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OPERATION First, we say 17 in £100, is 17)£100 10s. 3d.( £5 contained 5 times and £15 remaining; and since these £15, as well as the 10s., are yet to be
20 divided among the 17 men, we 17)310(18s. reduce the pounds to shillings, and add the 10s., making 310s. ;
140 we find 17 to be contained 18
136 times in 310s. with 4s. remain
4 der. We reduce the 4s. to
12 pence, and add the 3d., making 17)51(3d. 51d., which divided among the
51 17 men, gives 3d. each.
Collecting, we have | £5 18s. 3d.
NOTE.—We do not divide 100 pounds by 17 men, which .s impossible; but we separate £100 into 17 equal parts. Each part is expressed by the quotient, and contains £5, (Art. 64. Note.)
Or, adhering to the general definition of Division, (Art. 22 and ART. 64,) we suppose a pound set apart for each man, and then find how many times £17, the number thus set apart, is contained in £100; the quotient will be an abstract number. The answer will, of course, be as many pounds to each man as there are parcels of £17 in £100; that is, as there are units in the quotient.
Had the divisor been one of the nine digits, the work might have been performed by Short Division.
We therefore have this general
I. Place the divisor on the left of the dividend, as in Sim. ple Division. Begin at the left-hand and divide the number of the highest denomination by the divisor. . Reduce the re. mainder, if any, to the next lower denomination, to which add the number of the dividend expressing that denomination, and then divide the sum by the divisor. 9. Divide 673141da. Chr. 58m. 24sec. by 1843.
II. Proceed in the same way for all the denominations. If there is a remainder after the last division, place it over the divisor, and annex it in a fractional form to the quotient. Each quotient will be of the same denomination as its dividend.
Having placed the divisor as in Simple Division, how do you proceed? When, in dividing any particular denomination, there is a remainder, how do you dispose of it? Bohat denomination will the respective quotients be ?
Ans. 365da. 5h. 48m. 48sec. :0. Divide imi. 255 ft. 10in. by 365. Ans. 15 ft. 2in.
When the divisor is a composite number, we may divide by the factors of the number successively.
11. Bought 15 sheep for £5 12s. 6. How much did one sheep cost ? FIRST OPERATION.
SECOND OPERATION. £ s. d.
£ s. d. 3)5 12 6 cost of 15 sheep. 5)5 12 6 cost of 15 sheep. 5)1 17 6 cost of 5 sheep. 3)1 2 6 cost of 3 sheep
0 7 6 cost of 1 sheep. 0 7 6 cost of 1 sheep.
From this example, we see that it makes no difference which factor is first used.
12. If 24yds. of cloth cost £18 6s., how much is that per yard ?
Ans. 15s. 3d. 13. From a piece of cloth containing 128yds. Iqr., a tailor made 18 coats, which took one third of the whole piece. How many yards did each coat contain ?
Ans. 2yds. lqr. 2na.
87. QUESTIONS INVOLVING THE FOUR PRECEDING RULES.
1. Twenty-four mer. agree to construct 7mi. 1 fur. 24rd of road; after completing ã of it, they employ 8 more men What distance does each man construct before and after the 8 men were employed ? S 16rd. before.
? 1 fur. 20rd. after. 2. A silversmith has seven tea-pots, each weighing 116. 3oz. 13pwt. llgr. What is the whole weight ?
Ans. 91b. loz. 14pwt. 5gr.
3. A farmer has 1000 bushels of apples, which he puts into 350 barrels. How many does each barrel hold ?
Ans. 2bu. 3pk. 34qt. 4. If it require 1 sheet of paper to print 24 pages of a book, how many reams, allowing 18 quires to the ream will it take to print 3000 copies, of 250 pages each?
Ans. 72 reams, 6 quires, 2 sheets. 5. An estate worth £2570 is to be divided as follows: the widow has one third of the whole, the remainder is to be divided equally between seven children. How much does the widow receive, and how much does each child have?
The widow has £856 13s. 4d.
Each child has £244 15s. 2d. 34 far. 6. Divide 100 acres, 3 roods, 8 rods of land, between four persons, A, B, C, and D, so that A shall have one sixth of the whole, B one fourth of the remainder, C one third of what then remains, and D the rest. How much does each one have ?
SA had 16 A. 3R. 8P.
B had 21 0 0.
(D had 42 0 0. 7. A, B, C, and D, having 13cwt. Iqr. 416. of sugar, they agree to divide it as follows: A is to have one half of the whole, B is to have one third of the remainder, C je to have one fourth of what then remains, and D is to take what is left. What were their respective portions ?
SA had 6cut. 2qr. 1616. Ans.
B had 2 0 24. 1 C had 1 0 12. (D had 3 1 8.