Money Rules. TABLES OF ENGLISH MONEY. PENCE TABLE. 2 Farthings make 1 Halfpenny, written thus, d. 2 Halfpence 12 Pence..... ... 1 Penny, 1 Shilling, id. 1s. 1 Pound, £1 57. The same value may be expressed in different forms; thus, 7 shillings, and 84 pence, are the same in value, but different in name. 58. When a value is expressed in one form, the process by which we find its equivalent value in another form, is termed REDUCTION. 59. We speak of farthing as a lower name than shillings, and shillings as a higher name than pence. Reduction is therefore of two kinds,-ascending and descending; the money table written thus will show the relation of these processes to each other. Ascending. pound shillings pence farthings Descending. D 60. If we have a number of farthings given to find their value in pence, shillings, or pounds, we do so by ascending reduction. 61. If we wish to find the number of shillings, pence, or farthings in so many pounds, we use descending reduction. 62. Descending Reduction. RULE.-Multiply the number of the highest name mentioned, by as many units of the next lower name as make one of the higher. Add to the product any units of this lower name that may be contained in the given sum, and proceed thus, step by step, to the units of the name required. EXAMPLE:-Reduce £367 16s. 8d. to farthings. £367 16s. 8d. Reduce to farthings: - Ex. 36. (1-6) 4d.; 8d.; 7d.; 11d.; 13d.; 15d. (7-13) 44d.; 64d.; 84d.; 174d.; 94d.; 123d.; 113d. (14-22) is.; 3s.; 5s.; 17s.; 16s.; 28s.; 19s.; 14s.; 25s. (23-30) 13s. 2d.; 15s. 5d.; 16s. 7d.; 19s. 8d.; 21s. 2d.; 14s. 5d.; 18s. 9d.; 11s. 11d.; (31-39) 16s. 8d.; 17s. 91d.; 11s. 114d.; 12s. 93d.; 15s. 63d.; 25s. 43d.; 38s. 64d.; 27s. 54d.; 298. 113d. (40-53) £1; £2; £3; £8; £12; £15; £17; £28; £49; £386; £217; £914; £388; £126. (54-60) £1 11s.; £3 14s.; £47s.; £2 12s.; £17 53.; £186 15s.; £214 13s. (61-68) £19 8s. 6d.; £17 15s. 4d.; £13 Os. 8d.; £164 14s. 5d.; £386 17s. 2d. ; £17 13s. 9d.; £386 14s. 2d.; £178 18s. 9d.; (69-73) £179 14s. 6d. ; £215 13s. 84d.; £386 13s. 83d.; £169 11s. 5d. £177 15s. 8d. (74-78) Reduce to pence :-£17; £13 15s. 4d.; £19 16s. 8d.; 2168s.; £38 15s. 5d. (79-83) Reduce to shillings :-£38 15s.; £2968 17s.; 875 guineas; 396 guineas; £287 19s. (84-89) Reduce to halfpence :-£4 19s. 2d. ; £9 9s. 9d.; £376 Os. 31d.; £309 7s.; 2179 guineas; £18 12s. 111⁄2d. 63. Ascending Reduction. RULE.-Divide the given amount by as many units of the same name as make one of the next higher, and proceed thus, step by step, to the units of the name required. EXAMPLE:-Reduce 21856 pence to pounds. 20)1821 shillings. 4 pence. £91 1s. 4d. Ex. 37. (1-5) Reduce to pence:-2168 farthings; 3872 farthings; 21986 farthings; 1773 farthings; 18675634 farthings. (6-9) Reduce to shillings:-8167 pence; 937124 farthings; 9284 groats; 72148 threepenny-pieces. (10-20) Reduce to pounds :-2349 shillings; 67931 farthings; 247899 farthings; 476937 threepenny-pieces; 7000 groats; 1789 guineas; 4897 half-crowns; 14289 sixpences; 999 florins; 6879119 farthings; 740987 pence. (21-30) Reduce to guineas :-£668; 973698 farthings; 2769 pence; 300 half-crowns; 7390 farthings; 8876914 groats; 37911 crowns; 17943 half-sovereigns; 99813 halfpence; 76139 threepenny-pieces. (31-38) Reduce to crowns:-£786; 21733 farthings; 3976410 halfpence; 2197 pence; 699 guineas; 34779 groats; 943 threepenny-pieces; 4297 half-guineas. (39-50) Reduce to florins:-£39 16s.; 428 farthings; 7296 groats; 6890 guineas; 741 half-crowns; 8900 halfpence; 72 crowns; 98476 pence; 7217930 farthings; 3670 sixpences; 9763 threepenny-pieces; 81919730849 farthings. (51-59) Reduce to sixpences :-904 crowns; 27896 farthings; £379; 41837 halfpence; 274 guineas; 1780 pence; £891 10s. 6d.; 716 half-crowns; 81907 groats. (60-71) Reduce to groats:-£86; 9107 farthings; 721904 pence; 1617 shillings; 2179 crowns; 32710 pence; 34219 threepenny-pieces; 702 guineas; £6921 17s. 8d.; 41679 farthings; 92718493 halfpence; 73814 half-crowns. 64. Questions of the same class as the following, involve the principle of reduction. Divide £1816 16s, amongst 5 men and 17 boys, giving to each man 3 times as much as to each boy. Here 5 men receive as much as 15 boys; therefore 5 men and 17 boys receive as much as 32 boys. Dividing the sum by 32, we have £56 15s. 6d. as one boy's share; as one man's share we have 3 times £56 15s. 6d., that is £170 6s. 6d. Therefore the share of 5 men will be £170 6s. 6d. x5 £851 12s. 6d. 17 boys will be £56 15s. 6d. × 17=£965 3s, 6d. Ex. 38. (1) A number of pence were divided amongst 19 boys and 28 girls, so that each boy had four times as many pence as each girl. Each girl received 9d., and there was 3d. left. How many pence were divided? (2) How long will it take 9 boys to do a piece of work which 12 men, each of whom does twice as much as a boy, can do in 18 days? (3) In a town 864838 gallons of water are consumed per day by a population of 7680 men, 2650 women, and 13928 children. How many gallons would be consumed in a day by 20 men, 50 women, and 100 children, supposing the same quantity to be required for 6 children, 4 women, or 3 men? (4) A house is worth six times as much as the garden, and together they are worth £763: what is the house worth? (5) A farmer bought 35 oxen, 7 horses, and 24 sheep, for £1883; each ox cost half as much as a horse and 5 times as much as a sheep: what was paid for the oxen, what for the horses, and what for the sheep? (6) 3024 lbs. of tea are to be made into 84 parcels of each of 4 sizes; the second size is 3 times the first, the fourth 3 times the second, and the third 5 times the first: what is the size of each of the 4 parcels? (7) A number increased by 14 times itself is 13875. Find the number. (8) A draper bought 35 bales of linen, each containing 54 pieces, and 42 bales of calico, each containing 27 pieces; each piece of calico contains 4 times as many yards as a piece of linen. There are in all 115668 yards. How many yards of linen are there, and how many of calico ? Addition of Money. 65. RULE.—Arrange the amounts so that pence are under pence, shillings under shillings, and pounds under pounds. Add up the column of farthings. Reduce the sum to pence, set down the remainder under the column added, and carry the quotient to the next column. Proceed thus with each column, always reducing the sum to units of the next higher name, setting down the remainder, and carrying the quotient to the next column. |