EXAMPLES. Re 12 mainder. Proof. 9 7 36 4 3 Divide 10006 by 11. Divisor. Dividend. 1 1) 1 0 0 0 6 Quot. 9097 Re11 mainder. Proof. 10 0 0 6 In this example I place the divisor at the left of the dividend with a separating line between them, and a line under the dividend. I then inquire how often 2 is contained in the two left hand figures of the dividend 15. I find it contained 7 times and 1 remaining; I set the 7 down under the 5, and conceive the remainder 1, as prefixed to the next dividend figure 2, which will make 12; I now inquire how often 2 is contained in 12, which is 6 times; I set down the 6 at the right of the last quotient figure 7, and so proceed. In the third example I found 11 contained 9 times in 100, and 1 remaining, which 1 prefixed to the next figure 0 made 10, in which 11 is not contained; I therefore set down 0 at the right of the last quotient figure 9, and conceive the next dividend figure 6 annexed to the 10, making 106, in which 11 is contained 9 times, and 7 remains. LONG DIVISION admits of several Čases, in all of which the divisor is to be placed at the left, and the quotient (when found) at the right of the dividend, with separating lines between them. CASE I. When the figures of the divisor are all significant, or have no ciphers' annexed. Inquire how often the divisor is contained in as many of the left hand figures of the dividend as are necessary, and set the resulting figure at the right of the dividend, for the first figure of the quotient. Multiply the divisor by this quotient figure, and place the product under that part of the dividend used, and subtract it therefrom.. To the remainder, annex the next figure of the dividend, and inquire how often the divisor is contained in this number; place the resulting figure in the quotient, at the right of the other, and so proceed till all the divi-dend figures are brought down. When a dividend figure is annexed to a remainder, and the divisor is not contained in this increased number, set 0 in the quotient, and annex another, &c. When the last dividend figure is annexed, if the divi-sor is not contained in that number, it will be the true remainder, and 0 must be set in the quotient. Divide 271138 by 26. Divisor. Dividend. Quotient. 26)271138 ( 10428 EXAMPLES. In this example, after finding the first remainder 1, and annexing the next. dividend figure 1: thereto, I find 26 is not contained in 10 Rem. it, there being but 11, I set O in the quotient, and annex 26 26 111 625684 104 20856. 73 52 2.18 208 10 Remainder. 271138 Proof. the next dividend figure 1. which makes 111, &c... CASE II. When ciphers are annexed to the divisor. Separate them from the significant figures, and also an equal number of figures or ciphers from the right of the dividend; divide the remaining figures as usual, and to the remainder (if any) annex the figures separated from the dividend; if there be no remainder the figures separated from the dividend will be the true remainder. Hence it is evident that any number may be divided by 10, by separating one figure from the right of the dividend; and by 100, by separating two, &c. CASE III. When the divisor can be found in the multiplication table, take the two figures which produce it; divide by one of them, as in Short Division, then divide the quotient by the other, the second will be the true quotient. 7300 93600 Quotient. 336469 8.1232 93600 7300 3600 964800 10 364172,5% 1000 If there be a remainder in one, or both operations, multiply the first divisor by the last remainder; to the product add the first remainder, the sum will be the true remainder. SUPPLEMENT TO SIMPLE DIVISION. CASE I. When the divisor is a fraction. Multiply the dividend by the denominator of the fraction, and divide the product by the numerator. ΝΟΤΕ. This Case, and Case I of the Supplement to Simple Multiplication, prove each other. NOTE. If the numerator of the fraction be 1, multiply the dividend by the denominator only, (as I will not divide). the product will be the trùe quotient. CASE II. When the divisor is a mixed number. Multiply its whole number by the denominator of the fraction, and to the product add the numerator, for a new divisor; multiply the dividend by the denominator of the fraction for a new dividend; divide this new dividend, by the new divisor; the result will be the true quotient. EXAMPLES. CASE III. When the dividend is a mixed number. Multiply it by the denominator of the fraction; to the product add the numerator for a new dividend. Multiply the divisor by the denominator of the fraction for a new divisor, then proceed as in the last Case, Examples are needless. ADDITION OF FEDERAL MONEY. THE denominations of Federal Money are expressed in the following Table. |