( COMPOUND ADDITION. Compound Addition teaches to collect several numbers of different denominations into one sum. RULE. .* 1. Place the numbers so, that those of the same denomination may stand directly under each other, and draw a line under them. 2. Add the figures in the lowest denomination, and find how many ones of the next higher denomination are contained in their sum. 3. Write the remainder, and carry the ones to the next denomination; with which proceed as before; and so on through all the denominations to the highest, whose sum must be all written; and this sum, together with the several remainders, is the whole sum required. The method of proof is the same as in Simple Addition. *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 nothing more than providing a method of digesting the money, arising from each column, properly in the scale of denominations; and this reasoning will hold good in the addition of compound numbers of any description what ever. RULE.* 1. Place the less number under the greater so, that those parts, which are of the same denomination, may stand directly under each other, and draw a line under them. 2. Beginning at the right, take the number in each denomination of the lower line from the number in the same denomination over it, and set the remainders in a line under them. 3. But if the lower number be greater than that above it, increase the upper number by as many as make one of the next higher denomination, and from this sum take the lower number and set the remainder as before. 4. Carry one for the number borrowed to the next number in the lower line, and subtract as before; and so on, till the whole is finished; and all the several remainders, taken together as one number, will be the whole difference required. The method of proof is the same as in Simple Subtraction. * The reason of this rule will readily appear from what has been said in Simple Subtraction; for the borrowing depends upon the very same principle, and is only different, as the numbers to be subtracted are of different denominations. 2. 3lb. of green tea, at 9s. 6d. per pound. 3. 5lb. of loaf sugar, at 1s. 3d. per lb. 4. 9cwt. of cheese, at 11. 11s. 5d. per cwt. Ans. 11. 8s. 6d. Ans. 61. 3s. Ans. 141. 2s. 9d. 5. 12 gallons of brandy, at 9s. 6d. per gallon. Ans. 51. 14s. CASE 1. If the multiplier exceed 12, multiply successively by its component parts, instead of the whole number at once, as in Simple Multiplication. EXAMPLES. 1. 16cwt. of cheese at 11. 18s. 8d. per cwt. 2. 28 yards of broad cloth, at 19s. 4d. per yard. Ans. 271. 1s. 4d. 3. 96 quarters of rye, at 11. 3s. 4d. per quarter. 4. 120 dozen of candles, at 5s. 9d. per doz. Ans. 1121. Ans. 341. 10s. 5. 132 yards of Irish cloth, at 2s. 4d. per yard. Ans. 151. 8s. 6. 144 reams of paper, at 13s. 4d. per ream. Ans. 961. |