36 Pounds of sugar, at 91 cents per pound 3 Hogsheads of molasses, 63 galls. each, at 27 cents a gallon 5 Casks of rice, 285 pounds each, at 5 cts. per pound 2 Chests of tea, 86 pounds each, at 96 cts. per pound 69 Chests of tea, at $55.65 per chest 126 Bags of coffee, 100 pounds each, at 124 cents per pound 167 Boxes of raisins, at $2.75 per box 800 Bags of almonds, at $18.50 per bag 9004 Barrels of shad, at $7.50 per barrel 60 Barrels of oil, 32 gallons each, at $1.08 per gall. Amount, Received the above in full, JACOB THRIFTY. DENOMINATE NUMBERS. 180. A DENOMINATE NUMBER is a denominate unit, or a collection of such units. 181. Two numbers are of the same denomination, when hey have the same unit; and of different denominations, when they have different units. 182. A COMPOUND DENOMINATE NUMBER is one expressed by two or more different units; as, 3 yards 2 feet 3 inches. 183. A SCALE is a connecting link between two denominations. Its value, is the number of units of the less denomination, which make 1 unit of the greater. 184. Kinds of Units. There are eight different Units of Arithmetic : II. UNITS OF CURRENCY; III. UNITS OF LENGTH; IV. UNITS OF SURFACE; V. UNITS OF VOLUME, OR CAPACITY; VII. UNITS OF TIME; VIII. UNITS OF CIRCULAR MEASURE. 186. The United States Currency, is the Decimal Currency established by a law of Congress, in 1792. 180. What is a denominate number? 181. When are two numbers of the same denomination? When of different denominations? 182. What is a compound denominate number? 183. What is a scale? What is its value? 184. How many kinds of units are there in Arithmetic? Name them. 185. What is an abstract number? Repeat the Table. What are the scales, in Abstract Numbers? Are they uniform, or variable? 186. What is United States Currency? What are its denominations? Repeat the Table. What are the scales? II. ENGLISH CURRENCY. 187. The English Currency, is the Currency of Great Britain. SCALES.-1. Beginning at the lowest unit, the scales are 4, 12, and 20. If we begin at the highest unit, the order is reversed, and the scales are 20, 12, and 4. The connecting link, or scale, between any two denominations, is, however, the same in both cases. 2. The scales are uniform, only in abstract and decimal numbers; in all others, variable. 3. Farthings are generally expressed in fractions of a penny: Thus, 1far. d.; 3far. 3d. = id.; 2far. 4. By reading the second table from left to right, we can see the value of any unit expressed in each of the lower denominations. Thus, 1d. = 4far.; 1s. = 12d. = 48far.; £1 = 20s. = 188. REDUCTION is the operation of changing the unit of a number, without altering the value of the number. 187. What is English Currency? What are its denominations? Repeat the Table. What are the scales? Are they uniform, or variable? 188. What is Reduction? 189. REDUCTION DESCENDING is changing the unit from a greater to a less. 190. REDUCTION ASCENDING is changing the unit from a less to a greater. 191. Reduction Descending. 1. Reduce £27 6s. 8d., to the denomination of farthings. ANALYSIS.-Since there are 20 shillings in £1, in £27 there are 27 times 20 shillings, or 540 shillings, and 6 shillings added, make 546s. Since 12 pence make 1 shilling, we next multiply by 12, and then add 8d. to the product, giving 6560 pence. Since 4 farthings make 1 penny, we next multiply by 4, and add 2 farthings to the product, giving 26242 farthings for the answer: Hence, the following Rule. OPERATION. £27 6s. 8d. 2far. 20 546s. 6560d. 4 26242, Ans. I. Multiply the highest denomination by the scale, and add the units, if any, of the next lower denomination : II. Proceed in the same manner through all the denominations, till the number is brought to the required unit. 192. Reduction Ascending. 1. In 26242 farthings, how many pounds, shillings, and pence? OPERATION. 4) 26242 12) 6560. 2far. rem 210) 546. 8d. rem. 27.. 6s. rem. Ans. £27 6s. 8d. 2far. |