When the divisor exceeds 12, work by RULE II. or LONG DIVISION. Take for the first dividual as few of the left hand figures of the dividend as will contain the divisor, try how often they will contain it, and set the number of times on the right of the dividend-multiply the divisor by this number-subtract its product from the dividual, and to the remainder affix the next figure of the dividend, to form a second dividual: or if this be not sufficient, set a cypher on the right of the dividend, and affix the next figure, and so on, till a sufficient number of figures are affixed-try how often the divisor is contained in this second dividual, and proceed as before. Continue this process till all the dividend figures are employed as above directed; or till the number they form, when affixed to a remainder, is not large enough to contain the divisor. When the work is done, the figures on the right of the dividend form the quotient. Note 1. Cyphers on the right of the divisor may be omitted in the operation, observing to separate as many figures from the right of the dividend, which annex to the remainder. EXAMPLES. 1. Divide 146340 by 5400. Facit 27, remainder 540. 54|00)1463|40(27 Note 2. When the divisor is the exact product of any two factors in the multiplication table, the division may be performed thus:-Divide first by one of the factors agreeably to rule 1; then divide the quotient by the other factor in the same manner. When a remainder occurs in the first operation and none in the last, it is the true one: but a remainder in the last operation must be multiplied by the first divisor, and its product added to the first remainder (if any) for the true remainder. EXAMPLES. 1. Divide 46508974 by 96. Facit 484468. Rem. 46 8)46508974 12)5813621-6 first remainder. 484468-5 last remainder. 8 40 6 46 true remainder. 1. As division is a short method of discovering how often one number is contained in another, how often is 3 contained in 3699? Ans. 1233 times. 2. How many times is 25 contained in 132? Ans. 5 times with 7 over. How many Ans. 40. 3. There are 12 pence in one shilling. shillings are there in 480 pence? 4. The price of a pair of shoes is 2 dollars. How many pair may be had for 56 dollars? Ans. 28. 5. Fifty-four apples are to be divided, equally, between two boys. How many must each boy have? Ans. 27. 6. Suppose a man travel 40 miles a day: how many days will he be in travelling 240 miles? Ans. 6. ADDITION AND DIVISION. 1. If I add 167, 394, and 447; and divide their amount by 12: what number will result? Ans. 84. 2. A person has in money, 5000 dollars; in bankstock, 3500 dollars; and in merchandise, 12500 dollars. He intends to divide this property, equally, among his 3 sons. What will be the share of each son? Ans. 7000 dollars. 3. Suppose a farmer, who has a plantation of 520 acres, buys an adjoining one of 375 acres, and divides the whole into five equal portions: how many acres will there be in each portion? Ans. 179. SUBTRACTION AND DIVISION. 1. Subtract 2468 from 5796, and divide the remainder by 26. Result 128. 2. William bought 12 pears: he kept 6 of them, and divided the rest between his two sisters. did each sister receive? How many Ans. 3. 3. A man, at his decease, left property, amounting to 12426 pounds. He directed in his will that 1000 pounds should be given to his niece; and that the re mainder of the property should be divided, equally, between his two nephews. What is the share of each nephew? Ans. 5713 pounds. MULTIPLICATION AND DIVISION. 1. Multiply 145 by 12, and divide the product by 6. Result 290. 2. To find how many dollars are contained in any number of pounds, we multiply the pounds by 8, and divide their product by 3. How many dollars are there in 456 pounds? Ans. 1216. 3. To find how inany pounds are contained in any number of dollars, we multiply the dollars by 3 and divide their product by 8. How many pounds are there in 8576 dollars? FEDERAL MONEY. Ans. 3216 OR MONEY OF THE UNITED STATES. The denominations of Federal Money are; Eagle Dollar, Dime, Cent, and Mill. 10 mills (m.) make 10 cents 1 cent, cts. 1 dime. 10 dimes (or 100 cts.) 1 dollar, D. or $ 1 eagle. 10 dollars These denominations have precisely the same ela tive values as those of unit, ten, hundred, &c. and are also similarly ranged in Numeration. Federal money is therefore added, subtracted, multiplied, and divided by the same rules that are given for simple Addition, Subtraction, Multiplication, and Division. It must be remarked, however, that in writing sums of Federal Money, parts of a cent are generally used instead of mills; and that, in reading those sums, neither the eagles nor dimes are mentioned: the former being considered as tens of dollars; and the latter as tens of cents. The parts or fractions of a cent, used instead of mills, are expressed by two numbers, placed one above the other, with a line drawn between them. The under number denotes the part; and the upper one informs how many of that part are designed to be expressed: as, one fourth; three fourths; one third; & two thirds; a half. NUMERATION OF FEDERAL MONEY. In writing sums of Federal Money, the cents are placed on the right of the dollars, and are separated from them by a point. If there are not more than 9 cents in the sum, a cypher is put in the tens' place; and if there are no cents, two cyphers are used. If the point which separates the dollars from the cents be removed or supposed to be removed, the sum may be considered as cents only: and when the sum is cents only, if two figures be separated from the right, all on the left of these will be dollars. See the following TABLE. Thousands of dollars Dimes or tens of cents 1 2 4... 1 0.. 23 2 0. 1 dol. 34 cents, or 134 cents 12 dols. 10 cents, or 1210 cents 23 dols. 20 cents, or 2320 cents 560 0 7. 560 dols. 7 cents, or 56007 cents 6 cts. and 4 or 642064 c. 12 cts. and or 6004124c. 18 cts. and or 9126184c. 642 0 64 642 dols. 1 2 6004 dols. EXAMPLES. To be read by the learner as dollars and cents, and also as cents only. 1.49 3.26 4.75 9.18 17.90 21.09 14.02 125.00 426.00 900.00 340.064 3911.10 4006.182 76420.01 19560.00 11904.10 4896.73 . 400.00 4500.06. |