COMPOUND SUBTRACTION.

COMPOUND SUBTRACTION shows how to find the difference between any two numbers of different denominations.—To perform which, observe the following Rule:

RULE.*-Place the less number below the greater, so that those parts which are of the same denomination may stand directly under each other; and draw a line below them. Begin at the right hand and subtract each number or part in the lower line from the one just above it, and set the remainder straight below it. -But if any number in the lower line be greater than that above it, add so many to the upper number as make 1 of the next higher denomination; then take the lower number from the upper one thus increased, and set down the remainder.-Carry the unit borrowed to the next number in the lower line; after which subtract this number from the one above it, as before; and so proceed till the whole is finished. Then the several remainders, taken together, will be the whole difference sought.

The method of proof is the same as in Simple Subtraction.

5. What is the difference between 737. 51d. and 197. 13s. 10d?

Ans. 531. 6s. 71d.

6. A lends to B 1007., how much is B in his debt, after A has taken goods of him to the amount of 737. 12s. 4åd? Ans. 261. 7s. 71d.

7. Suppose that my rent for half a year is 107. 12s., and that I have laid out for the land-tax 14s. 6d., and for several repairs 17. 3s. 3 d., what have I to pay of my half year's rent? Ans. 87. 14s. 23d.

8. A trader, failing, owes to A 35l. 7s. 6d., to B 917. 13s. 04d., to C 531. 7 d., to D 877. 5s., and to E 1117. 3s. 53d. When this happened, he had by him in cash 231. 7s. 5d., in wares 537. 11s. 104d., in household furniture 631. 17s. 73d., and in recoverable book-debts 25l. 7s. 5d. What will his creditors lose by him, suppose these things delivered to them? Ans. 2121. 5s. 31d.

The reason of this Rule will easily appear from what has been said in Simple Subtraction, for the borrowing depends upon the same principle, and is only different as the numbers to be subtracted are of different denominations.

20. The line of defence in a certain polygon being 236 yards, and that part of it which is terminated by the curtain and shoulder being 146 yards 1 foot 4 inches; what then was the length of the face of the bastion?

Ans. 89 yds. 1 f. 8 in.

COMPOUND MULTIPLICATION.

COMPOUND MULTIPLICATION shows how to find the amount of any given number of different denominations repeated a certain proposed number of times.

RULE.-Set the multiplier under the lowest denomination of the multiplicand, and draw a line below it.-Multiply the number in the lowest denomination by the multiplier, and find how many units of the next higher denomination are contained in the product, setting down what remains. In like manner, multiply the number in the next denomination, and to the product carry or add the units, before found, and find how many units of the next higher denomination are in this amount, which carry in like manner to the next product, setting down the overplus. Proceed thus to the highest denomination proposed; so shall the last product, with the several remainders, taken as one compound number, be the whole amount required.

The method of Proof, and the reason of the Rule, are the same as in Simple Multiplication.

EXAMPLES OF MONEY.

1. To find the amount of 81b. of Tea, at 5s. 8d. per lb.

I. IF the multiplier exceed 12, multiply successively by its component parts, instead of the whole number at once.

II. If the multiplier cannot be exactly produced by the multiplication of simple numbers, take the nearest number to it either greater or less, which can be so produced, and multiply by its parts as before. Then multiply the given multiplicand by the difference between this assumed number and the multiplier, and add the product to that before found when the assumed number is less than the multiplier, but subtract the same when it is greater.

COMPOUND DIVISION teaches how to divide a number of several denominations by any given number, or into any number of equal parts.

RULE.—Place the divisor on the left of the dividend, as in Simple Division.— Begin at the left hand, and divide the number of the highest denomination by the divisor, setting down the quotient in its proper place.—If there be any remainder after this division, reduce it to the next lower denomination, which add to the number, if any, belonging to that denomination, and divide the sum by the divisor.-Set down again this quotient, reduce its remainder to the next lower denomination again, and so on through all the denominations to the last