INTRODUCTION TO ARITHMETIC, PART X. CONTAINING, PRACTICE AND TARE AND TRET, PRACTICE. THIS is a short way of finding the value of goods : any question in the Single Rule of Three direct, where the first term is unity or one, may be answered by Practice. The rule is generally performed by taking aliquot parts for a divisor, as, 20 quills at a farthing each; how much do they come to? We readily know that 20 quills cost 20 farthings, and that if we divide 20 by 4, the quotient will be the answer in pence, viz. 5 pence. Again, 20 at 2 farthings each. We perceive in a moment that 20 halfpence will make 10 pence; therefore we say two farthings make the half of a penny; divide 20 by 2, the quotient will be the answer in pence. Twenty at 3 farthings each: here we reflect and find, that the half of 20, and the half of that half, will make the answer; for it must be three times as much as the first quantity at one farthing; therefore say, 2 farthings make the half of a penny, and a farthing is the half of a halfpenny; divide the given number by 2, that quotient by 2, add the two quotients together, and the answer will be 15 pence; Thus, 20 at 3 farthings: 20 1110 5 This is taking aliquot or even parts. See Card 32. 15d. = 10 2 = or 56 In order to learn expeditiously, we must get the following table by heart. TABLE. to | Iqr. or 28 b. = 1 4 4 1/ 을 6 8 21 2 1 3 5 16 14 Of a gr. of a cut. 33 lb. = } 18 4 7 14 1/3 을 When reading the above table we say, “ Half a shilling equals 6 pence; one third of a shilling equals 4 pence; one fourth of a shilling equals 3 pence,” &c. “One half of a pound equals 10 shillings; one third of a pound equals six shillings and eight pence,” &c. “ Two hundred weight equal one tenth of a ton; two and a half hundred weight one eighth of a ton,” &c. “One quarter or 28 lbs. equal one fourth of a hundred weight; two quarters or 56 lbs. equal one half of a hundred weight,” &c. Then we say, “ Three and a half pounds equal one eighth of a quarter of a hundred weight; four pounds equal one seventh," &c. CASE 1. RULE. Divide by the aliquot parts that are in a penny, then by 12 and by 20, which will give the answer. LESSON 1. Bought 7612 pipes at 1 farthing each ; 7612 at 2 farthings, and 4712 at 3 farthings each; what did the parcels come to separately, in pounds, shillings, &c.? Ans. at 1q. £7 18s. 7d., at 2q. £ 15 17s. 2d., and at 3q. £14 14s. 6d. 19.1 d. 7612 at 19. 29. £d. 17612 at 29. 12 1903 12 3806 20 1518 7d. 210 | 3117 2d. Ans. £ 7 18s. 70. Ans. £ 15 178. 2d. CASE 2. RULE. Divide by the aliquot part or parts in a shilling, add the quotients together and divide by 20 as before to ascertain the pounds. LESSON 2. LESSON 3. See Card 32. 1d. 18.17612 at id. Id.l123.8612 at 1d. lg. 210 6314 4d. Ans. £ 31 14 4 19. d. 717 8 1795 |