give the quotient required. But as it sometimes happens that there is a remainder to each of the quotients, and neither of them the true one, therefore, to find the true remainder, multiply the first divisor by the last remainder; to that product add the first remainder, which will give the true one. Here is 3 for the first remainder, and 4 for the second; then say 9 times 4 are 36, and 3 are 39, the true remainder. 9438 by 24. Quotient, 393, Remainder, 6. 2. Divide 19, 9. 42. 189, 10. 56. 60. 70. 8. 719623 by 84. LONG DIVISION is that wherein the divisor exceeds 12. RULE. For the first dividual take as many of the first figures of the dividend as will contain the divisor: seek how often the divisor is contained therein. Set the result down for the first quotient figure; multiply this figure into the divisor; subtract the product from the dividual; annex the next figure of the dividend to this remainder, which will be the second dividual and so proceed until all the figures are used. Proof-As in Short Division. Examples. 1. Divide 6197348 by 191. Thus, 191)6197348(32446 Quotient. 573 467 382 853 764 894 764 1308 1146 162 Remainder. 2. Divide 6471235427 by 4792753. Quot.1350, Rem. 1018877. 71826 by 964. 66 574315 by 7162769 by 543795 by 6437 by 9999 by When there are one or more ciphers on the right of the divisor, omit them in the operation, separating from the right of the dividend as many figures, which must be annexed to the remainder. 1. Divide 76420000 by 9500. Thus, 95,00)764200,00(8044 Quotient. 760 420 380 400 2000 Remainder. 1. Sold 93 acres of land, for 2883 dollars-How many dollars was it per acre? Dolls. 93)2883(31 Answer. Ans. 31. 279 93 93 2. Bought 19 cords of wood, for 57 dollars-What was it per cord? Ans. 3 dolls. 3. How many barrels of flour can I buy for 594 dollars, at 6 dollars a barrel? Ans. 99. 4. If 27 men have 648 dollars, what is it a piece? per Ans. 24 dolls. 5. Sold a quantity of hay for 143 dollars, at 11 dollars per ton: I desire to know how many tons there were? Ans. 13. 6. If a man spend 216 dollars in a year, what is it month? Ans. 18 dolls 7. A gentleman has a garden, containing 9600 square feet; the breadth is 80 feet-What is the length? Ans. 120 feet. 8. What is the value of one thousand shingles, when 25 thousand are sold for 200 dollars? Ans. 8 dolls. 9. A prize of 5184 dollars is to be divided equally among 432 sailors-What is each man's share? Ans. 12 dolls. 10. Divide 75 dollars equally between Harry, and tell each one's share? 11. Sold 14 hundred weight of bacon, for 84 dollars: I desire to know how much it was per hundred? Ans. 6 dolls. Tom, Dick and DECIMAL FRACTIONS. A DECIMAL FRACTION is a part or parts of a unit, varies in the same proportion, and is managed by the same method of operation, as a whole number: it is denoted by a point prefixed to a figure or figures, thus, .7, .78, .789. The first figure denotes so many tenths of a unit; the second, so many hundredths of a unit; the third, so many thousandths of a unit. And as whole numbers, reckoned from right to left, increase in a tenfold proportion, so decimals, reckoned from left to right, decrease in a tenfold proportion: thus, 7 = seventenths; .07 seven-hundredths; .007 seven-thousandths. Ciphers annexed to decimals, neither increase nor decrease their value: thus, .7000 and 7 are equal. = ADDITION OF DECIMALS. Place the numbers according to their value, viz: units under units, tenths under tenths, &c.: then begin at the right hand, and add them up as in addition of integers. Be careful to put the point in the sum total exactly under those in the example. Acres. Examples. 27.1 19.62 3.147 15.0274 64.546 17.4 146.8404 Dollars. 971.125 12.16 109.007 16.1145 243.12 96.143 1447.6695 Note.-Cents are decimal parts of a dollar. Application. 1. Borrowed at one time 574 dollars; at another, sixty dollars and ninety-seven cents; at a third, eighty-seven cents. What sum did I borrow in all ? Dolls. 574. 60.97 .87 635.84 Answer. 2. Add 57.6, 93.741, 64.104, 5.1814, together, and tell the amount. Ans. 220.6264. SUBTRACTION OF DECIMALS. RULE. Place the numbers as in addition, with the less under the greater. Begin at the right hand, and subtract as in integers; and set the point in the remainder directly under those in the example. 1. From 70.41 take 16.42, and tell what is left. Ans. 53.99. 2. Borrowed two hundred dollars, and paid one hundred and eighty-seven dollars and sixty-four cents-How much do I yet owe? Ans. 12.36 dolls. 3. Deposited in bank one thousand dollars; and having drawn checks to the amount of six hundred and twenty dollars and seventy-four cents-I demand what sum I have in bank. Ans. 379.26 dolls. MULTIPLICATION OF DECIMALS. RULE. Place the factors, and multiply them as in whole numbers; and from the product towards the right hand cut off as many places for decimals as there are in both factors together; but if there should not be so many places in the product, supply the defect with ciphers to the left hand. Examples. 1. Multiply 54328.716275 by .1235. Thus, 54328.716275 .1235 271643581375 162986148825 108657432550 54328716275 6709.5964599625 Product. |