PRACTICAL ARITHMETIC BY A NATURAL METHOD, WITH DICTATION EXERCISES. FOR COMMON SCHOOLS, HIGH SCHOOLS, NORMAL SCHOOLS, BY GEO. A. WALTON, A. M., AND ELECTA N. L. WALTON, NEW YORK J. W. SCHERMERHORN & CO. 1871. ARITHMETICAL TABLE. Entered according to Act of Congress, in the year 1864, by G. A. WALT N, in the Clerk's Office of the District Court of the District of Massachusetts. For Explanation, sce Manual and Key," pages 23, 25, etc. 21 20 13 18 17 16 15 14 13 12 11 10 98 7 6 5 4 3 2 1 0 2 5 9 8 7 9 1 5 3 1 7 1 8 4- A 8 8 4 4 2 5 8 7 5 9 9 5 3 3 7 6 8 6 7 26 1 7 8 7 2 6 9 2- C A-9 8 7 4 4 9 8 2 0 6 8 6 2 2 0 6- K 3 46 2 1-M 15 8 4- N N-1 4 4 8 6 8 1 5 2 1 6 0 2 1 6 1 1 7 2 9 0 0 8 4 5 7 5 4 9 0 9 4 0- Р 9 4 1 8 0 8 7 6 7 0 0- Q 9 6 5 9 49 0 2 2 9 8- R 78 0 6 3 9 61 75- S 6 4 8 4 6 2 7- T 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Entered according to Act of Congress, in the year 1869, by in the Clerk's Office of the District Court of the District of Massachusetts. HARVARD 55*24 PREFACE. THE plan of the Illustrative Practical Arithmetic is indicated by its title; it embraces the following GENERAL PRINCIPLES. 1. The subjects taught are presented in their natural order. Part I. contains an elementary course in the fundamental operations with applications to United States Money, Bills and Receipts. Part II. contains concise reviews of the fundamental operations, with rules; Properties of Numbers; Fractions, Common and Decimal; Compound Numbers and Metric System; Percentage, with its applications; Ratio and Proportion, with Partnership; Involution and Evolution; Mensuration. Contractions in Multiplication and Division, Annual Interest, etc., being incidental, are placed in an Appendix. 2. Ideas are excited by familiar illustrations, in which reference is always had to the objects themselves. See the treatment of the funda mental operations, Fractions, Percentage, etc. This principle is 3. The unknown is taught through the known. illustrated in every part of the book, which is so arranged that the occasion for knowledge which the pupil acquires is found in an illustration or in knowledge he previously possessed. See 4. Each synthetic statement follows from a previous analysis. the manner of deriving definitions and rules from the analysis of illustrative examples, with accompanying questions to be answered synthetically. 5. The language is an exact expression of the ideas excited by the illustrations. See definitions and explanations throughout the book. It has been necessary in some instances to reject stereotyped forms of expression as meaningless, inappropriate, or contradictory, and to adopt language that describes the operations with greater accuracy, and which in many cases is much more simple. See explanation of Subtraction, Multiplication, Fractions, Mensuration, etc. 6. Usually but one process is taught for a particular operation, and that the most practical. See Subtraction; Division of Integral Numbers and of Decimals; Interest; Evolution, etc. 7. Matter and methods which have become obsolete or useless to the general student are rejected; such as English Notation; much of Com |