The latter method is generally employed. Hence the rule: To multiply a number by a fraction, multiply by the number above the line, and divide the product by the number below the line. M. £53 75. 2d. by .£58 17s. 9d. by 2. (3) £110 175. 1d. by .258 14s. old. by . (5) £56 18s. 4. by 23.74 16s. 3. by 33. 7 47 19s. 1od. by 5. (8) 264 10s. 1d. by 24. (9) 529 yds. 3 qrs. 2 nls. by 63. (10) 67 tons 9 cwt. 3 qrs. 8 lbs. by 7%. (1) 19 m. 5 f. 14 p. 3 yds. by 2417. (12) 24 a. 2 r. 32 p. 17 sq. yds. by 5318. SECTION IV. When the divisor is a compound quantity. Example. Divide £23 18s. 43d. by £1 15s. 84d. 15s. 81d., or £17 16s. 10d., from £23 185. 4d., we get £6 15. 64d.; and now subtracting 3 times £1 15s. 81d., or £5 75. old., from £6 1s. 61d., we get 14s. 5d.; therefore we have subtracted £1 15s. 84d., 10 times and 3 times, or 13 times, from £23 18s. 4 d. and there is a remainder 14s. 5d.; that is, £23 18s. 4 d., divided by £1 15s. 8d., gives a quotient 13 times, and a remainder 14s. 5d. This method may be applied in all similar cases, but though the process is simple in theory, the difficulty of finding the quotient figures, and the tediousness of the compound multiplications and subtractions, preclude its adoption in practice. The following method is therefore generally employed : 1713) 22963 (13 5833 5139 694 Explanation.-Taking the same example as before, reduce both the given quantities to farthings; we then get 1,713 farthings for the divisor, and 22,963 farthings for the dividend; dividing, we get 13 times for the quotient, and a remainder 694 farthings, or 14s. 5d., the same as before. Rule III-Reduce the given quantities to the same denomination, and divide as in Simple Division. The quotient will be an abstract number, that is, a number of times, and the remainder, if any, will be of the same denomination as the given quantities were reduced to. Divide (5) Examples. (6) (4) N." £13 8s. 8d. by £1 135. 7d. (2) £17 19s. 41d. by 15s. 71d. £32 6s. by 13s. 5d. £131 by 2s. 8 d. 6 £45 by £1 175. 6d. £56 135. 4d. by £2 16s. 8d. 21 guineas by £1 11s. 6d. (8)63 by 2 guineas. 35 florins by 7 halfcrowns. 49 half-crowns by 3s. 6d. (10) (9) Find the quotient and the value of the remainder in the following: (2) £23÷ 18s. (3) £14 84d. ÷ 8d. 13 O."£5 135. 9d. 175. 6d. 165.5 half-crowns. (£7 135. yds. 2 qrs. I nl. ÷ 1 yd. 3 qrs. lbs. 3 qrs. 21 lbs. (7) 36 lbs. II (6) (5) 9 cwt. 2 qrs. 14 oz. 16 dwts. 18 (10) 7 f. 29 p. 3 yds. 16 p. 35 grs. ÷ 4 lbs. (8) 18 m. 3 f. 24 p.÷7 f. miles ÷ 17 yds. 14 p. 2 yds. (11) 16 a. 3 r. 27 p. 16 p. 221 sq. yds. (12) 17 yrs. 53 days3 yrs. 287 days (1 year = 365 days). P. Among how many persons may £38 7s. 8d. be divided so that each may receive 13s. 8d.? (2) How many persons may receive 3s. 9d. each out of 63 half-crowns? (1) (3) How many pounds of tea at 2s. 9d. a lb. may be bought for £2 6s. 9d.? A person bought an equal number of pounds of tea at 2s. 6d. a lb. and coffee at 1s. 5d. for £2 IOS. IId.; how many pounds of each did he buy? (5) An equal number of pounds, half-crowns, and florins amount to £49; how many are there of each? (6) Divide £47 4 florins into an equal number of guineas, half-guineas, crowns, half-crowns, and sixpences. (7) If £14 ́6s. 9d. be divided among an equal number of men, women, and children, so that each man may receive 4s. 6d., each woman 25. 9d., and each child 6d., how many persons are there altogether? (8) If a person's income-tax, at 77. in the pound, amount to 15 guineas, what is his income? (9) How many times will a wheel 4 ft. 7 in: in circumference turn round in 2 miles 20 poles? (10) £54 35. is divided among 17 men, and a certain number of women; each man has £I 75. 9d., and each woman 13s. 7d. Find the number of women. (1) A poulterer gains 1d. a score on eggs, id. a lb. on butter, and 9d. a couple on fowls; if he sell Io score of eggs and 43 lbs. of butter, how many fowls must he sell to gain 8s. altogether? (12) A goldsmith manufactured 3 lbs. 8 dwts. of gold into rings, each containing 9 dwts. 8 grs. ; he sold the rings at £2 6s. 8d. each; how much did he receive for them? MISCELLANEOUS EXAMPLES. A father is five times as old as his son, and the difference of their ages is 28. Find the son's age. Since the father is 5 times as old as the son, the difference of their ages is 4 times the son's age. Therefore 4 times the son's age = 28 years; 7 years. A publican buys 9 barrels of beer at £1 195. per barrel. Three of the casks being leaky, he loses thereby 27 gallons. At what rate per pint must he sell the remainder in order to gain £7 45. on his outlay? Bought 9 barrels, or 324 gallons. Sold 27 Cost of 9 barrels at 39s. per barrel = 3515. Gain on the whole Selling price of 297 gallons Therefore the selling price of 1 gal. = 4955.÷297. = : 144. = 495s. = IS. 8d. = IS. 8d.÷8. = = 23d |