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terms, produces the fraction

answer.

189 L.; this reduced to its proper quantity is the

320

3. If my friend lends me 10 guineas for 10 weeks and 3 days, how long ought I to lend him 57. 4s. 6d. to acquit myself of the obligation?

Reduction.

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I find that the answer will be greater than the second term, consequently I mark the less extreme, and proceed as before.

4. If by walking 24 miles an hour I can perform a journey in 89 days, how many days will another who can walk. 3+ miles an hour require to go the same distance, allowing 12 hours to the day?

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7. If 3 ounces of gold cost 177. 15s. 6d. what sum will pur

chase 44 ounces? Ans. 211. 11s. 8d..

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buy? Ans. 14lb. 2oz. 14dr.fr.

9. Paid 21. 2s. 8d. sum will pay for 21 168.6d.4.

5

L. what quantity will 21. 3s. 4d.

for the carriage of lewt. 2qr. 14lb.; what cwt. carried the same distance? Ans. 31.

6

10. If of a calf be worth of a pound, what is the whole

12

calf worth?

Ans. 21. Is. 1d..

7

11. If 7 men can mow a hay-field in 4 days, how long would 4 men require to mow the same? Ans. 81 days.

3 8

12. Paid 11 shillings for of a gallon of brandy; what must Ans. 71. 2s. 5d.

be given for 4 gallons at the same rate?

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of a block of mahogany cost 2§L. what sum will

9

purchase the remaining ? Ans. 11. 16s. 3d.

11

14. Suppose 15 feet of plank 9 inches wide sufficient to make a side-board, how many feet of plank 14 foot wide will be required to make another of equal dimensions? Ans. 7 feet 6 inches.

15. If 9 English ells of linen cost 1. 17s. 6d. what cost 10 Flemish ells? Ans. 11. 5s.

16. What is the value of 5 fother of lead, at 16s. 4d. per cwt.? Ans. 41. 11s. 6d. 3.

17. A corn-chandler charges 91. 5s. 6d. for a load of barley; what must be given for 34 bushels at that price? Ans. 15s. 2d.z. 18. Suppose 120 men can build a ship in 15 weeks, how long will it be building if 87 men only are employed? Ans. 21w. 5d..

19. If 5l. 6s. 8d. be paid for the use of 1731. 2s. 6d. what sum must be paid for the use of 310L. for the same time? Ans. 81. 19s. 6d.7.

2 5

2 3

20. After using of a Cheshire cheese, of the remainder

sold for 13s. 5d; what was the whole cheese worth?

11. 2s. 5d..

Ans.

21. If 3 yards of cloth 1 yard wide will make a suit of

5.

clothes, what quantity of cloth

9

yard wide will be necessary

to make a similar suit? Ans. 10yd. 1qr. 0‡n.

22. If

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of 3 guineas will purchase

of a lottery-ticket,

8

how many tickets can be had for a thousand pounds? Ans.

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my brother, and afterward sold of my remaining share for

2251. 10s.; what is the privateer worth?

24. How many yards of carpet 1 yard wide will be required to cover a floor 83 yards long, and 65 yards wide?

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" This rule depends on the same reasons as Compound Proportion in whole numbers, and its operations are performed in the same manner, as far as relates to the general principle, differing only as a fractional differs from an integral process.

• It will be found more convenient to place the fractions all in one line, with the divisors inverted; thus,

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·L. 31. 1s. 2d.49 as above.

Explanation.

Having stated the question, and marked the divisors, &c. the complex fraction which arises from the operation is reduced to a simple one, by multiplying 5 by 60, and 14 by 7; the result is next reduced to its lowest terms, and then to its proper quantity, which is the answer.

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4. If 9 students spend 10L. in 18 days, how much will 20

students spend in 30 days? Ans. 39l. 18s. 4d.3.

5. If 100L. gain 44L. interest in a year, what sum will gain

5 6

5 L. interest in of a year? Ans. 138l. 18s. 11d..

6. A trench is required to be dug 100 feet in length, and 10 men have been employed 63 days in digging 493 feet of it; how long will 12 men require to finish the remainder? Ans. 5d. 87h. at 12 hours to the day.

7. If 13 feet of deal 9 inches wide cost 3s. 4d. what sum will pay for the floor of a room 15 feet long and 12 wide? 31. 3s. 8d..

Ans.

DECIMAL FRACTIONS.

212. If unity be supposed to be divided into 10, 100, 1000, &c. equal parts indefinitely, that is, into ten parts, or any multiple of ten, that which expresses any number of such parts less than that the unit is divided into, is called a Decimal Fraction.

NOTATION OF DECIMALS.

213. It is well known, that the value of any figure is increased tenfold by removing it one place to the left hand of the place it occupies; thus 1 removed one place to the left (by placing a cipher to the right of it) becomes 10, or ten times 1; remove it one place farther, and it becomes 100, or ten times 10; remove it one place farther, and it becomes 1000, or ten times 100; and so on without end. Hence likewise it follows, that if any figure be removed in a contrary direction from the left hand towards the right, its value will be decreased tenfold at every step of such removal; thus, by removing I one place to the right, 1000 becomes 100, or one tenth of 1000; 100 becomes 10, or one tenth of 100; 10 becomes 1, or one tenth of 10; and, since 1 is the least whole number, this is as far as we can go in whole numbers.

214. But it is plain, that 1 may be removed step by step indefinitely towards the right; if therefore we put a point to the right hand of the place of units to distinguish it, and then place the 1 to the right hand of the point, thus .1, it is evident from what has been said that it will express one tenth of an unit, or

1

10

if we remove the 1 a place farther to the right, by interposing a cipher between the point and the 1, thus .01, this will

t

express one tenth of or one hundredth part of unity; if two

10'

ciphers be interposed, thus .001, it will express one tenth of

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