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GEORGE E. ATWOOD
Eduatlo 02.160 liraies
A new edition, thoroughly revised, and printed
The work usually undertaken in Arithmetic in the last year of the grammar school course is a general review of the subjects studied in the preceding grades and the study of those topics that have not been presented before. This book has been made to meet these requirements. Beginning with divisibility of numbers, the book contains a thorough review of all the subjects presented in the other books of the series. Then follows the study of partnership, ratio and proportion, involution, evolution, longitude and time, metric system, mensuration, and the elements of Algebra.
The plan of the book differs materially from the other books of the series. The purpose for which it is made makes the topical arrangement necessary. Accompanying each topic will be found a sufficiently large number of examples and problems to illustrate the principles involved. The book also differs from the others in that it contains no oral work except on those pages devoted to Algebra. In view of the abundance of oral exercises contained in the preceding books, it is not so important that such exercises should be continued through this grade.
But if teachers wish to continue the mental arithmetic in eighth grade classes, they will find it quite convenient to make use of the oral pages found in the fifth, sixth, and seventh grade books.
A little inore of the formal work of Algebra is introduced into this book. The work begins here, as it does in the seventh grade book, with exercises that are intended to develop the idea of representing nunbers by letters, the
meaning of the equation, and its application to the solution of problems. Following these pages will be found the treatment of the fundamental processes of addition, subtraction, multiplication, and division. Under each of these heads are enough examples to develop a good degree of skill in these algebraic processes. These pages also contain several exercises in finding the numerical value of algebraic expressions, which are given for the purpose of making clear the law of the algebraic notation and the signification of the coefficient and exponent. Here is about as much of Algebra as most teachers will think best to attempt in the grammar school course. Pupils who do this work intelligently will be well prepared to take up the academic course in Algebra.
In the preparation of this book the author has received valuable assistance from F. E. Spaulding, Superintendent of Schools, Passaic, N. J.; J. C. Lyford, Principal of Winslow Street School, Worcester, Mass. ; Charles L. Van Cleve, Superintendent of Schools, Troy, Ohio; and W. H. Baker, Instructor in Mathematics, State Normal School, San Jose, Cal., for which he desires to make grateful acknowledgment.
G. E. A.
COMPLETE GRADED ARITHMETIC
An Exact Divisor of a number is a number that is exactly contained in that number.
A Prime Number is a number that has no exact divisors except itself and 1 ; as, 11, 17, 23, 29.
A Composite Number is a number that has exact divisors besides itself and 1; as, 15, 18, 45, 63.
An Even Number is a number that is exactly divisible by 2. If even, the right-hand figure is even or 0.
An Odd Number is a number that is not exactly divisible by 2; as, 7, 11, 19, 33.
Any number is exactly divisible :
By 3, if the sum of its digits is divisible by 3; as, 738, 825, 804, 498, 888.
By 4, if the number expressed by its two right-hand digits is divisible by 4 ; as, 728, 936, 760, 544.
By 5, if its right-hand digit is 5 or 0; as, 475, 730. By 6, if it is even and is divisible by 3 ; as, 534, 738.