Perform the following examples by long division. 8)25648(3206 24 16 16 48 48 The divisor not being contain ed once in the left hand figure of the dividend, we join this figure with the next. After bringing down the 4, we find the divisor is not contained in it; therefore, we place a 0 in the quotient, and bring down the next figure. 9. How many times 5 are there in 43 906? 10. How many times 9 are there in 70 223? 11 How many times 6 are there in 901 500? 12. How many times 7 are there in 161 635? 13. How many times 24 are there in 3762? 24)3762(156 24 · 120 162 144 18 This operation is performed in the same manner that it would have been, if the divisor had consisted of only one figure. The two following examples will show the method of determining when a figure placed in the quotient is too great, and when it is too small. 4. How many times is 18 contained in 12 532 ? 18)12532(697 108 173 162 112 126 In this example, we have chosen 7 for the last figure of the quotient; but it appears, that 7 times 18 are more than 112, therefore 18 is not contained 7 times in 112. The 7 and the product arising from it must be rubbed out, and a smaller figure must be placed in the quotient. K* 15. How many times is 35 contained in 45 817? 35)45817(1308 35 108 105 317 280 37 Here we have chosen & for the last figure of the quotient; but, after. subtracting 8 times 35 from 317, there remains, 37. This remainder will contain 35, once more; therefore, we must rub out the 8 and the work resulting from it, and must put 9 in the place of 8. 16. How many times is 47 contained in 804 ? 17. How many times is 53 contained in 1625 ? 18 How many times is 68 contained in 94 605 ? 19. How many times is 71 contained in 661 419? 20. How many times is 108 contain d in 216? 21. How many times is 325 conta ed in 7134? 22. How many times is 476 conta ed in 92 107? 23. How many times is 504 con' ned in 1008 ? 24. How many times is 651 cor ained in 43 126? RULE FOR DIVISION. When the divisor does not exceed 9, draw a line under the dividend, find how many times the divisor is contained in the left hand figure, or two left hand figures of the dividend, and write the figure expressing the number of times underneath: if there be a remainder over, conceive it to be prefixed to the next figure of the dividend, and divide the next figure as before. Thus proceed through the dividend. When the divisor is more than 9, find how many times it is contained in the fewest figures that will contain it, on the left of the dividend, write the figure expressing the number of times to the right of the dividend, for the first quotient figure; multiply the divisor by this figure, and subtract the product from the figures of the dividend considered. Place the next figure of the dividend on the right of the remainder, and divide this number as before. Thus proceed through the dividend. PROOF. Multiply the divisor and quotient together and to the product add the remainder: the sum will be equal to the dividend, if the work be right. 25. Divide 46242 by 252, and prove the operation. 26 Divide 74 201 by 625, and prove the operation 27. Divide 408 732 by 9, and prove the operation. 28. Divide 15 362 by 88, and prove the operation. 29. Divide 57 026 by 492, and prove the operation. 30. Divide 982 700 by 53, and prove the operation. 31. Divide 162 941 by 256, and prove the operation. 32. Divide 648 035 by 14, and prove the operation. 33. Divide 106 401 by 333, and prove the operation. 34. Divide 62 509 by 4423, and prove the operation. 35. Divide 1 071 400 by 29, and prove the operation. 36. How many acres of land, at 22 dollars an acre, can be bought for 8514 dollars? 37. Suppose a man to earn 35 dollars a month; how many months will it take him to earn 490 dollars? 38. If a man travel 48 miles a day, in how many days will he perform a journey of 3264 miles? 39. If 774 dollars be divided equally among 18 sail ors, how many dollars will each sailor receive? 40. If a man's income be 2555 dollars a year, how much is it a day, there being 365 days in a year? 41. The income of the Chancellor of England, is 99 280 dollars a year. How much is it per day? 42. 63 gallons of water will fill a hogshead. How many hogsheads will 5166 gallons fill? 43. How many hogsheads can be filled from 19721 gallons?—and how many gallons will there be left? 44. Suppose a regiment of 512 men have 8192 pounds of beef; how many pounds are there for each man? 45. If a dividend be 46 319, and the divisor 807, what is the quotient?—and what the remainder? SECTION 4. ABBREVIATIONS. When there are ciphers on the right hand of a divisor, cut them off, and omit them in the operation; also cut off and omit the same number of figures from the right hand of the dividend. Finally, place the figures cut off from the dividend, on the right of the remainder. 1. How many times 900 are there in 741 725 ? 900)741725 We divide 7417 by 9; there remains 1, to which we annex the 824 125 25, making the true rem. 125. 2. How many times 70 are there in 8 563 512 ? 3. How many times 300 are there in 6374 ? 4. How many times 5000 are there in 46 578? 5. How many times 40 are there in 80 603? 6. How many times 600 are there 675 700? 7. How many times 8000 are there in 16 000? 8. Divide 65 237 by 59, and prove the operation. 9. Divide 567 289 by 100, and prove the operation. 10. How many times 570 are there in 35 871? 11. How many times 280 are there in 6423 ? 12. How many times 4200 are there in 91621? 13. How many times 9060 are there in 287 000? When the divisor is 10, 100, 1000, &c., cut off as many figures from the right hand of the dividend, as there are ciphers in the divisor; the other figures of the dividend will be the quotient, and the figures cut off will · be the remainder. 14. How many times 10 are there in 240? 15. How many times 10 in 435; and how many over? 16. How many times 100 are there in 4000? 17. How many times 100 in 748; and how many over? 18. 100 cents are equal to 1 dollar. How many dollars are there in 5400 cents? 19. In 642 cents, how many dollars are there; and how many cents over? 20. In 1937 cents, how many dollars are there; and how many cents over? When factors of the divisor can be found, (that is, when two numbers can be found, which, being multiplied together, produce the divisor,) you may divide the dividend by one of the factors, and the quotient thence arising by the other: the last quotient will be the true one. 21. In a certain school there are 36 scholars, among whom 540 quills are to be equally divided. How many will 1 scholar receive? Let us suppose the school to be divided into 4 classes, allowing 9 scholars to be in each class. Then we will. find how many quills 1 class will receive, and from this number, find how many 1 scholar will receive. 4)540 number of quills for the school. 15 number of quills for 1 scholar. Observe in the above example, that the divisors 4 anu 9, are the factors of 36: and, if we had divided first by the 9, and then by the 4, our last quotient would have been the same it now is. 22. Divide 11 376 by 72; using the factors of 72. 23. If 1024 dollars be divided equally among 64 men, how many dollars will 1 man receive? 24. How many times is 42 contained in 1176? 25. If 27 yards of cloth cost 216 dollars, how many dollars does 1 yard cost? 26. Suppose 1952 to be a dividend, and 32 the divisor; what is the quotient? To obtain the true remainder, where factors have been used as divisors, multiply the last remainder by the first divisor, and to the product add the first remainder. 27. Suppose 622 to be a dividend, and 35 the divisor; what is the quotient; and what the remainder? 28. Suppose 99 to be a dividend, and 25 the divisor, what is the quotient; and what the remainder? 29. Suppose 4862 to be a dividend, and 81 the divi sor, what is the quotient; and what the remainder ? 30. Divide 1739 by 56. |