OF ARITHMETIC AND THEIR APPLICATION TO BUSINESS EXPLAINED IN A POPULAR MANNER, AND CLEARLY ILLUSTRATED BY SIMPLE RULES AND NUMEROUS EXAMPLES. For the Use of Schools. BY ALEXANDER INGRAM, IMPROVED AND ENLARGED BY ALEXANDER TROTTER, TEACHER OF MATHEMATICS, ETC., EDINBURGH; BIBLIOTHECA Fifty-sixth Edition. AUG 1882 Edinburgh: BODLEIANA OLIVER AND BOYD, TWEEDDALE COURT. LONDON: SIMPKIN, MARSHALL, AND CO. 1881. Price One Shilling. 181. g. 215. PREFACE TO NEW EDITION. THE chief object of Mr INGRAM in composing this work was to supply at a cheap rate a proper text-book for juvenile classes, elucidating the fundamental principles of Arithmetic in their application to business; and the success of his labours is abundantly demonstrated by the rapid sale of so many editions. The Elementary Rules are explained in concise and intelligible language, adapted to the capacity of youth; and the various exercises are so arranged-commencing with the most simple, and increasing in difficulty by imperceptible degreesthat no obstruction to the progress of the pupil can possibly be apprehended. Each rule is followed by an example wrought out at length, and is illustrated by a great variety of practical questions, applicable to business, the solving of which, while it strengthens the judgment and sharpens the invention of the learner, cannot fail to make him an accurate and expeditious calculator. To make the work still more acceptable, Tables and Exercises on the Metric System have been added to this edition. These will be found amply sufficient for instructing pupils in the principles of that system, and exhibiting the advantages to be gained from uniformity in the method of forming multiples and sub-multiples of the unit. A confident expectation is therefore entertained, that this text-book of Arithmetic may continue to maintain the high reputation which it has so long and so generally held. EXPLANATION OF ARITHMETICAL TERMS AND SIGNS. NUMBER is either a unit, or consists of a collection of units; it is the name given to our conception of things considered as one or many. ABSTRACT NUMBERS. When we consider numbers in their general nature, without referring them to any particular subject, they are then called abstract; as, 3, 7, 10, etc. CONCRETE OF APPLICATE NUMBERS. When we consider number not in its general nature, but as applied to certain particular things, as, two pounds, three pence, etc., it is termed concrete or applicate. A WHOLE NUMBER consists of one or more units. A FRACTION Consists of one or more parts of unity. A MIXED NUMBER consists of a whole number and a fraction. A COMPOUND NUMBER consists of several applicate numbers joined together in one expression; as, £4, 6s. 8d. AN EVEN NUMBER is that which can be divided into two equal whole numbers. AN ODD NUMBER is that which cannot be divided into two equal whole numbers. A PRIME NUMBER is that which can only be divided by itself and unity, without a remainder; and numbers are said to be prime to each other when no number but unity will divide both without a remainder. A SQUARE NUMBER is the product of any number by itself. A CUBE NUMBER is the product of a number and its square. A COMPOSITE NUMBER is that produced by multiplying two or more numbers together; thus 28=4x7 is a composite number, and 4 and 7 are called its component parts. An ALIQUOT PART is a number which is contained in a greater an exact number of times; thus 4 is an aliquot part of 16, but not of 17, as it is contained exactly 4 times in the former, and in the latter four times and 1 over. AN INTEGER is any whole number; as, a pound, a mile, etc., or, 1, 2, 4, 6, 9, etc. MINUEND is the greater number in Subtraction. MULTIPLICAND in Multiplication is the number to be multiplied or repeated. MULTIPLIER is the number by which we multiply, or which expresses how often the multiplicand is to be repeated. |