COMPOUND SUBTRACTION.

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

* PLACE the less number below the greater, so that the parts 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 as 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 73/ 51d and 19/ 13s 10d?

Ans. 53/ 6s 74d.

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

Ex 6. A lends to B 100/, how much is B in debt after A has taken goods of him to the amount of 73/ 12s 43d? Ans. 26/7s 74d.

7. Suppose that my rent for half a year is 20/ 12s, and that I have laid out for the land-tax 14s 6d, and for several repairs 1/3s 31d, what have I to pay of my half-year's rent? Ans. 18/ 14s 23d.

8. A trader, failing, owes to A 35/ 7s 6d, to B 917 13s id, to C 531 74d, to D 871 5s, and to E 1117 3s 52d. When this happened, he had by him in cash 23/ 7s 5d, in wares 53/ 11s 101d, in household furniture 637 17s 73d, and in recoverable book-debts 25/7s 5d. What will his creditors lose by him, suppose these things delivered to them?

Ans. 212/ 5s 3žd.

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 ft 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; which is performed by the following rule.

1

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,

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 8 lb of Tea, at 5s 82d per lb.

6. 10 cwt of Cheese, at 2/17, 10d per cwt. Ans. 28 18

7. 12 cwt of Sugar, at 3/7s 4d

per cwt.

4

Ans. 40 8 0

CONTRACTIONS.

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

Ans. 81 0 0

Ans. 3

7 6

Ex. 5. 63 gallons of Oil, at 2s 3d per gall.

0

4 0

0

6. 70 barrels of Ale, at 1/4s per barrel. Ans. 84 7. 84 quarters of Oats, at 1/12s 8d per qr. Ans. 137 8. 96 quarters of Barley, at 1/3s4d per qr. Ans. 112 9. 120 days' Wages, at 5s 94 per day. Ans. 34 10 10. 144 reams of Paper, at 13s 4d per ream. Ans. 96

.

0 0

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.

EXAMPLES.

I. 26 yards of Cloth, at 3s 03d per yard.

65

12 10

3 10

45

6 10

2. 29 quarters of Corn, at 21 55 31⁄2d per qr. Ans. 3. 53 loads of Hay, at 3/ 15s 2d per load. Ans. 199 4. 79 bushels of Wheat, at 11s 53d per bush. Ans. 5. 97 casks of Beer, at 12s 2å per cask. Ans. 59 0 2 6. 114 stone of Meat, at 15s 34d per stone. Ans.

87 5 7