ELEMENTARY ARITHMETIC FOR USE IN PUBLIC, ELEMENTARY, AND COMMERCIAL SCHOOLS. BY H. T. SORTWELL, HEAD MASTER OF THE DIOCESAN COLLEGE, OXFORD. LEIAN LONDON: GEORGE PHILIP & SON, 32 FLEET STREET; PREFACE. THAT Arithmetic should form an important feature in the routine of every School, and especially in those departments, whose special object is, to prepare pupils for business and mercantile life-is an admitted fact on all sides. It cannot, however, be overlooked, that the results of teaching, as evidenced by the examinations of Her Majesty's Inspectors and others, are not at all satisfactory, considering the time usually devoted to this subject. The reason of this, I think, lies in the fact, that teachers of the present day aim too much at the accurate and quick working of mechanical examples-sums, which involve no thought, and by which the reasoning powers are not in any way brought into play. I venture to think that if teachers would deal more with applied questions, or problems, as they are sometimes called, instead of with examples which call forth nothing but a mechanical application of figures, the results would amply repay them. So many works on Arithmetic have appeared, and especially of late, that the Author would consider this unpretending manual superfluous, if he did not think that he had embodied some new method in its compilation. He has endeavoured to make the exercises graduate from the easy to the difficult, by a succession of intermediate steps-the exercises are copious and original, and have been constructed with a view to utility, as well as to interest. Every exercise is accompanied by a model example, and a short explanation of the process by which it is worked. Great stress has been laid upon the advantage of solving problems by what is known as the method of First Principles, because this method, above all others, is calculated to exercise the reasoning faculties of the pupil, and to make him use his common sense. The Author cannot urge too strongly upon teachers the importance of working numerous examples on the black-board in the presence of the class, and of requiring the pupils to enter neatly in an exercise book any problem which presents a difficulty. The Answers to the Exercises are published in a separate form to prevent an injurious reference to them on the part of pupils. It is hoped that this little manual may be alike useful to Teachers and Scholars. Diocesan College, Oxford. H. T. SORTWELL. ELEMENTARY ARITHMETIC. Arithmetic is the art of computing by numbers It consists of two parts-whole numbers and fractions. In Whole Numbers, Arithmetic consists of entire quantities, which are not divided into parts less than a unit. In Fractions, it consists of parts of some whole quantity, or of a unit. Number is either a unit, or a collection of units, and is the name given to our conception of things, considered as one or many. Abstract Number. When Number is considered in its general nature, and is not referred to any particular subject, it is called Abstract, as 5, 8, 17, &c. Concrete Number. When we apply Number to certain particular things, as three pecks, two pence, it is termed Concrete or Applicate. An Even Number is that which is divisible into two equal whole numbers. An Odd Number is that which is not divisible into two equal whole numbers. A Whole Number is a Unit, or a Multiple of one or more Units. A |