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Ex. 1. £5527. 10s. 6d.÷243. 2. £18568. 12s. 1 d.÷1296. With these two examples the preceptor may form almost any number, by varying the divisors. The several numbers which were before made use of as multipliers, may now be used as divisors.

III. When the divisor is greater than 12, and not a composite number ?

RULE. The several quotients must be found by the method of Long Division, (see pp. 28 and 29), reducing the remainders to the next lower denomination, and taking in those numbers of the dividend which are of the same denomination. Ex. Divide £1350. 10s. 11d. by 240.

£. s. d.

240) 1350 10 11(57.

1200

150

20

240) 3010(125.

2880

130

12

240)1571(6d.

1440

131

4

240) 524(

480

44

Having divided the pounds by 240, I find a remainder of 150, this I reduce to shillings, taking in the 10, and divide again; the next remainder is 130, which I bring into pence, and take in the 11, and then divide again: the remainder now is 131, which I bring into farthings, and divide as before; the last remainder is 44, under which I place the divisor thus, 44 The true answer being 51. 12s. 6d.

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44

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1001

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3761

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22. 3604 10 10

24. 6534 16 3

40

IV. When the divisor consists of a number not exceeding 12, with one or more cyphers.

RULE. Cut off, by a line, as many places in the pounds as there are cyphers in the divisor, and divide by short division; then reduce the remainder to the next lower denomination, as in the lust rule.

Ex. Divide £5645. 14s. 41d. by 1200.

12,00)56,45 14 4

£. 4-845

20

12,00)169,14

S. 14-114

12

12,00) 13,72

d. 1-172

4

688

Having cut off two figures in the pounds to answer to the cyphers in the divisor, I divide by 12; the remainder is 845, which I reduce to shillings, and take in the 14, and divide as before: the second remainder is 114, this I multiply by 12, and take in the 4, and divide the remainder is now 172, which, reduced to farthings, gives 688; this not being equal to the divisor, I set down the answer 41. 14s. id.-. But as it was obvious, from inspection, that the remainder, 172, would not, when reduced, contain the divi or once, the answer might.

have stood 41. 14s. 1d.: for the value of 1d. is equal to 62880

1200grs.*

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* When the divisor is 1, with any number of cyphers, there is no division care is only necessary in cutting off the true number of figures in each separate dividend. Ex. 8698741. 12s. 9d. 1000.

£. s. d.

1,000) 869,879 12 9

20

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In all questions of interest, commission, buying and selling of stock, &c. &c. the divisor is 100; of course care must be taken, in cases of those kinds, to cut off the two right-hand figures in each part of the dividend.

+ The student need not dwell on these varieties,

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Ex. 1. If 17 yards of cloth cost 19l. 3s. 9d., what is it per yard? 2. What is the price of one pound of sugar, if slb. cost nine shillings?

3. The expenses of a journey amounting to 971. gs. 6d. are to be defrayed by six persons: how much will each have to pay?

4. I have bought 12 gallons of wine for 71. 16s. 6d.: how much is that per gallon?

5. Twelve boys are to have a guinea and a half divided among them: what will be each boy's share?

6. A hundred and twenty-five sailors have taken 8465l. prize-money: how much will each man be entitled to?

7. I have bought 144 pair of stockings for 271.: at what rate can I sell them so as to gain by each pair one shilling?

8. What did I pay a piece for sheep, having bought 75 for 135l.? 9. Cheese at 31. 12s. 6d. per cwt.: how much is that per lb. ? 10. If 81 oxen cost 17811. 12s. 6d. : what is the value of one? 11. If a pipe of wine cost 951.: how much is that a dozen, which contains three gallons?

12. Bought 50 dozen of wine for a hundred guineas: how much is that per bottle?

13. Divide a thousand guineas between 23 people, and see how much it is for each?

14. If 12 pieces of linen cloth contain 250 yards, what is the length of a single piece?

15. How much can I afford to spend a day, a week, and a month, if my income be 500l. per annum?

16. If 12 tea-spoons weigh 9 oz. 17 dwt. 12 gr.: what is the weight of each spoon?

Miscellaneous Questions.

Ex. 1. It is said that Syrius, or the Dog Star, is the nearest of all the fixed stars, and that its distance is computed at 2,200,000,000,000 miles how many years, (each containing 365 days, 6 hours exactly,) would a cannon ball be in passing from the earth to Syrius, supposing it travelled at the rate of 480 miles per hour?

Ex. 2. The planet Mercury is about thirty-seven millions of miles from the Sun; Venus sixty-eight millions; the Earth ninety-five millions; Mars a hundred and forty-five millions; Jupiter four hundred and ninety-three millions; Saturn nine hundred and eight, and the Herschel one thousand eight hundred millions of miles from the Sun: put these several distances down in figures, and add them together as a sum in Addition.

Ex. 3. How much nearer the Sun is Mercury than Mars; and how much farther is the Herschel than the Earth? See Ex. 2.

Ex. 4. The beautiful planet Venus travels, in its annual journey round the Sun, at the rate of 75,000 miles in an hour: how many miles does she travel in one of her years, or in 2284 days?

Ex. 5. The Earth travels, in her annual course, at the rate of 68,400 miles in an hour: how many miles therefore do we move in a second? Ex. 6. There are in the Qld Testament 39 books and 929 chapters, and in the New there are 27 books, and 260 chapters: how many books and chapters are there in the Bible?

Ex. 7. There are 23214 verses in the Old Testament, and 7959 in the New: how much therefore do the verses in the former exceed those in the latter?

Ex. 8. There are 592439 words in the Old Testament, and 181258 in the New: how many words are there in the Bible?

Ex. 9. In the Old Testament there are 2,728,100 letters, and in the New there are 838,380: what are the sum and difference of these twe numbers?

Ex. 10. There are in the Bible 3,566,480 letters: how long would a person be in counting them, supposing he could count 200 in a minute?

Ex. 11. A printer charges 54d. for every 1000 letters that he sets up: how many thousand must he set up to earn 17. 15s, per week.

Ex. 12. If a printer set up 8500 letters per day, how long would he be in composing the Old Testament, and how long in composing the whole Bible? See Ex. 9 and 10.

Ex. 13. If a printer be desired to set up the Bible in Latin, how much would he earn in the business, at the rate of 33d. per 1000 letters, supposing there are as many letters in Latin as there are in English?

Ex. 14. If there be as many letters in the Greek Testament as there are in the English, how much would a printer earn in setting it up at 83d. per thousand?

Ex. 15. The name of JEHOVAH occurs 6855 times in the Old Testament: what proportion therefore does this word bear to all the other words in that book?

Ex. 16. The word and occurs in the Bible 46227 times: what proportion does that bear to the other words? See Answer to Ex. 8.

Ex. 17. There are in the northern side of London 126 houses newly built, and unlet, the average rent of which is 85.; and 75 houses at 501. each, and 68 at 30 guineas each: what is the total annual loss of these empty houses to the proprietors ?

Ex. 18. There are 1100 hackney coaches in London, each of which earns on an average 18s. per day: how much is expended weekly, monthly, and annually, on these vehicles?

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