mainder, if any, to the next lower denomination, to which add the number of the dividend expressing that denomination, and then divide the sum by the divisor. II. Proceed in the same way for all the denominations. If there is a remainder after the last division, place it over the divisor, and annex it in a fractional form to the quotient. Each quotient will be of the same denomination as its dividend. Having placed the divisor as in Simple Division, how do you proceed? When, in dividing any particular denomination, there is a remainder, how do you dispose of it? Of what denomination will the respective quotients be? lb. oz. pwt. gr. 13)10 8 16 3(0lb. 9oz. 18pwt. 31gr. 12 13)128(9oz. 11 20 13)236(18pwt. 13 106 104 2 24 13)51(31gr. 12 remainder. (4.) mi. fur. rd. yd. ft.mi. fur. rd. yd. ft. in. 23)100 4 30 14 2(4 2 39 3 0 7. 92 8 8 23)68(2 fur. 22 40 23)910(39rd. 69 220 207 13 52 23)73 (3yd. 69 4 3 23)14(0 ft. 12 23)168( 7.7 in. 7 remainder. 5. Divide 10tuns 2hhd. 17gal. 2pt. by 67. 6. Divide 51A. 1R. 11P. by 51. Ans. 39gal. 6pt. Ans. 1A. OR 1P. Ans. 1gi. Ans. £3 13s. 4d. 9. Divide 673141da. 9hr. 58m. 24sec. by 1843. Ans. 365da. 5h. 48m. 48sec. 10. Divide Imi. 255 ft. 10in. by 365. Ans. 15 ft. 2in. When the divisor is a composite number, we may divide by the factors of the number successively. 11. Bought 15 sheep for £5 12s. 6. How much did one sheep cost? From this example, we see that it makes no difference which factor is first used. 12. If 24yds. of cloth cost £18 6s., how much is that per yard? Ans. 15s. 3d. 13. From a piece of cloth containing 128yds. 1gr., a tailor made 18 coats, which took one third of the whole piece. How many yards did each coat contain ? Ans. 2yds. 1qr. 2na. 87. QUESTIONS INVOLVING THE FOUR PRECEDING RULES. 1. Twenty-four men agree to construct 7mi. 1 fur. 24rd. of road; after completing of it, they employ 8 more men. What distance does each man construct before and after 16rd. before. 1 fur. 20rd. after. the 8 men were employed? Ans. { 2. A silversmith has seven tea-pots, each weighing 176. 3oz. 13pwt. 11gr. What is the whole weight? Ans. 9lb. 1oz. 14pwt. 5gr. 3. A farmer has 1000 bushels of apples, which he puts into 350 barrels. How many does each barrel hold? Ans. 2bu. 3pk. 34qt. 4. If it require 1 sheet of paper to print 24 pages of a book, how many reams, allowing 18 quires to the ream, will it take to print 3000 copies, of 250 pages each? Ans. 72 reams, 6 quires, 2 sheets. 5. An estate worth £2570 is to be divided as follows: the widow has one third of the whole, the remainder is to be divided equally between seven children. How much does the widow receive, and how much does each child have? The widow has £856 13s. 4d. Ans. {{ Each child has £244 15s. 2d. 34 far. 6. Divide 100 acres, 3 roods, 8 rods of land, between four persons, A, B, C, and D, so that A shall have one sixth of the whole, B one fourth of the remainder, C one third of what then remains, and D the rest. How much does 7. A, B, C, and D, having 13cwt. 1qr. 4lb. of sugar, they agree to divide it as follows: A is to have one half of the whole, B is to have one third of the remainder, C is to have one fourth of what then remains, and D is to take what is left. What were their respective portions? 8. What is the weight of the following coins: 10 guineas, each weighing, 5 pwt. 9 grains; 7 sovereigns, each weighing 1 pwt. 81 grains? Ans. 3oz. 3pwt. 8 gr. of gold. 9. What is the weight of 13 crowns, each weighing 18 pwt. 4 grains; 14 shillings, each weighing 3 pwt. 15 gr.; 9 sixpences, each weighing 1 pwt. 19 gr. ? Ans. 1lb. 3oz. 3pwt. 15gr. of silver. 10. In one eagle there is 232 grains of pure gold, 12 grains of silver, and 12 grains of copper, and the same proportions of gold, silver and copper, from all other American gold coin. In 10 eagles, 7 half-eagles, 5 quartereagles, how many grains of gold, silver and copper? 3424-95 gr. of gold. 11. One pound of pure gold is sufficient for how many dollars of gold coin, if it require dollar? 23-22 grains for one Ans. 248.062 dollars. 12. One pound of pure silver is sufficient for how many dollars of silver coin, if it require 371.25 grains for one dollar? Ans. 15.515 dollars. DENOMINATE FRACTIONS. 88. UNDER ART. 64, we defined a denominate number as one whose unit has reference to a particular thing. For a similar reason, a denominate fraction is a part of a unit having reference to a particular thing. Thus, of a yard is a denominate fraction, expressing a part of the particular unit one yard; of a pound is also a denomi |
