=Other Sign of Division.=--In the study of fractions it is shown that a fraction expresses the quotient of its numerator by its denominator, so that the preceding identity may be written 72/8 = 9, or more generally D/d = q, and another sign of division is a horizontal line separating the dividend written above it from the divisor written below it. =Proof of the Division.=--We prove a division by multiplying the divisor by the quotient and adding the remainder, if there is any; the result thus obtained must equal the dividend. When there is a remainder, the formula of division is D = dq + r. By 2.--A number is divisible by 2 when it is an even number, that is to say when it ends with 0, 2, 4, 6 or 8, as 70,836. By 3.--A number is divisible by 3 when its residue is zero or is divisible by 3. By 4.--A number is divisible by 4 when the number formed by the last two figures to the right is divisible by 4; 7528 is divisible by 4 because 28 is divisible by 4. By 5.--A number is divisible by 5 when it ends with 0 or 5, as 75,270. By 6.--A number is divisible by 6 when it is divisible by 2 and 3, as 474, because when a number is divisible by several others it is divisible by their product. By 8.--A number is divisible by 8 when the number formed by the last three figures to the right is divisible by 8; 37104 is divisible by 8 because 104 is divisible by 8. By 9.--A number is divisible by 9 when its residue is 9 or 0. By 10.--A number is divisible by 10 when the last figure to the right is 0. By 100.--A number is divisible by 100 when the last two figures to the right are 00. By 11.--A number is divisible by 11 when the sum of the figures of even rank subtracted from the sum of the figures of uneven rank (increased by 11 if necessary) is 0 or divisible by 11, as 95832, 3304081. By 12.--A number is divisible by 12 when it is divisible by 3 and 4, as 756. By 15.--A number is divisible by 15 when it is divisible by 3 and 5, as 255. Suggestions for the Study of Arithmetic By ERNEST L. CRANDALL Former Civil Service Examiner There are certain “standard errors,” so to speak, that the unsuccessful candidate makes nine times out of ten, and if these are eliminated every one, with a little practice, may put himself in line for 100 per cent. While the examples may take the form of “problems,” the only processes involved will be simple addition, subtraction, multiplication and division--no fractions or decimals. In addition there is but one thing to be observed. If your numbers are not all of equal length arrange them so that the last figures are all in the same column. Suppose you have to add 357,856, 7,596, 452 and 29,360. Following are the right and wrong ways to arrange them: Right way. Wrong way. 357,856 357856 7,596 7596 452 452 29,360 29360 ------- ------