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and one hundred and seventy-four gallons make two hogsheads and 48 gallons ; I write the 48 under the gallons, and carry two to the hogsheads, which I add as in Simple Addition.
Ex. (1.) hhds. gals. qts.
hhds. gals. qts. 31 14 1
34 16 3 32 57 3
14 2 56 17 2
56 13 1 104 54 1
49 60 2 35 60 2
50 17 1 36 8 3
Answers to Liquid Measure. (1.) 297 hhds. 24 gals. (2.) 227 hhds. 59 gals. 1 qt.
ADDITION OF DRY MEASURE. Purchased the several quantities of wheat here specified : what is the total quantity ? Commence at the half gallons, then
qrs. b. p. gals. add the gallons whose amount is three, 4 6 3 1 or one peck and one gallon; carry one 20 7 1 0 to the pecks, whose amount is eight,
14 5 2 1 13
6 at four pecks to the bushel, make two
1 0 bushels; write a cipher under the
54 2 0 1 pecks, and carry two to the bushels, which when added make twenty-six; eight bushels make one quarter, therefore twenty-six bushels make three quarters, and 2 bushels over; write the 2 under the bushels, and carry three to the quarters, which are added as in Simple Addition. Should the amount be required in loads, you divide the total quarters by ten, the quotient is the number of loads, and the remainder the quarters.
Ex. (1.) qrs. bus. pks. 53
7 2 56 6 1 27 4 3 16 5 2 17 4 3
Ex. (2.) qrs. bus. pks.
17 4 3 106 3 3 49 1 1 37 5 3 41 6 0 79 7 2 332 5 0
172 4 3
ADDITION OF TIME.
How many years in the following number of weeks, days, hours, minutes, and seconds ?
d. h. The total number of seconds is
36 4 23 59 47 132, at 60 seconds to a minute
17 2 18 30 17 these make 2 minutes and 12 se
19 5 13 47 37 conds; write 12 under the
20 2 21 49 31 seconds and carry two to
42 2 6 7 12 the minutes, whose total is 187; at 60 minutes to the hour these make three hours and seven minutes ; write 7 under the minutes and carry three to the hours, which amount to seventyeight; now as twenty-four hours make one day, seventyeight hours are equal to three days, and six hours over; write the 6 under the hours and carry three to the days; whose amount is sixteen; at seven days to the week, 16 days are equal to two weeks and two days; write the 2 days under the days, and carry two to the weeks, whose amount is 94 ; now fifty-two weeks make one year, therefore 94 weeks is one year and forty-two weeks; write 42 under the weeks, and the one to the left, taking care to dot between it and the 42.
MISCELLANEOUS. Purchased the several parcels of wheat here specified, and for the sums severally annexed to each parcel ; what is the quantity of wheat, and how much did it cost? Ans. 9. b. p.
d. 54 6
3 for 120 9 61 56 4 1
121 14 3 57 3 2
120 19 63 49 13 6
78 13 2 74 2 18 113 16 51
Sold 5 bags of hops, the net weight and prices of which are here stated; what is the total weight, and for what sum did they sell ? Ans. cwt. qrs. Ib.
d. 2 3 14 for 10 14 7 1 2 27
8 17 41
21 19 71
7 14 6
A nobleman had a service of plate, which consisted of twenty dishes, weighing 203 oz. 8 dwt. ; 36 plates, 408 oz. 9 dwt.; 5 dozen spoons, 112 oz. 9 dwt.; 6 salts and 6 pepper-boxes, 71 oz. 7 dwt. ; knives and forks, 7 oz. 4 dwt.; with sundry small articles weighing 105 oz. 5 dwt: the weight of the whole in lbs. oz. and dwt. is required. Ans.
What is the amount in quarters, bushels, pecks, and gallons, of the quantities of grain here stated ?
Q. b. p. g.
Proof of Addition. See directions for proving Simple Addition.
In stating sums to be worked in this rule, the smaller sum must be written under the larger ; and care must be taken to write each figure under its proper denomination. You then begin at the right-hand figure or lowest denomination, and see whether the quantity in the upper line is large enough to admit of that in the lower line being subtracted from it; if it is not, you must borrow as in Simple Subtraction; only that you must bear in mind, that in Simple Arithmetic the sum we borrow is always ten, which is one of the next higher denomination; so the sum you borrow here is just as many of whatever denomination you may be working on as would make one of the next highest denomination, whatever that may be. If you subtract farthings from the upper line, and there should happen to be none, or if less than the lower line, you add four to the upper line, and then to repay it you add one to the pence the bottom line, being in lieu of the four farthings you added to the upper line. Thus subtract £7 10s. 6 d.
from £9 4s. 3d. In the example the larger sum having no farthings, we bor
9 3 row four for the occasion, then taking
7 10 63 3 from 4, 1 remains, which is written in
1 13 84 the third line, as a remainder; now four being the number of farthings contained in a penny, to repay it I add one to the pence of the bottom line, making it 7; as I cannot take 7 from 3, I add to it twelve, the pence contained in a shilling, making it fifteen; the difference between seven and fifteen we know to be 8, which I write down as a remainder, carrying or adding one to the shillings in the bottom line, which makes it 11; I cannot take it from 4, the shillings of the top line, I therefore add twenty, the shillings of a pound, to it, which make twenty-four; now 11 from 24 and 13 remain, which is written under the shillings, and one added to the pounds in the bottom line, which is then eight, and 8 from 9 and 1 remains.
Having shewn how pounds, shillings, and pence are subtracted, and explained fully in Addition the quantity or number of one denomination that is contained in another denomination, I trust that by occasionally referring to the examples of Addition, the learner will be able to work with ease the following sums; always bearing in mind, that he must never attempt to add or subtract bushels, gallons, and pecks from pounds, shillings, and pence, nor these latter from years, days, and months. When you add or subtract quantities, they must be, as it were, of the same family, indeed quantities from the same arithmetical table; hence arose the necessity of giving so many examples in Compound Addition. I hope that the learner, where he finds a difficulty to remember the denominations, will refer to them when working this and the other two compound rules.