have £568. 14s. 4d. more than the second, and the second £728. 18s. 2d. more than the third. (2) If a person spend £152. 10s. a-week; what must be his daily income that in 15 years he may lay by £7522. 10s.? (a year=52 weeks). (3) Find how often 3 cwt., 2 qrs., 27 lbs., 15 oz. is contained in 4 tons, 13 cwt., 2 qrs., 27 lbs., 7 oz.; and verify the result. (4) A person bought 4 bales of cloth, each bale consisting of 6 pieces, and each piece of 27 yards, at £16. 4s. per bale; what was the price of the whole, and what the rate per yard? (5) Supposing 5000 persons, and 1500 carriages to pass over Waterloo Bridge, daily, during the present year, the former paying a toll of a half-penny each, the latter a toll of 2d. each; what will be the amount of toll raised at the year's end? (6) If a person spend 200 guineas during the first six calendar months of the year 1853, what is his average daily expenditure? (7) What quantity of tea at 4s. 53d. per lb., must be given in exchange for 5 cwt., 3 qrs. of sugar, at 7s. 101d. per stone? (8) A father left 5 sons; and his property consisted of £500 in cash, and 5 bills of £48. 10s. 6d. each. He ordered £20 to be bestowed on his burial, and his debts, amounting to £164, to be paid: then the residue of the property to be thus divided, viz., one-third part to go to the eldest son, and the remainder to the other four sons in equal portions: what was the share of each son? XII. (1) A gentleman sent a tankard to his silversmith, which weighed 100 oz., 16 dwts., and ordered him to make it into spoons, each weighing 2 oz., 16 dwts.: how many spoons did he receive? (2) A gentleman's estate, for the 5 years ending with 1849, yielded £1227. 15s.: how much could he spend one day with another, so as to lay by 135 guineas? (3) The length of a year being 3651 days, and that of a lunar month being 29 days, how many lunar months are there in 19 years? (4) What is the value of a talent of silver, if silver be worth 5s. per oz., and a talent consists of 1000 shekels, each weighing 219 grains? (5) Divide £17. 3s. 5d. by £14. 3s. 6d. to 4 places of decimals. Can these sums be multiplied together? (6) A merchant bought 7 pieces of cloth, each 27 yards, for £55. 128. ; and sold 56 yards at 5s. 31d. per yard; at what must he sell the remainder per yard in order to gain £3. 118. on the whole? (7) A certain number of men, twice as many women, and three times as many boys earned in 5 days £7. 15s. ; each man earned 1s. 6d., each woman 10d., and each boy 8d. a-day. How many were there of each? (8) A bankrupt owes his creditors £2963, and pays them 6s. 81d. in the pound. How much does he pay them altogether? REDUCTION OF FRACTIONS. 132. To find the value of a fractional part of a number of one denomination in terms of the same or lower denominations. RULE. Multiply the given number by the numerator of the fraction, and divide the product (if possible) by the denominator; if there be a remainder, multiply the numerator of the fraction which remains by the number of units connecting the given denomination with the next lower denomination, and divide the product by the denominator; if there still be a remainder, proceed with it in the same way as with the last remainder, and so on, till you come to the lowest denomination. The compound number formed of the integral parts reserved from the successive quotients, and of the result of the last reduction, will be the value required. Note. If the given number comprise different denominations of the same kind: reduce the different denominations to the lowest denomination involved, and the above rule may be then applied; or the value may be found by the method shewn in Art. (128). 20s. 58. Ex. 5. Find the value of of £15. +3% of £1.+} of § of 3 of £1.+} therefore required value = £4. 5s. 84d. + £3. 8s. 64d.+2s. 104d. +33d. Ex. 6. = £7. 17s. 54d. therefore required value = 2 pks., 17 qts. -5 qts. =1 pk., 4 qts. Ex. XLVIII. (1) Find the respective values of, 1. 2. 3 of £1; of £1; § of £1; 2 of a guinea; & of a guinea. of £1. 10s.; of £2; 3 of half-a-crown; & of 13s. 4d. 13 of £1; of 1s.; & of 6s. 8d.; & of 1s. 6d. ; & of 3s. 6d. 4. 23 of 7s. 6d.; § of £2. 3s. 9d.; of a moidore; 3. 5. 6. 16s. 103d. 16 of £135. of 4s. 7d.; 13 of £1. 2s. 9d.; × 11 of 21s.; } of 3 of 9s. 101d. 3 of 2s. 6d.; of £4. 14s. 5d.; & of of 10s. 6d.; of 100 guineas. 7. % of of 20 of 5 guineas; of £16. 16s. 31d.; 1000 of £441. 12s. 6d. 8. 9. 10. of a cwt.; 2 of a lb. Avoird.; of a mile; § of an acre. of a mile; of a day; of a yard; of 3 cwt., 1 qr., 14 lb. 7% of a lb. Avoird.; 12 of a lb. Troy; 23 of a gal.; 45 of an acre. 11. 3 of a hhd. of beer; 23 of a tun of wine; 633 of a bus. 12. 21 of a load; 310% of a cub. yd.; 91⁄2 guineas. 14. 49 5 1 of 11 of £16. 8s. 1d.; of 13 of 121 of of £2×4. 15. of £1x53; of of £1÷1. 44 16. 19 of £5. 1s. 11d. 459.; 23 of £8. 14s. 2d.÷8. of of 10s. 6d. + gs.+ of 28.6d. 5. § of £1-§ of 1s.+§ of a guinea - § of a moidore. 4 of £1. 123.+ 15 of £3. 5s. + 1 of 1 guineas. 10. 2 of 5 of £1+% of 5 of 2s. 6d. + 1⁄2 of 10žd. of 21s. + of 1⁄2 of £1-1 of 2 of 5s. + of § of 1s. |