REDUCTION. Terms to be explained :-Lower denomination, higher denomination, reduction. MENTAL EXERCISES. a. Reduce to halfpence 14d., 3d., 34d., &c. b. d. f. h. to shillings 45d., 69d., 74d., &c. to shillings £1, 1s., £2, 4s., £3, 16s., &c. to pence £1, 4s., £8, £7, 15s., &c. to farthings £1, 10s., £2, 5s., £3, 10s. 6d., &c. to farthings 2 crowns, 3 half-crowns, &c. 10s. to the fraction of £1; 5s. to the fraction of £1; ls. to the fraction of 1 crown, &c. Reduce to shillings: XXXI. (1.) £93 (ans. 1860), £476, £874. (2.) 89 guineas, 768 guineas, 496 guineas. (3.) 86 half-sovereigns, 98 half-guineas, 896 florins. (4.) 978 crowns, 1001 half-crowns, 8341 half-crowns. Reduce to pence :— (5.) £896 (ans. 215040), 896 guineas, 975 half-sovereigns. (6.) 832 half-crowns, 1111 florins, 439 sovereigns. Reduce to farthings: (7.) £897 (ans. 861120), 356 crowns, 1099 half-crowns. Reduce (8.) £987, 13s. to shillings (ans. 19753); £473, 19s. to shillings; £856, 11s. to shillings. (9.) 83 guineas, 13s. to shillings; 891 crowns, 4s. to shillings; 813 half-guineas, 9s. to shillings. (10.) £83, 19s. 6d. to pence; £742, 13s. 8d. to pence; £645, 17s. 9d. to pence. (11.) £916, 13s. 44d. to farthings (ans. 880002); £891, 17s. 8d. to farthings; £813, 1s. 74d. to farthings. (12.) 49 guineas, 13s. 8d. to farthings; 89 half-sovereigns, 8s. 9 d. to farthings; 412 crowns, 2s. 71⁄2d. to farthings. (13.) £47, 13s. 8d. to halfpence; £96, 11s. 44d. to halfpence; £111, 17s. 9 d. to halfpence. (14.) 48 half-crowns, 2s. 34d. to halfpence; 91 halfguineas, 8s. 11 d. to halfpence; 98 sovereigns, 19s. 11 d. to halfpence. (15.) £981, 17s. 6d. to sixpences; 99 guineas, 13s. 9d. to threepenny-bits; 45 half-crowns, 1s. 8d. to fourpenny-bits. Reduce XXXII. (1.) 9768 farthings to pence (ans. 2442), 4976 farthings to pence, 8761 halfpence to pence. (2.) 1967 shillings to pounds (ans. £98, 7s.), 2898 shillings to pounds, 3976 sixpences to pounds. (3.) 9876 pence to shillings, 8764 halfpence to shillings, 9781 farthings to shillings. (4.) 7986-fifths of a penny to pence, 8764-eighths of a penny to pence, 9764-twelfths of a penny to pence. (5.) 97689 farthings to pounds (ans. £101, 15s. 21d.), 87642 farthings to pounds, 68324 farthings to pounds. (6.) 36745 farthings to pounds, 97684 farthings to pounds, 19843 farthings to pounds. (7.) 98742 halfpence to pounds, 97511 halfpence to pounds, 76489-thirds of a penny to pounds. (8.) 79841 farthings to half-sovereigns, 73691 halfpence to half-sovereigns, 49693 farthings to sovereigns. (9.) 68955 farthings to pounds, 768459 farthings to guineas, 964711 halfpence to guineas. (10.) 51990 threepenny-bits to pounds, 9763 fourpennybits to pounds, 896543 pence to sovereigns. (11.) 450 florins to crowns, 456 florins to half-crowns, 1020 halfpence to half-crowns. (12.) 960 halfpence to half-guineas, 71 half-crowns, 1s. to half-guineas, 1890 half-guineas to pounds. (13.) 2499 threepenny-bits to guineas, 80418 farthings to guineas, 89 guineas to pounds. (14.) 930 guineas, 8s. to pounds, 9768 crowns to guineas, 8764 half-crowns to guineas. (15.) £1015, 7s. to guineas, 9768 half-crowns, 1s. 6d. to half-guineas, 897 half-crowns to half-guineas. Find how often XXXIII. (1.) 4s. 5d. is contained in £1, 6s. 6d. (ans. 6), 3s. 9d. in £1, 10s., 4s. 11d. in £2, 14s. 1d. (2.) 2s. 7 d. in £1, 3s. 7 d., 5s. 11ąd. in £3, 11s. 9d., 4s. 91⁄2d. in £4, 11s. Od. (3.) £2, 6s. 7d. in £11, 12s. 11d., £3, 9s. 8d. in £31, 7s. 6 d., £6, 4s. 114d. in £68, 14s. 3d. (4.) £3, 6s. 4 d. in £11, 12s. 3 d., £7, 6s. 9åd. in £39, 3s., £6, 11s. 2d. in £60, 13s. 34d. Reduce the following fractional expressions to their lowest terms : (8.) 3d. is of ls. (ans. ); 4d. of 1s.; 11⁄2d. of 1s. (9.) 4s. of £1; 5s. of £1; 2s. 6d. of £1. (10.) 3s. 4d. of £1; 6s. 8d. of £1; 1s. 3d. of £1. (11.) 12s. of £1; (12.) 10s. of £2; Reduce 15s. of £1; 13s. 4d. of £1. 12s. 6d. of £3; 17s. 6d. of £4, 10s. (13.) 3s. 9d. to the fraction of 5s. 74d. (ans. ), £6, 7s. Old. to the fraction of £6, 18s. 6d., £4, 6s. 104d. to the fraction of £5, 12s. 31d. XXXIV. (1.) Andrew has £5, 6s. 74d., and Thomas has £7, 18s. 3d. How much money must Thomas give to Andrew that the latter may have 6000 farthing? (2.) A gentleman's income is £967. What amount of income-tax must he pay at the rate of 5d. in the £ ? (3.) At an entertainment 500 people paid 3d. each, 450 paid 6d. each, and 197 paid 1s. each. What was the amount drawn? (4.) A French franc is worth 93d. What is the value in English money of 987 francs? (5.) An American dollar is worth 4s. 2d. What is the value of 2000 dollars ? (6.) In India 16 annas are equal to one rupee, which is worth 2s. What is the value of 1600000 annas? (7.) The property of a certain city is valued at £15,000,000. What assessment would be raised at the rate of 7 d. in the £? (8.) Add together a halfpenny, a penny, a shilling, a crown, a half-crown, a sovereign, a guinea, and a halfguinea, and find how often the amount is contained in £481. (9.) How many yards at 3s. 5d. a yard, may be had for £5, 10s.? (10.) If mutton be 111⁄2d. per lb., and beef 9d. per lb., how many lbs. of mutton must be given for 18 lbs. of beef? (11.) How many gallons of water must be added to 16 gallons of spirits, at 18s. a gallon, so that the mixture may be sold at 12s. a gallon? (12.) A man divides £17 among 4 people, so that for every 6d. one gets another gets 5d., another 4d., and another 2d. What does each receive? COMPOUND ADDITION, MENTAL EXERCISES. a. d. + lid. + 2d. ; 34d. + 4d. + 7 d., &c. b. 1s. 6d. 2s. 3d. + 58. 9d. ; £4, 10s. + £6, 15s. + £2, 5s., &c. c. 1 shilling + 1 florin + 1 half-crown; 1 sovereign + 1 guinea +1 half-guinea, &c. d. 3d. + 24d. + 24d. + 24d., &c. ; 4s. + 2s. 9d. + 2s. 9d. + 2s. 9d., &c.; £2 + £3, 15s. + £3, 15s. + £3, 15s., &c. |