« ΠροηγούμενηΣυνέχεια »
26. How many chests of tea, weighing 24 pounds, at 43 cents a pound, can be bought for $ 1548?
27. Joseph Eldredge received $ 10, as a birthday present, from his father, on every 29th day of February, from 1837 to 1857. How much less than $ 200 did he receive, in all?
Ans. $ 150.
28. If 25f- grains of standard gold be worth $ 1, how many pounds avoirdupois of standard gold will be worth $ 1,000,000? Ans. 3685f pounds.
29. A merchant, who had bought 188 gallons of molasses, at 40 cents a gallon, intended to have it sold at the rate of 50 cents a gallon; but his shop-boy retailed half of the quantity at 12£ cents a quart, beer measure, when, finding he had made a blunder, he sold the balance at 14 cents a quart, wine measure, thereby expecting to exactly make up for the mistake. How much less did the whole bring than was intended?
ADDITION OF COMPOUND NUMBERS.
115t Addition of Compound Numbers is the process of finding the amount of two or more compound numbers.
Ex. 1. Required the amount of 31£. 17s. 9d. 2far.; 16£. 16s. 6d. lfar.; 16£. lis. lid. lfar.; 19£. 19s. 9d. 3far.; 61£. 17s. Id. 2far. Ans. 147£. 3s. 2d. lfar.
Operation. Having written units of the same
£ d" far. denomination in the same column, we
3 1 1 7 9 2 fin(l tne sum 0f farthings in the right
16 16 6 1 hand column to be 9 farthings = 2d.
16 11 11 1 lfar. We write the lfar. under the
19 1 9 9 3 column of farthings, and carry the 2d.
6 1 i 7 1 2 to the column of pence; the sum of which is 38d. = 3s. 2d. We write
Ans. 1 4 7 3 2 1 the 2d. under the column of pence,
and carry the 3s. to the column of shillings; the sum of which is 83s. = 4£. 3s. Having written the 3s. under the column of shillings, we carry the 4£. to the c olumn of pounds, and find the entire amount sought to be 14 7£. 3s. 2d. lfar.
The same result can be arrived at by reducing the numbers as they are added in their respective columns. Thus, beginning with farthings, we can add, in this way: 2far. -f- 3far. = 5far. = Id. lfar.; and lfar. =• Id. 2far., and lfar. — Id. 3far., and 2far. = 2d. lfar. Writing the lfar. under the column of farthings, we carry the 2d. to the column of pence; and add, 2d. (carried) -f- 1 = 3d., and 9d. = 12d. = Is., and lid. = Is. lid., and 6d. = 2s. 5d., and 9d. = 3s. 2d. Writing the 2d. under the column of pence, we carry the 3s. to the column of shillings; and add, 3s. (carried) -)- 17s. = 20s. = l£., and 19s. = l£. 19s., and lis. = 2£. 10s., and 16s. = 3£. 6s., and 17s. = 4£. 3s. Writing the 3s. under the column of shillings, we carry the l£. to the column of pounds, and so find the whole amount to be, as before, 147£. 3s. 2d. lfar.
The last method of operation may be rendered more concise, as it should always be in practice, by merely naming results as the adding is performed (Art. 45).
From the illustrations given, it is evident that the adding of compound numbers is like that of simple numbers, except in carrying; which difference holds also in subtracting, multiplying, and dividing compound numbers.
Rule. —Write all the given numbers, so that units of the same denomination may stand in the same column.
Add as in addition of simple numbers; and carry, from column to column, one for as many units as it takes of the denomination added to make a unit of the denomination next higher.
Proof. — The proof is the same as in addition of simple numbers.