OF

COMPOUND ADDITION;

Or, Addition of Money, Weights, and Measures.

219. This branch of our subject, after what we have learned, ought to be a very simple and easy matter. Calling to mind what is said in the last lesson, paragraphs 196 to 210, on the notation of compound numbers, and especially to what is said in paragraph 207, on the necessity of ascertaining, first of all, the manner in which the money, the weights, or the measures, which you have to calculate, are divided; calling these things to mind, and, if you yet feel any uncertainty on the subject, clearing it up by reading over those paragraphs, beginning with that numbered 196; doing this, you will require no further instructions to enable you to work correctly the few following sums; or, indeed, any other, coming under this rule, which may elsewhere present themselves.

(1) What is the amount of the following sums of money, £23. 5. 31, £13. 11. 9, £45.9.2, £8. 12.5?

£.

(2) I have paid, on several accounts, these sums, £15.7.6, £29. 14.3, £75.16.42, £130.6.9; what is the total amount aid?

(3) The yearly expenses, in the undermentioned articles, of a certain family, were as here specified; groceries, £75.18.3; butcher's meat, £82.3.4; meal, or flour, £30. 14. 82; malt and hops, £15. 19.7; clothes, £105. 17.6; assessed taxes and parish rates, £53. 12. 2: now, what was the total expenditure of these items?

(4) Add together the following weights, (avoirdupoise): 15cwt. 1 qr. 3lbs; 3qrs. 19 lbs.; 12 cwt. 2 qrs. 11 lbs. ; 19 cwt. 1qr. 25 lbs.; & 8 cwt. 3 qrs. 7lbs.

cwt.

15

0

12

19

8

qrs.

1

3

2

1

3

lbs.

3

19

11

25

7

(5) A grocer has received five butts of currants, severally weighing, 18 cwt. 2 qrs. 3 lbs.; 12cwt. 1qr. 12 lbs.; 17 cwt. 3 qrs. 16 lbs.; 18 cwt. Oqr. 27 lbs. 19 cwt. 0 qr. 2 lbs. nett; what is the whole weight of currants, in cwts. qrs. and lbs. ?

(6) Received by waggon, 7 packages, severally weighing as here stated; what is the total weight thereof? 3 cwt. 2 qrs. 15 lbs.; 5 cwt. 1 qr. 22 lbs,; 2cwt. 3qrs. 19 lbs; 4cwt. 2qrs. 12 lb; lcwt. Oqr. 11 lb; 7 cwt. 1 qr. 3 lb.; 6 cwt. 2 qrs. 14 lbs.

(7) How many bushels, pecks, and gallons, are there in the following quantities; 5b. 1p. 2g; 3b. 2p. Og; 6b. 3p. 0g; 3p. 1g; 7 b. 2 p. 1g?

(8) What is the amount in quarters, bushels, pecks, and gallons, of the quantities of grain here stated?

b.

5

3

6

ས

p.

g.

7

2-2332

(9) In six weeks, a stable-keeper used, week by week, the undermentioned quantities of oats; what was the total quantity used in the time? 6q. 4b. 2p. 0g.; 9q. 2b. 1p. 1g.; 7q. 5b. 3p. 1g.; 5q. 6b. 2p. 0g.; 8q. 3b. 1p. 1g.; 10q. 2b. Op. 1g.

(10) A maltster sold the undermentioned quantities of malt: what were the total sales? 15q. 4b. 3p.; 7b. 5p. 2p.; 12q. 3b. 1p.; 9q. 7b. 2p.; 5q. 5b. 2p.; 4b. 1p. 5q. 2b. Op.

(11) Purchased the several parcels of wheat here specified, at the prices and sums severally annexed to each parcel; what is the total quantity of wheat, and what the amount of money paid for the whole?

(12) Sold six hogsheads of fine Jamaica sugar, the nett weight, and the prices of which are as here stated: what is the total weight, and what the total sum for which they are sold?

COMPOUND SUBTRACTION.

220. In stating the sums to be worked in this rule; in writing the smaller quantity underneath that from which it is to be subtracted, always be careful to place each figure right under those of the same denomination. And then, beginning at the right hand, with the lowest denomination, you see whether the quantity in the upper line be large enough to admit of that in the lower being taken from it. If, as in the first example here given, there be no figure, or only a cypher, under the first of the upper line, you then, of course, bring down the upper figure, undiminished. If there be a figure in the lower line, smaller than that above it, you then, as in the second example, write down the difference.

221. But, if the lower figure be the larger, you must borrow, as you do in simple Subtraction, and as you see here done, in the third example: ONLY, OBSERVE, and this, mind, is THE PRINCIPLE always to be acted on, that whilst, as you remember, in simple arithmetic, the sum you borrow, in these cases, is, always, ten, which is but one of the next higher station, so the sum you borrow here, is just as many of the denomination you may, at the time · be working on, as make one of the next higher denomination, whatever that may be: thus; if they be farthings that you have to subtract from

the upper line, and there be none, or not a sufficient number in the upper line to admit of the subtraction, the sum you borrow is 4; that is, 4 farthings, which, making one penny, is repaid, by carrying one to the pence in the lower line; and, if you then find them too many to be subtracted from those in the upper, the sum you have to borrow is twelve, that is, the number of pennies in a shilling, and this you repay, in like manner, by adding one to the shillings in the lower line. And so you go on, if there be occasion, borrowing again in the shillings, in which case, of course, you borrow twenty, and pay by adding one to the lower line of pounds; which, being the highest denomination of the series of which you treat, you proceed as in simple Arithmetic; that is, if you have occasion to borrow, the number you borrow is ten, and you pay by carrying one, as before.

222. And now, my pupils, you are prepared, I trust, to work the following sums; and to do this with ease, on looking to the manner in which the foregoing are performed.

SUBTRACTION OF MONEY.

(1) From £217 12s. 4d, subtract £83 158. 2d.