The reductions, in all the denominate numbers, are made in the same manner. EXAMPLES. 1. In £5 5s., how many In 5040 farthings, how shillings, pence, and far- many pence, shillings, and things? pounds? 4)5040 farthings. 105 shillings. 12 1260 pence. 4 5040 12)1260 pence. 2|0)105 shillings. In this example, the reduction is from a less to a greater unit. Here the reduction is from a greater to a less unit. 2. In 55 guineas, how many shillings, pence, and farthings? 3. Reduce £54 11s. 91d. to farthings. 4. Reduce £77 11s. 104d. to halfpence. 5. Reduce £94 14s. 8d. to pence. 6. Reduce £47 14s. 4d. to twopences. 7. Reduce £34 11s. 9d. to threepences, and to pence. 8. In £108 11s. 6d., how many sixpences? 9. How many crowns, half-crowns, shillings, sixpences, pence, and farthings are there in £54? 10. Reduce £74 13s. 9d. into shillings, threepences, and farthings. 11. In 11520 farthings, how many pence, shillings, and pounds? 12. In 17880 pence, how many pounds? 15. In 12050 shillings, how many crowns and pounds? 16. Reduce 311040 pence into shillings, crowns, and pounds. 17. Reduce 177b. 5oz. troy weight to grains. 18. Reduce 6720 grains to ounces. 19. In 14 ingots, or bars of silver, each weighing 27oz. 10pwt., how many grains? How many in one? 20. How many grains of silver in 47b. 6oz. 12pwt. ard 7gr.? 21. How many pounds, ounces, pennyweights, and grains of gold in 704121 grains? 22. How many of each denomination in 351262 grains? 23. In 25t, apothecaries weight, how many ounces, drams, scruples, and grains? 24. In 907920 grains, how many ounces and pounds? 25. In 15 13 13 19 2gr., how many grains? 26. In 174947 grains, how many pounds? 27. In 16 103 13 149 7gr., how many grains? 28. In 12 tons, avoirdupois weight, how many pounds? 29. In 31360lb. of iron, how many tons? 30. In 375cwt. 292lb. of copper, how many pounds? 31. Reduce 740900oz. into cwts. and tons. 32. In 9T. 19cwt. 3qr. 27lb. 14oz., how many ounces? 33. In 14478406oz., how many tons, cwt., qrs., lb., oz., and drs.? 34. In 314 yards of cloth, how many nails? 35. In 576 French ells, how many yards? 36. Reduce 97yds. 3qrs. to English ells. 37. In 57 pieces of cloth, each 35 ells Flemish, how many ells English and nails? 38. In 14 bales of cloth, each 17 pieces, each piece 56 ells Flemish, how many yards, ells English, and ells French? 39. In 471 miles, long measure, how many furlongs and poles? 40. In 123200 yards, how many miles? 41. In 50 miles, how many yards, feet, inches, and barleycorns ? 42. Reducc 37mi. 7fur. 37rd. 6yd. 5ft. to feet. 43. How many barleycorns will reach round the earth, each degree being 69 miles? and how many quarters of barley are contained in such a number of barleycorns, admitting 7922 barleycorns to fill.a pint? 44. In 77A. 1R. 14P., land measure, how many perches? 45. In 17280 perches, how many acres? 46. In 50A. 3R. 10P. 9sq. yd. 789sq. ft., how many square feet? 47. In 175 square chains, how many square rods? 48. In 14976 perches, or square rods, how many acres? 49. In 83789263 P., how many squaré miles? 50. In 28 tons of round timber, how many solid inches? 51. In 155 cords of wood, how many solid feet? 52. In 17 cords of wood, how many solid inches? 53. In 56320 solid feet, how many cords? 54. Reduce 349938 cord feet to cords. 55. In 32hhds., wine measure, how many quarts? 56. In 3276 gallons, how many tuns? 57. In 75hhds., how many pints? 58. In 77hhds. of brandy, how many half-ankers? 59. In 10tuns 2hhds. 18gals. of wine, how many gills? 60. In 98 hogsheads of ale, how many pints? 61. In 38 butts of porter, how many pints? 62. In 516 barrels of beer, how many half-pints? 63. How many gallons of beer are contained in 50 barrels ? 64. In 44 quarters of corn, how many pecks? 65. In 30720 quarts, how many lasts? 66. How many sacks in 103 London chaldrons and 12 bushels of coal? 67. How many seconds in a year of 365da. 6hr.? 68. How many seconds in 6 years of 365da. 23hr. 57m. 39sec. each? 69. In 7569520118 seconds, how many years of 365 da each? 70. In 5927040 minutes, how many weeks? ADDITION. 48. The sum of two or more numbers, is a number which contains as many units, and no more, as are found in all the numbers added; and ADDITION is the process of finding the sum or sum total of two or more numbers. If 3 be added to 5 their sum will be 8, and the unit of the number 8 will be the same as the unit of the numbers 3 and 5. The numbers 3 and 5, which are thus added, must have the same unit; for, if 3 denoted tens, and 5 expressed units of the first order, their sum would neither be 8 tens nor 8 simple units. So if 3 expressed yards, and 5 feet, their sum would neither be 8 yards nor 8 feet. 49. Small numbers may be added mentally; but it is not convenient to add large numbers without first writing them down. How are they to be written? If we place one above the other, units of the same kind will fall in the same vertical line, and the units of the same order will fall directly under each other in the sum. OPERATION. 3 5 Sum 8 |00| OPERATION. hundreds. tens. units. Again, let it be required to add together 324 and 635. In the first number there are 4 units, 2 tens, and 3 hundreds. In the second, 5 units, 3 tens, and 6 hundreds. Let the figures of each order of units be placed under those of the same order, and added: their sum will be 9 units, 5 tens, and 9 hundreds, or nine hundred and fifty-nine. 324 635 Sum 959 QUEST.-48. What is the sum of two or more numbers? What is addition? What numbers can be blended into one sum 49. How may small numbers be added? How are numbers written down for addition? In this example, the sum of the units is 11, which cannot be expressed by a single figure. But 11 units are equal to 1 ten and 1 unit; therefore, we set down 1 in the place of units, and 1 in the place of tens. The sum of the tens is 12. But 12 tens are equal to 1 hundred, and 2 tens; so that 1 is set down in the hundred's place, and 2 in the ten's place. The sum of the hundreds is 14. The 14 hundreds are equal to 1 thousand, and 4 hundreds; so that 4 is set down in the place of hundreds, and 1 in the place of thousands. The sum of these numbers, 1531, is the sum sought. We OPERATION. 894 637 11 The example may be done in another way, thus : Having set down the numbers, as before, we say, 7 and 4 are 11: we set down 1 in the units place, and write the 1 ten under the 3 in the column of tens. then say, 1 to 3 is four, and 9 are 13. We set down the 3 in the tens place, and write the 1 hundred under the 6 in the column of hundreds. then add the 1, 6, and 8 together, for the hundreds, and find the entire sum 1531, as before. 1531 We When the sum in any one of the denominations exceeds 10, or an exact number of tens, the excess must be written down, and a number equal to the number of tens added to the next higher denomination. This is called carrying to the next column or higher denomination. The number to be car QUEST.-50. What is the sum of the units? What of the tens? What of the hundreds? What the entire sum? |