« ΠροηγούμενηΣυνέχεια »
We have thus far treated of the most simple methods of collecting and separating Simple Numbers; we shall next explain the corresponding methods of collecting and separating Compound Numbers.
A Compound Number is one in which an unit in one column does not represent the same part of the same quantity, as another unit standing in some other column of the same number.
in this example every figure denotes time, but no two units in different columns, express the same space of time. The 1 at the right hand is 1 second, and the 1 in the next column represents 60 seconds; but were it a simple number, the 1 in the second place, would stand for 10 seconds. If all the figures in the above example, denoted seconds, minutes, or hours, &c. the number would be a simple one. 1111 seconds is a simple number, because the 1 standing in the second place, equals 10, and the 1 in the third place, equals 100 seconds.
Abbreviation is one letter or more standing for a whole word; as y. for years, gal. for gallons, &c. Denomination. By a denomination is meant those figures which represent that part of a quantity ascertained by any particular weight or measure.
The words, tons, hundreds, quarters, pounds, ounces, drams, are the names of the denominations in one manner of ascertaining the weight of several kinds of goods, and the figures below them express so many units of each particular denomination. Each denomination is a simple number by itself, because the units expressed by one figure, are equal to the same number of units contained in any other figure of the same denomination. In the denomination of drams, the right hand figure denotes one dram, and the 1 in the 2d place, denotes 10 drams. But the whole number taken together, that is, the tons, hundreds, quarters, &c. is a compound one, for an unit in the denomination of drams, is not equal to an unit in either of the other denominations, as an unit in either of the other denominations, expresses a greater quantity. Remark.-From what has been said, we infer that we cannot add and subtract compound numbers, in every respect by the same methods that we did simple numbers; yet the general principles in both cases are the same. As 10 in one denomination, does not equal 1 in a higher denomination, when we obtain 10 by adding up any denomination, we cannot add one to the next denomination, as in simple numbers; but to obtain the exact amount, we must add 1 to a higher denomination for as many of the less, as it takes to equal 1 in the higher. In simple numbers we carry for 10; in compound numbers we carry for some other number, and this is all the essential dif. ference between the operations in simple and compound numbers.
ADDITION OF COMPOUND NUMBERS.
Addition of compound numbers is collecting two or more compound numbers, so that the several numbers may be expressed by one.
State the question by setting down one of the numbers, and all the others below it in such a manner, that every denomination may stand under the place of its own name in the upper number, having the least denomination at the right hand.
Add the least denomination the same as in simple numbers, and carry one to the place of the next higher denomination for as many as it takes of the denomination added, to equal one in the next higher, and set down what remains. Proceed in the same manner with all the other denominations.
JNote 1. If the greatest denomination in the given numbers, be the highest denomination in that particular weight or measure, we add them in all respects as simple numbers.
TABLE OF ENGLISH . MONEY.
Abbreviation. - Abbreviations. 4 Farthings, qr. make 1 Penny, d. 12 Pence, - “ 1 Shilling, s. 20 Shillings, “, 1 Pound, £
Operation. £ s. d. qr. 135 18 9 2 Illustration.—By ad
25 12 0 1 ding up every denomi100 - 15 1 3 nation of the given num- bers, we must obtain Ans. 262 - 5 11 2 a compound number, which shall equal all the given numbers. In the last question, the 2 farthing” which we set in the place of farthings, and the fpenny which we carried to the column of pence, (which is equal to the other 4 farthings,) equal the number of farthings in the three given numbers; the 11 pence are equal to all the pence in the three given numbers, together with the 1 penny which was brought from the farthings; the 5 shillings are equal to the three given numbers of shillings, except the 40, which were carried to the pounds; and the 262 pounds equal the three given numbers of pounds, together with the two which was brought from the shillings; therefore 262.É. 5 s. 11 d. 2 qr, equal all the denominations of the three given numbers. 2. Add together 11 f. 19 s. 3 qr., 2600 £. 11 d. 2 qr, 111 f. 17 s. 11 d. 1 qr.
* fo. s. d. qr. Note 2. The best way, ii. 11 19 0 3 stating compound numbers for
adding or subtracting, is to set
2600 00 1 1 2 down the abbreviations in the 1 11 17 11 1 same order as they stand in the - tables, and it will then be easy to 2723 17 11 2 discover in what place the given
denominations must be set. It
often happens with beginners, that when there is no number given in any particular denomination, they place the number in the next less denomination in that place which must produce an error. Where there is no namber given in any denomination, the place of that denomination should be supplied with ciphers. . In the last example, had we placed the 3 qi. where the cipher is, it would have read 3 pence instead of 3 farthings, and of course a mistake would have occurred.
TROY WEIGHT. Abbreviation. Abbreviations. 24 Grains gr. make 1 Pennyweight, pvt. 20 Pennyweights 22 I Ounce, Oz. 12 Ounces 2, 1 Pound, lb.
By this weight are weighed gold, silver, jewels, electuaries, and all kinds of liquor.
20 Grains, gr. make 1 Scruple, sc. 3 Scruples 22 1 Dram, dr. 8 Drams 29 1 Ounce, oz. 12 ounces 35 1 Pound, lb.
Apothecaries and physicians mix their medicines by this weight; but drugs are bought and sold by avoirdupois. (6.)
16 Drams, dr. make 1 Ounce, 02, 16 Ounces 33 1 Pound, lb. 28 Pounds 25. 1 Quarter, gr. 4 Quarters 53 1 Hundred, capt. 20 Hundreds 32 1 Ton. T.