11. Divide 46323 by 9 Facit 5147 204342 Rem. 6 ,13. 6730214 by 10 673021 When the divisor exceeds 12 work by RULE II. 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 num. ber-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 ail 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. PROOF. As under Rule I. 49, Remainder 31 1. Divide 4633 by 41 Facit 113 47 17 Rem. 6 40231 by 75 536 31 601 40058 1323 37640 26 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. 54100) 1463|40(27 108 383 378 540 2. Divide 320 Facit 238 Rem. 13 2892 294 4. 15463420 by 16001 9664 1020 5. 99607765 by 27000 3689 4765 6. 1345680000 by 120000 ,11214 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 agree ably 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. 46 true remainder 2. Divide 34320 by 99 Facit 346 Rem. 66 3. 20208 by 48 421 4. 5704392 by 108 52818 48 APPLICATION. 1. As division is a short method of discovering how of ten 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. 3. There are 12 pence in one shilling. How many shillings are there in 480 pence? Ans. 40. 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? Ags. 6. ADDITION AND DIVISION. 1. If I add 167, 394, and 447; and divide their amount by 12: what number will result? Ans. 34. 2. A person has in money, 5000 dollars; in bank-stock, 3500 dollars; and in merchandize, 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. How many did each sister receive? 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 remainder 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 many pounds are contained in any ber of dollars, we multiply the dollars by 3 and divide their product by 8. How many pounds are there in 8576 dollars? Ans. 3216. num 23 FEDERAL MONEY, OR MONEY OF THE UNITED STATES. The denominations of Federal Money are; Eagle, Dollar, Dime, Cent, and Mill. 10 mills (m.) make 1 cent, cts. -1 dime. 1 eagle The relative values of these denominations are precisely the same as those of unit, ten, hundred, &c. For, as 10 units make 1 ten, and 10 tens make 1 hundred, &c. so, 10 mills make 1 cent, and 10 cents make 1 dime, &c. And, as in writing numbers the units are placed at the right hand, the tens next, &c. so, in writing sums of Federal Money, the mills are placed at the right hand, the cents next, &c For these reasons Federal Money is 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. See the following Table, Thousands of dollars Eagles or tens of dollars mana Dimes or tens of cents O=Cents 1 2 2 3 5 6 0 6 4 2 6 O 0.4 9 1 2 6 3 4 i dollar 34 cents 10 12 dollars 10 cents 2 0 .... 23 dollars 20 cents 07 560 dollars 7 cents 0 61... 652 dollars 6 cents and a fourth 1 21...6004 dollars 12 cents and a half 1 8...9126 dollars 18 cents and three-fourths Ç 2 |