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COMPOUND SUBTRACTION.

COMPOUND SUBTRACTION shows how to find the differ-ence 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 liigher denomination; then take the lower number from the upper one thus increased, and set down the remainder. Carry the unit borrowed to the next Aumber 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.

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5. What is the difference between 731 5 d and 19/ 13s 10d?

Ans. 531 68 7d.

* 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 1001, how much is B. in debt after A has taken goods of him to the amount of 731 12s 4 d?

Ans. 26178 7d. 7. Suppose that my rent for half a year is 201 12s, and that I have laid out for the land-tax 14s 6d, and for several repairs 1/ 3s 3d, what have I to pay of my half-year's rent?

Ans. 181 14s 2 d. 8. A trader, failing, owes to A 351 7s 6d, to B 911 13s įd, to C 531 7d, to D 871 5s, and to E 11113s 5d. When this happened, he had by him in cash 231 7s 5d, in wares 531 11s 10d, in household furniture 637 17s 7d, and in recoverable book-debts 2517s 5d. What will his creditors lose by him, suppose these things delivered to them?

Ans. 2121.5s 3d.

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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.

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 se'veral 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 83d per lb.

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4 lb of Tea, at 7s 8d

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Ans. 1 10 8
3. 6 lb of Butter, at 9 d per lb. Ans. 0 4 9
4. 7 lb of Tobacco, at 1s 8d per lb. Ans. 0 11 11
5. 9 stone of Beef, at 2s 74d per st. Ans. 1 1 0
6. 10 cwt of Cheese, at 2l 175 1Od per cwt. Ans. 28 18
7. 12 cwt of Sagar, at 31 7s 4d per cwt.

Ans. 40 8 0

CONTRACTIONS.

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

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2. 20 cwt of Hops, at 417s 2d per

cwt. 3. 24 tons of Hay, at 317s 6d per

ton. 4. 45 ells of cloth, at 1s 6d per ell.

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Ans. 87 3
Ans. 81 0
Ans. 3 7 6

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

Ans. 7 1 9 6. 70 barrels of Ale, at 1/ 4s per barrel. Ans. 84 0 7. 84 quarters of Oats, at 1l 12s 8d per qr. Ans. 137 4 8. 96 quarters of Barley, at 113s 4d per qr. Ans. 112 0 9. 120 days' Wages, at 5s 9d 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

1

I. 26 yards of Cloth, at 3s 0 d per yard,

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5

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1 2. 29 quarters of Corn, at 21 5s 3 d per qr. Ans. 63 12 10 3. 53 loads of Hay, at 31 15s 2d per load. Ans. 199 3 10 4. 79 bushels of Wheat, at 11s5d per bush. Ans. 45 6 10 5. 97 casks of Beer, 'at 12s 2d per cask. Ans. 590 2 6. 114 stone of Meat, at 15$ 3d per stone. Ans. 87 -5

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