COMPOUND ADDITION

IS the adding of several numbers together, having different denominations as Pounds, Shillings, Pence, &c.

Tons, Hundreds,

Quarters, &c.

RULE.*

1. Place the numbers so that those of the same denomination may stand directly under each other.

II. Add the first column or denomination together as in whole numbers; then divide the sum by as many of the same denomination as make one of the next greater, setting down the remainder under the column added, and carry the quotient to the next superiour denomination, continuing the same to the last, which add as in simple addition.

As the denominations of Federal Money increase like whole numbers, in a ten fold ratio, the operation is the same as in whole

* The reason of this rule is evident from what has been said in Simple Addition: For, in addition of money, as 1, in the pence is equal to 4 in the farthings; 1, in the shillings, to 12 in the pence; and 1, in the pounds, to 20 in the shillings; therefore, carrying as directed, is the arranging the money, arising from each column, properly, in the fcale of denominations; and this reasoning will hold good in the addition of compound numbers, of any denomi nation whatever.

numbers. But in denominations which do not increase in the same manner, the operations are somewhat different. Thus, in Ex. 1. of English Money, I find the sum of the peace to be 54. Now 54 pence are 4 shillings and 6 pence; therefore, I set down 6 under the pence, and carry 4 to the shillings, which I then find to be 68. But 68 shillings are 3 pounds and 8 shillings. I set down the 8 under the shillings, and carry 3 to the pounds, and the sum of the pounds is 35, which I set down. The sum of the whole is then 35 pounds, 8 shillings and 6 pence. The process is similar in each Example. In all sums of different denominations, the student should be careful to find the numbers by which the denominations in the Table increase, for by them he is to carry from one denomination to another.

In the 1st Ex. I find the sum of the grains to be 113. Now 113 grs. are 4 pwts. and 17 grs. because 24 is contained in 113, four times, and 17 is the remainder. Then I set down 17 under the grs. and carry 4 to the pwts. and their sum is 96. Now 96 pwts. are 4 oz. and 16 pwts. for 20 pwts. make 1 oz.; therefore I set 16 under the pits. and carry 4 to the ounces, which makes their sum 59. But 59 oz. are 4 lbs. and 11 oz. because 12 oz. make a lb. ; therefore I set down 11 oz. and carry 4 to the lbs. which makes their sum 3027. The answer, then is 3027 lbs. 11 oz. 16 pwts.

COMPOUND SUBTRACTION

TEACHES to find the difference, inequality, or excess; between any two sums of divers denominations.

RULE.*

Place those numbers under each other, which are of the same denomination, the less being below the greater; begin with the least denomination, and, if it exceed the figure over it, add as many units as make one of the next greater; subtract it therefrom; and to the difference add the upper figure, remembering, always, to add one to the next superior denomination, for that which you added before.

EXAMPLES.

1. FEDERAL MONEY.

The reason of this Rule will readily appear, from what was faid in Simple Subtraction; for the adding depends upon the fame principle, and is only different, as the numbers to be fubtracted are of different denominations.