15 A TREATISE = OF ARITHMETIC, DESIGNED FOR THE USE OF THE ELEMENTARY SCHOOLS; FOLLOWED BY THE PRINCIPLES FOR MEASURING THE SURFACE, AND THE SOLIDITY OF THE BODIES. Montreal: PRINTED BY LOVELL & GIBSON, ST. NICHOLAS STREET. 2-21-47 ADE 3-12-45 52013 EXPLANATION OF ARITHMETICAL TERMS. NUMBER is either a unit, or consists of a collection of units; being 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, &c. CONCRETE OR APPLICATE NUMBERS. When we consider number not in its general nature, but as applied to certain particular things, as, two pounds, three pence, &c., it is termed concrete or applicate. A WHOLE NUMBER consists of one or more units. A COMPOUND NUMBER consists of several applicate numbers joined together in one expression; as £4 6s Sd. 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 multiply 4 ARITHMETICAL TERMS AND SIGNS. ing two or more numbers together; thus 28=4×7 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 4 times and 1 over. An INTEGER is any whole number; as, a pound, a mile, &c., or, 1, 2, 4, 6, 9, &c. 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. PRODUCT is the sum or result of the operation in Multiplication. FACTORS. The multiplicand and multiplier are called factors of the product. DIVISOR in Division is the number by which we divide. is the number to be divided. DIVIDEND QUOTIENT is the number which shows how often the divisor is contained in the dividend, or the result of the operation. DENOMINATION in applicate numbers is the name of the subject to which the number is applied; as, pounds, shillings, yards, miles, &c. NUMERATOR is the upper number of a fraction, and shows how many parts of unity are expressed by the fraction. DENOMINATOR is the under number of a fraction, and shows into how many parts the unit is divided. A COMMON MEASURE is any number that will divide two or more numbers without a remainder, and their greatest common measure is the greatest number that will do so; thus 2 is a common measure of 12 and 18, and 6 is their greatest common measure. MULTIPLE. One number is said to be a multiple of another when the former contains the latter an exact number of times; thus 8 is a multiple of 4. A COMMON MULTIPLE of two or more numbers is any number that contains each of them an exact number of times, and the least number that will do so is called their LEAST COMMON MULTIPLE; thus 48 is a common multiple of 12, 6, and 4, and 12 is their least common multiple. addition; =(equal to) denotes equality; thus 21s.=1 guinea. +(plus) thus 6+4-10. -(minus) subtraction; thus 7-3 4. (multiplied by). . multiplication; thus 4x 3-12. +(divided by). . . . division; thus 18+ 6 3. :(is to): (as) are signs used in proportion to denote an equality of ratios; thus 4:6:: 8:12 denote that the ratio of 8 to 12 is the same as that of 4 to 6, and is read, 4 is to 6 as 8 is to 12. represents a farthing, or the quarter of any thing. a halfpenny, or the half of any thing. three farthings, or three quarters of any thing. |