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.

AVOIRDUPOIS WEIGHT.

cwt. qr.lb.oz.dr. cwt.qr.lb.oz.dr. cwt. qr. lb. oz.dr.

COMPOUND MULTIPLICATION.

Compound Multiplication teaches to find the amount of any given number of different denominations by repeating it any proposed number of times.

RULE.*

1. Place the multiplier under the lowest denomination of the multiplicand.

2. Multiply the number of the lowest denomination by the multiplier, find how many ones of the next higher denomination are contained in the product.

3. Write the excess, and carry the ones to the product of the next higher denomination, with which proceed as before; and so on through all the denominations to the highest, whose product, together with the several excesses, taken as one number, will be the whole amount required.

The method of proof is the same as in Simple Multiplica; tion.

EXAMPLES OF MONEY.

1. 9lb. of tobacco, at 2s. 8d. per lb.

2s. 8d.
9

11. 4s. 41. the answer.

* The product of a number, consisting of several parts or denominations, by any simple number whatever, will evidently be expressed by taking the product of that simple number and each part by itself, as so many distinct questions; thus, 251. 12s. 6d. multiplied by 9 will be 2251. 108s. 54d.=(by taking the shillings from the pence, and the pounds from the shillings, and placing them in the shillings and pounds respectively) 2301. 12s. 6d. which is agreeable to the rule; and this will be true, when the multiplicand is any compound number whatever.

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.

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.

6. 144 reams of paper, at 13s. 4d. per ream.

Ans. 151. 8s.

Ans. 961.

CASE 2.

If the multiplier cannot be produced by the multiplication of small numbers, find the product of such numbers nearest to it, either greater or less, then multiply by the component parts as before; and for the odd parts, add or subtract as the case requires.

EXAMPLES.

1. 17 ells of holland, at 7s. 8d. per ell.

3. 46 bushels of wheat, at 4s. 74d. per bushel.

Ans. 101. 11s. 94d.

4. 59 yards of tabby, at 7s. 10d. per yard.

5. 94 pair of silk stockings, at 12s. 2d. per pair.

Ans. 231. 2s. 2d.

Ans. 571. 3s. 8d.

Ans. 1301. 3s. 3d.

6. 117 cwt. of Malaga raisins, at 11. 2s. 3d. per cwt.