8. In the partition of lands in a certain settlement, A. had 757 acres allotted to him; B. 2104; C. 16410; D. 12881; E. 11008; F. 9813; H. 13800; and I. 8818 acres. Now as the above allotments want 416 acres to make them just one fifth of the whole, how many acres did the settlement contain? Ans. 380035 acres. DIVISION. DIVISION Shows how often one number is contained in another; as 24 divided by 6, produce 4 in the quotient; that is, 6 are contained 4 times in 24. The number to be divided is called the dividend. The number by which we divide is called the divisor. The number of times the dividend contains the divisor is called the quotient. The remainder, if there be any, will be less than the divisor. It is called Simple Division, if the dividend and divisor have but one and the like name. RULE. On the right and left of the dividend draw a curved line, and write the divisor on the left, and the quotient as it arises on the right hand. Assume as many figures on the left hand of the dividend as contain the divisor once or more, and place the number in the quotient. Multiply the divisor by the quotient figure, and set the product under the assumed part of the dividend; subtract it, and to the remainder bring down the next figure of the dividend; which number divide as before, and thus proceed until the whole is divided. NOTE 1.-If after a figure is brought down, the number be less than the divisor, place a dipher in the quotient, and bring down the next figure of the dividend. NOTE 2.-Remember that the products of the divisor and the several quotient figures, must always be less than the parts of the dividend under which they are set, unless they chance to be just the same numbers; and that every remainder must be less than the divisor. PROOF.-To the product of the divisor and quotient, add the remainder, which sum will be equal to the divi dend, if the work is right. Or, cast the nines out of the divisor, and place the excess or remainder on the left side of a cross or X: do the same with the quotient, and place the excess on the right hand; multiply these two figures together, add their product to the remainder of the division, if there be any, cast out the nines in the sum, and set the excess at the top of the cross; cast the nines out of the dividend, and place the excess at the bottom; then, if the top and bottom figures are alike, the work is right. NOTE. If there be no remainder, the quotient is the perfect answer to the question; but if there is, to com plete the quotient, put the remainder at the end of it, and the divisor below it, drawing a line between the two. CONTRACTIONS. CASE. I. When there are ciphers at the right hand of the divisor, cut them off; likewise cut off the same number of digits from the right hand of the dividend; then divide as usual, and to the remainder annex the digits cut off from the dividend. CASE II-When the divisor is any number not exceed ing 12. RULE. First seek how often the divisor can be had in the first figure, or figures, of the dividend; put the result under the dividend; multiply this quotient figure and the divisor together; mentally subtract their product from the part of the dividend taken; what remains call so many tens, which place, in idea, before the next figure of the dividend for a new dividual; and so proceed through the whole dividend. When in subtracting, nothing remains, take the next figure; if that be less than the divisor, take the next two, and place a cipher under the first. CASE III.-If the divisor be a product of two or more numbers, divide continually by those numbers instead of the whole at once. NOTE. It sometimes happens that there is a remainder to each of the quotients, and neither of them the true one, but the true remainder may be found by the following rule. RULE. Multiply the last remainder by the last divisor but one, and to the product add the preceding remainder; multiply this sum by the next preceding divisor, and to this product add the next preceding remainder, and so on until all the remainders and divisors are used; and the last sum will be the true remainder. Divide 6421671 by 448 Divide 27162 by 63 8x8x7-448 8)6421671 8)802708-7 7)100338-4 Quotient. 14334-4x8+7-39 Remainder. APPLICATION. 1. Divide 3656 dollars equally among 8 men. Ans. 457 dols. to each. 2. There are 124 men who have 372 dollars among them; how much is one man's share, if it be divided equally? Ans. 3 dols. 3. If I wish to perform a journey of 3264 miles in 136 days, how far must I travel each day to complete it? Ans. 24 miles. 4. A payment of 1272 dollars was made by a number of men, each of whom paid 3 dollars; how many men were there? Ans. 424. 5. I would plant 2072 trees, in 14 rows, 25 feet asunder; how long must the grove be? Ans. 3675 feet. 6. Divide 1000 dollars between A, B, and C, and give A 129 more than B, and B 178 less than C. Ans. 360 dols. A's, 231 B's, and 409 C's. 7. Part 1500 acres of land between Saul, Seth, and Silas; and give Seth 72 more than Saul, and Silas 112 more than Seth. S 4143 Saul's share, 4863 Seth's, and 598 Silas's. Ans. 8. A brigade of horse consisting of 384 men, is to be formed into a column, having 32 men in front; how many ranks will there be ? Ans. 12. 9. In order to raise a joint stock of 10,000 dols., L, M, and N, together, subscribe 8500, and O the rest. Now, M and N are known together to have set their hands to 6050, and N has been heard to say that he had undertaken for 420 more than M. What did each proprietor advance? Ans. L 2450, M 2815, N 3235, and O 1500. PRACTICAL QUESTIONS, UNDER THE PRECEDING RULES. 1. Add fourteen thousand, five hundred and nine; one thousand, nine hundred and twenty-one; six hundred and twenty thousand, three hundred and forty-seven; and five million, twenty-three thousand, and nineteen, together. Ans. 5659796 sum. 2. What is the sum of 76129+54216+39127+62357 +514026 ? Ans. 745855. 3. What is the difference between four million two hundred and ten thousand and twelve; and six hundred and fifty-nine thousand seven hundred and ninety-seven? Ans. 3550215. 4. Take nine hundred and one thousand and fifteen, from one million one thousand one hundred and one? Ans. 100086. 5. A farm of 460 acres is let for 2 dollars per acre; how much does the rent amount to? Ans. 920 dols. C |