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When a number is to be changed to a higher denomina
Divide the given number by as many as it takes of that denomination to equal one in the denomination required."
Illustration.—The divisor being equal to one in the next greater denomination, every time we subtract it from the dividend, we take units enough from the dividend, to make one in the next higher denomination; therefore as many times as we can subtract the divisor from the dividend, we shall have so many units of the higher denomination in the quotient, for we place one in the quotient every time we subtract the divisor from the dividend.
The quotient will equal the dividend if there be no remainder, for every time we take a number from the dividend equal to the divisor, we put 1 in the quotient which is just equal to that number. If there be a remainder, the quotient and remainder will equal the dividend.
In the last question, 16 oz. being equal to 1 pound, by taking that number from the given ounces we subtract 1 pound, and as many times as we can subtract 16 from the 5792 ounces, so many pounds there will be 5–but the quotient expresses this number of times, therefore the quotient is pounds, and represents the same quantity which the dividend did. The same method may be observed in all similar questions. 2. If 1111 gal. of brandy be put into casks containing 47 gal. 3 qt. 1 pt. each, how many casks will be required ? Ans. 23 casks, and 9 gal. 3 qt. 1 pt. over. 3. How many times will a wheel, which is 15 ft. 7 in, in circumference, turn over in the distance of 2 M. 4 fur. 38 r. 11 ft. - Ans. 888.
36. In 24000 qr, how many pence? Ans. 6000. 37. In 6000 d. how many shillings 2 Ans. 500. 38. In 500 s. how many pounds 2 Ans. 25. 39. How many ounces in 2400 pwt.” Ans. 120. 40. How many pounds Troy in 120 oz. 2 Ans. 10. 41. In 31360 lb. how many quarters ? Ans. 1120. 42. In 1120 qr, how many hundred 2 Ans. 280. 43. How many tons in 280 cwt. 2 Ans. 14. 44. How many rods in 2455200 ft. 2 - Ans. 148800. 45. How many furlongs in 148800 r. 2 - o Ans. 3720. 46. In 3720 fur, how many miles 2 . - - Ans. 465.
Mote 2.—From several of the last questions, it may be seen that we have only to divide the several quotients as directed by the last rule, when a denomination is to be changed to another greater than that which is next to the given one.
If there be remainders, they will be of the same denomination as the dividend from which they were obtained, and they must be brought to the right hand of the last quotient.
48. In 36567890 square inches, how many acres 2 Ans. 5 A. 3 R. 12 r. 206 ft. 98 in. For dividing by 272; in the last question, see page 80.
49. 160 square rods equal 1 A. How many acres in 960098 square rods 2 Ans. 6000 A. 98 r. 50. In 960098 solid ft. of wood, how many cords? / Ans. 7500 C. 98 ft. . 51. How many tons of square timber in 46073 ft. A - Ans. 921 T. 23 ft. 52. In 136097 d., how many dollars ? Ans. 189 dol. 1 s. 5 d. 53. In 56328 d. how many eagles, an eagle being equal to 10 dollars 2. Ans. 78 eagles, 2 dol. 2 s. 54. How many chaldron of corn in 463049 pt. 2 Ans. 200 ch. 35 bus. 4 qt. I pt.
Questions to be worked by Reduction and Subtraction.
1. How much more land in a field which contains 179087 rods, than in one measuring 987 A. 3 R. ' Ans. 131 A. 2 R. 7 r. 2. A man wishes to draw the wine from a hind. into
pint bottles; having but 499 bottles there will be some
The following questions not belonging to any particular rule, are inserted here by themselves, and their various operations explained.
1. A man has 101 A. 3 R. 32 r. of land, which he
wishes to fence into lots of 12 A. 2 R. 39 r. each. How many lots will there be 2
Explansition.—As many times as we can take 12 A. 2 R. 39 r., (what each lot is to contain.) from the 101 A. 3 R. 32 r., there will be so many lots. As it is not generally so easy to divide one compound number by another, as it is to reduce them to the lowest denomination mentioned in either, and then divide, we reduce the divisor and dividend to rods. By illustration, page 121, 16312 rods equal 101 A. 3.R. 32 r., and 2039 rods equal 12 A. 2 R. 39 r. ; consequently we can take 2039 rods from 16312 rods as many times as we can 12 A. 2 R. 39 r. from 101 A. 3 R. 32 r.
JNote 1. If the multiplier contain a fraction, and the upper part of the fraction be 1, divide the multiplicand by the under part of the fraction, and add the quotient to the product of the other figures. 4. In 1936. how many crowns, a crown being 6 s. 7 d. 3 Ans. 57, and 4s. 9 d. over. 5. In 12.É. 18s. how many dollars ? Ans. 43. 6. How many parcels each 7 lb., can be taken from 15 cwt. 2 qr. 18 lb. of sugar, neat weight? Ans. 224. 7. How many pairs of sugar tongs, each weighing 7 pwt. 1 gr., can be made from 3 lb. of silver, if 8 gr. are allowed for waste? Ans. 102, and 1 pwt. 10 gr. over. 8. If a man step 2 ft. 10 in., how many steps will he take in travelling 4 fur. 11 r. 11 ft. 10 in.” * -- - Ans. 1000. 9. How many guineas 28 s. each, in 100:6.2 - - Ans. 71, and 12 s. over. 10. In 657012 dollars, how many pounds, how many guineas, and how many crowns? £ 197103, 12 s. Ans. & Guineas 140788, 8 s. (Crowns 598795, 4 s. 11 d. 11. How far apart must 12 spokes be inserted in a hub, whose circumference is 3 ft. 6 in. if each spoke be 1; in. thick? Ans. 2 in. 12. How many trees can be set on a right line, 16 r. 6 ft. in length, if the trees stand 15 ft. asunder? Ans. 19.
JNote 2. The number of trees will be one more than the number of spaces.