11. 25 masons built a house in 28 days, and each man's wages were 3s. 83d. per day. What is the whole pay?

12. The rent of some lodgings is £47. 18s. 9d. yearly. What will the rent amount to in 7 years 7 months?

13. The lead of an old tank, which weighs 7 cwt. 2 qrs. 17 lbs., is sold at £1. 18s. 9d. per cwt.; and a new one, which weighs 11 cwt. 1 qr. 24 lbs., is worth £2. ls. ld. What is the value of each tank, and the expense of the one more than the other?

per cwt.

14. Required, the duty on 143 cwt. 3 qrs. 12 lbs. of coffee, at £5. 4s. 8d. per cwt.?

15. What is the cost of 224 ac. 2 ro. 35 pl., at £12. 16s. 9d. per acre?

16. My daily expenses are £1. 5s. 5d. How much do I save yearly out of £600 ?

17. Compute the value of 501 yards, at £1. 1s. 1d. per yard?

18. Determine the expense of travelling 276 mi. 5 fur. 120 yds., at 11 d. per mile.

19. A man, 60 years old, weighs 2 cwt. 1 qr. 24 lbs. What was his weight 30 years ago, supposing it to have increased by what it was then?

20. If a square yard of marble cost 15s. 9d., what will be the value of a slab, 24 square yds. 7 ft. 100 in.?

21. If a gallon of a mixture cost 14s. 72d., it is required to ascertain the price of 53 gals. 2 qts. 14 pts.

22. Find the rent of 241 acres of land, at £2. 14s. 6d. per acre. 23. Three plots of land were sold,

the 1st containing 346 acres, at £14. 17s. 10d. per acre. 272 ac. 3 ro. 18 pl., at £17. 12s. 8d. 648 acres, at £15. 16s. 6d.

2nd

3rd

The value of the whole is required.

24. What is the amount of the following bill :

257 lbs. of green tea, at 4s. 4d. per lb.

424 lbs. of hyson

5s. 7 d.

25. Mr. John Dufour,

Worksop, 8th October, 1853.

Bought of Charles Clovis,

346 yards fine white linen, at 5s. 74d. per yd.

145

cambric

14s. 9d. 3s. 104d

26.

Sheffield, May 1st, 1853.

Thomas Harrison buys from John Rogers,

Silver castors, weight 52 oz. 4 dwts. 15 grs., at 7s. 6d. per oz.

8 oz. 11 dwts. 10 grs.,, 18 oz. 8 dwts. 14 grs.

Silver urn

A dozen silver spoons 2 lbs. 7 oz. 15 dwts.

Required, the whole amount.

DIVISION OF COMPOUND QUANTITIES.

255. In the division of compound quantities three cases present themselves:

1st, to divide a compound number by a simple number.

2nd, to divide a compound number by a mixed one, or by a fraction.

3rd, to divide a compound quantity by another.

256. First case: To divide a compound quantity by a simple number.

If 8 tons cost £21. 16s. 4d., what is the price of 1 ton?

Since 8 tons cost £21. 16s. 4d., 1 ton must evidently cost one-eighth part of that money. Now, of £21=£2, and £5 over, which, reduced into shillings, and adding the 16s., amount to 116s., the part of 116s. 14s., with '4s. over; 4s.=48d. and 4d. are 52d., and part of 52d. is 6d., and there remains 4d.; again, 4d. are 16 farthings, and the part of 16f. is 2f.

The price of a ton is, therefore, £2. 14s. 6d. written down as follows:

Thus we have taken one-eighth part of £21. 16s. 4d., or divided £21. 16s. 4d. by 8. Had the divisor been larger, the operation would have been performed by long division, as in the following example

:

If the clothing of 748 soldiers amounts to £3153. 5s. 9d., what is the cost per man?

Since 748 soldiers cost £3153. 5s. 9d. in clothing, therefore

1 soldier costs of £3153. 5s. 9d.,

or

£3153. 5s. 9d.
748

clothing, which quotient is found by the following process:—

in

161

20

3225

2992

233

12

2805

2244

561

4

2244
2244

The division may be effected by a process analogous to the one explained in (§ 245), by reducing the dividend to the lowest denomination, and dividing as in common division; and this quotient is brought back again into higher denominations. But this process is too laborious to be useful in practice.

257. EXERCISES.

1. If 1 cwt. cost £137. 18s., what is the price per lb. ?

2. A wheel makes 514 revolutions in passing over 1 mi. 467 yds. 1 ft. What is its circumference ?

3. How much will 1 piece of cloth cost, if 99 pieces cost £841. 10s. 10d.?

4. What are raisins per cwt., if 145 cwt. cost £167. 19s. 2d. ?

5. If 40 bales of cotton weigh 52 cwt. 3 qrs. 12 lbs., what is the average weight of a bale?

6. The duty on a pipe of port wine, containing 138 gallons, is £52. 6s. 6d. How much is the duty per gallon?

258. Second case: To divide a compound number by a mixed number, or by a fraction.

Ex. A piece of cloth, containing 64 yards, costs £75. 10s. 71d. f. What is the price per yard?

It has been proved before that the quotient is not altered, if both the dividend and divisor be multiplied by the same number; therefore, before dividing £75. 10s. 74d. f. by 64, we shall multiply these two numbers by 8, and then proceed to divide as in case 1.

The same result would have been obtained had we multiplied the divisor alone by 8; and after having performed the division, multiplied the quotient by 8.

If the divisor were a fraction, the same process would be followed, for we should multiply both divisor and dividend by the denominator of the divisor, and proceed to divide as in case 1.

Ex. Suppose it is required to divide £243. 4s. 9d. by

1. What quantity of hops will £100. 10s. 10d. purchase, at 15ąd. per lb. ?

2. An estate of 630 acres is let for £1543. 10s. 6d. What is the rent per acre?

3. 38 chests of tea weigh 18 cwt. 3 qrs. 24 lbs. What is the average weight of 1 chest?

4. How many yards of cotton can be made for £1, if £ pay for the making of 45 yds. 2 ft. 8 in. ?

5. If 70433 lbs. of tea cost £908. 10s. 10d., what is the price of 1 lb. ?

6. If a railway train goes 254 miles 3 fur. in 143 hours, at what rate does it travel per hour, including stoppages?

260. Third case: To divide a compound quantity by another. Here we shall have to consider whether the quotient is of different or of the same nature as the dividend.

First, when the quotient is not of the same kind as the dividend.

Ex. The making of a road cost £47. 19s. 5d. per mile. How many miles can be made for £2728. 17s. 10d. ?

Since £47. 19s. 5d. is the cost of a mile, as many times as £47. 19s. 5d. is contained in £2928. 17s. 10d., so many miles will be performed. Here, then, we must observe that the quotient will express a number of miles, furlongs, &c. Therefore, the lower denominations of the dividend cannot be adopted to determine the lower denominations of the quotient. On that account, in cases of this kind, the two quantities are reduced to the same denomination, and then the division is performed thus: £47. 19s. 5d. 11513d., and £2728. 17s. 10d.= 654934d.

=