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COMPOUND ADDITION. • COMPOUND ADDITION is the adding together of Compound Numbers.
RULE.-1. Write down the given numbers in such a way that those of the same kind or denomination may stand directly below one another-pounds under pounds, shillings under shillings, &c.
2. Add the numbers in the lowest denomination, and find how many of the next higher denomination are contained in the amount. Carry the quotient to the next column, marking any remainder below the column just added.
3. Add the numbers of the next denomination in the same way, including what has been brought from the previous column, and so on, till all the denominations have been added. The highest denomination is added as in Simple Addition. · Example 1.--Add together the following sums—£31, 12s. 74d., £73, 14s. 8 d., £69, 17s. 5 d., £87, 15s. 6 d., and £37, 12s. 31d. £ $. d.
Here, after writing down £ s. d., place the 31 12 77
pounds under £, the shillings under s., and the
pence with the farthings under d.; and draw a line 73 14 81
under the figures. Beginning with the farthings, 69 17 53 we have first ), or 2 farthings, then 1, 3, 2, 2 87 15 61
in all, 10 farthings. These are converted to pence, : 37 12 31 and make 24d. ; put down the , and carry £300 12 71
2d. to the pence column. This being added, makes 31 pence, or 2 shillings and 7 pence: write
the 7 under the pence, and carry the 2 to the unit row of shillings; adding it, we have 2, 2, 5, 7, 4, and 2—in all, 22: then, going to the next column, the figures in which are all tens, we say 22 and 10 are 32, then 42, 52, 62, 72-in all, 72 shillings, which, being converted to pounds, make £3, 12s. ; 12, therefore, is written under the shillings, and 3 carried to the pounds, which are now added, and the amount put down as in Simple Addition.
NOTE.-In adding the shilling column, the following is the most convenient method :-Add the unit row of shillings as already described : in the foregoing example, it amounts to 22; mark the last figure, 2, below the unit row, and carrying the tens, 2, to row, add it also: then halve the amount that is, divide it by 2); if 1 remains after halving, mark 1 below the tens' row, and carry the half to the pounds. If nothing remains on halving, carry the half to the pounds, but without marking anything below the tens' row of shillings. In the present example, the tens' row amounts to 7, which, being halved, makes 3, and l over; therefore mark the 1 below the tens' row of shillings, and carry 3 to the pounds.
The halving of the tens' row of shillings is merely a short way of dividing the amount of the shillings by 20, to convert them to pounds.
Example 2.-Add together 3 tons 7 cwts. 2 qrs. 17 lbs. 5 oz.; 7 tons 3 cwts. 2 qrs. 13 lbs.; 8 tons 12 cwts. 3 qrs. 4 lbs. 7 oz.; 6 tons 17 cwts. 2 qrs. 10 lbs. 9 oz.; 12 tons 9 cwts. 2 qrs. 18 lbs. 13 oz. tons. cuts. qrs. lbs.
Here having written down in a line 3 7 2 17 5 the marks for tons, hundredweights, 7 3 2 13 0 quarters, pounds, and ounces, write 8 12 3 4
each quantity under its proper name, 6 17 2 10 9
and draw a line under all. Commenc12 9 2 18 13
ing to add at the ounces, we find there
are 34; now, 16 ounces being a pound, 38 11 1 8 2 34 oz. are equal to 2 lbs. and 2 oz.: put
down the 2 oz. under the ounces, and
carry the 2 lbs. to the pound column. Adding this column, there are 64 lbs., which, being converted to quarters, gives 2 qrs. and 8 lbs. over ; the 8 lbs. are written under the pounds, and the 2 qrs. carried to the column of quarters. This being added, gives 13; and 13 qrs. converted to cwts., give 3 cwts. and 1 qr.; put down l under the qrs., and carry 3 to the cwts. Adding these, we find there are 51 cwts., which, being converted to tons, give 2 tons, and ll cwts. over ; write ll under the cwts., and carry 2 to the tons. These are now added, and their amount put down as in Simple Addition.
All compound quantities being added on the same principles as the above, it is unnecessary to give examples of the addition of the other weights and measures.