2. How many times is 7 contained in 56? If 4 horses are required to draw 1 wagon, how many wagons might be drawn by 168 horses? 8. How many yards of broad-cloth, that is sold at 6 dollars a yard, can be bought for 492 dollars? 9. If a man can travel 5 miles an hour, how hours will it take him to travel 205 miles? many 10. Suppose 69 to be a dividend, and 3 a divisor; what is the quotient? 11. Suppose 128 to be a dividend, and 4 a divisor; what is the quotient? 12. Suppose 486 to be a dividend, and 6 a divisor; what is the quotient? 13. How many times is 4 contained in 872? 4)872 218 4 in 8, 2 times; 4 in 7, 1 time, and there is 3 over; (we join this 3 with the 2, making 32,) then 4 in 32, 8 times. 14. How many times is 6 contained in 726? 15. How many times is 8 contained in 896? 16. How many times is 5 contained in 1605? 17. How many times is 7 contained in 924? 18. How many times is 4 contained in 6732? 19. Suppose 1585 to be a dividend and 5 the divisor; what is the quotient? 20. Suppose 4518 to be a dividend and 6 the divisor; what is the quotient? 21. How many times is 7 contained in 742? 7)742 The divisor not being contained once in the ten's place of the dividend we write a 106 O in the ten's place of the quotient. 22. How many times is 3 contained in 609? 23. How many times is 8 contained in 1624? 24. How many times is 5 contained in 4015? 25. How many times is 9 contained in 2880? 26. How many times is 7 contained in 10500? K 27. If I had 78 dollars to lay out for flour, and the flour was 6 dollars a barrel, how many barrels could I buy for all the money? 28. A drover received 268 dollars for sheep, that he sold at 4 dollars a head. How many were there? 29. If 1 ton of hay be worth 9 bushels of corn, how many tons of hay are 576 bushels of corn worth? 30. If 3 bushels of wheat will pay for a yard of cloth, how many yards will 105 bushels pay for? 31. How many soldiers may be clothed from 5708 yards of cloth, allowing 4 yards to make a suit? 32. How many muskets can be purchased for 2952 dollars; the price being 6 dollars ap ece? 33. If 76 dollars should be divided equally among 4 men, how many dollars would each man receive? If there were only 4 dollars to be divided, each man would receive just 1 dollar: therefore each man must receive as many dollars as there are fours in 76. 34. Suppose 5 men have to pay a bill of 95 dollars, how many dollars must each man pay? 35. If 171 biscuit be divided equally among a crew of 9 sailors, how many does each sailor receive? 36. A farmer planted 354 trees, in 6 equal rows. How many were there in 1 row? 37. A fisherman hired a boat, agreeing to give the owner 1 fish of every 7 that he might catch: he caught 434. How many should he give the owner? 38. 8 sailors received 1576 dollars for retaking their ship. How much did each sailor receive? 39. A man intending to go a journey of 336 miles, wishes to perform it in 6 days. How many miles must he travel each day? 40. 9 men have agreed to make up a purse of 2178 dollars. How many dollars must each one put in? 41. Suppose A to spend 3 dollars as often as B spends 1 dollar; how many dollars will B spend while A is spending 89004 dollars? 42. Suppose 3656 dollars have been equally divided among a number of men, and each man has received 8 dollars; how many men were there? 43. A number of men contributed 9 dollars apiece, and thereby made up a purse of 54 dollars. How many men were there? 44. Suppose 9 has been multiplied by some number, and the product is 54; what was the multiplier? 45. 5 men paid equal shares of a debt of 80 dollars. How much did each man pay ? 46. Suppose some number has been multiplied by 5, and the product is 80; what number was multiplied? 47. Two numbers have been multiplied together, and their product is 126: one of the two numbers multiplied is 7;- what is the other? 48. Divide 348 by 4; then prove the work to be right, by multiplying the quotient and divisor together? 4)348 87 4 348 We find by the quotient, there are 87 times 4 in 348. therefore we know that 87 times. 4, or 4 times 87, must make 348. Had our quotient been wrong, our product and dividend would not be equal. 49. Divide 72 by 8, and prove the work to be right. 50. Divide 5890 by 5, and prove the work to be right. 51. Divide 39781 by 7, and prove the work to be right. 52. Divide 90048 by 8, and prove the work to be right. 53. Divide 17604 by 9, and prove the work to be right. 54. A hatter has 130 hats finished; and, in order to send them to market, he must pack them in boxes, that will hold 8 hats apiece. How many full boxes can he send; and how many hats will remain on hand? 8)130 16 2 We have 2 units over. This 2 is a remainder; it shows that there are 2 hats, which cannot be divided into eights. 55. How many sheep, at 4 dollars a head, can a butcher, who has 747 dollars buy; and how many dolrs will he have remaining? If 5 yards of cloth will make a suit of clothes, uun any suits can be made from 96 yards; and how many yards will there be over? 57. How many times is 6 contained in 4637; and how many are there over? 58. How many times is 8 contained in 9150; and now many are there over? 59. Suppose 568 to be a dividend, and 7 the divisor; what is the quotient, and the remainder? 60. Suppose 1953 to be a dividend, and 7 the divisor; what is the quotient, and the remainder? 61. Divide 564 by 7, and prove the work to be right. The remainder, in division, is an undivided part of the dividend: therefore, the remainder must be added to the product of the divisor and quotient, to make the product equal to the dividend. 62. Divide 109 by 6, and prove the work to be right. 63. Divide 817 by 5, and prove the work to be right. SECTION 3. The method of dividing taught in the two preceding sections, is called Short division: the method taught in this section; is called Long division. In long division, we place the quotient on the right hand of the dividend, and perform some operations under the dividend, heretofore performed in the mind. 1. How many times is 4 contained in 95307 ? Dividend Divisor 8 15 12 33 32 Quotient Perceiving that 4 is contained in 9, twice, we place 2 in the quotient, multiply the divisor by 2, and subtract the product (8) 4)95307 (23826 from 9. This is the same as saying in short division, '4 in 9, 2 times, and 1 over. Now, since the 1 over must be joined with the 5, we bring the 5 down to the right of the 1: and then, perceiving that 4 is contained in 15, 3 times, we place 3 in the quotient, multiply the divisor by 3, and subtract the product as before. Thus we proceed to bring down every figure of the dividend, and unite it with the previous remainder. 10 8 27 24 Remainder 3 Perform the following examples by long division. 8)25648(3206 24 16 16 48 48 113 The divisor not being contained 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 24 136 120 162 144 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. 14. How many times is 18 contained in 12 532 ? In this example, we have chosen 7 for the last figure of the quotient; but it appears, that 7 times 18 are more theft? eg. therefore men have 8192 pounds 18)12532(697 108 173 162 ม Jeef; 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. |