(10) What are the fractions which express of 95. The Value of a compound quantity may be exhibited in the form of a fraction, whereof the unit is of a specified denomination. RULE. Reduce the proposed quantity to the lowest denomination contained in it, and also the proposed unit to the same denomination; then the fraction whose numerator and denominator are these results respectively, will be the one required. For, let it be required to represent 2 qrs. 15 lbs. as the fraction of 1 cwt.: then we have and of the 112 equal parts into which 1 cwt. is supposed to be divided, 71 are here taken, so that according to Article (71), the fraction required will be cwt. 96. By the two preceding rules, magnitudes of the same kind, consisting of fractions of simple or compound quantities, and connected by the operations of addition or subtraction, may be reduced to simple fractions of a given denomination. Ex. Find the fraction of £1, which is equivalent to the excess of of a guinea, above the sum of 2 of a shilling and of 7s. 6d. (1) Express 4s. 11d.; 17s. 114d.; 19s. 10 d. and £1. 13s. 11 d. 19f., as fractions of £1. (2) What fraction is 2 cwt. 1 qr. 16 lbs. of a ton; 2 ft. 9 in. of a pole, and 3 ro. 25 po. of an acre? (3) Express 5 bush. 3pks. 1 gal. as the fraction of a quarter; and 2 wks. 5 days 18 hrs. as the fraction of a year of 365 days. Answers: 47 64 and 79 1460 (4) What fraction of £2. 7s. 6d. is £1. 7s. 8d., and of 3 cwt. 2 qrs. 14 lbs. is 3 cwt. 19 lbs. 2 oz. ? (5) Reduce of 2s. 44d. to the fraction of a half crown; and 9s. 10 d. to the fraction of 13s. 21d. (6) Required the fractions of £1, which express the 63 values of of of £1. 12s. 14d. and of £5. 17s. 4d. 910 Answers: and (7) Find the simple fraction of £1. which expresses the sum of of of 13s. 4d. and 2 of 4 of 10s. 6d. (8) Express the sum of of a guinea, of a pound, of a shilling and of a penny, as the fraction of a guinea; and the excess of of £13. 10s. 101d. above of £1. 2s. 9d. as the fraction of £6. (9) Compare the values of of a pound, of a 97. If the Species of the unit be given, the value of a fraction of it may be expressed by means of its known parts. RULE. Multiply the numerator of the fraction by the number of parts of the next inferior denomination which are equivalent in value to the unit, divide the product by the denominator, and the quotient is the required number of parts of that denomination: proceed in the same way with the remainder, if any, and the parts of the next denomination will be found: and repeat this process till the lowest denomination, to which the unit is capable of being reduced, is obtained. For, if the fraction be of a yard, we have and therefore the value of of a yard, expressed in the known parts of a yard, is 2ft. 6in., or 30in. 98. The preceding Articles enable us to find the value of the sum or difference of fractional parts of magnitudes of the same kind. Ex. Required the sum and difference of of a pound and of a guinea. The same results may also be obtained as follows: and when fractions of the unit of the lowest order occur, this will be the more convenient method of the two. (1) Examples for Practice. Find the values of of a pound, of a shilling and of a guinea. Answers: 12s.; 64d. ƒ. and 5s. 10d. (2) Required the values of cwt., qrs. and 3lbs. Answers: 2qrs. 24lbs.; 10lbs. and 6oz. (3) What is the number of feet in of a mile; and the number of yards in of a league? Answers: 4224ft. and 4620yds. (4) Required the values of qrs., bush. and pks. and 1gal. 1qt. 1 pts. (5) What is the value of of a month of 28 days, and of of a week? Answers: 3 days. 17hrs. 36min., and 1 day. 22hrs. 40min. (6) Required the sum and difference of of 5 guineas and of of a pound. Answers: £4. 1s. 8d. and £2. 18s. 4d. (7) Add together of a guinea, of a pound, of a crown and of a shilling. Answer: 19s. 6d. (8) Find the sum of % of 6s. 8d., § of £2. 3s. 9d. 15 of £4. 14s. 5d.: also of £., of £140 7/ Answers: £5. 12s. 6d., and £50. and and 13 guineas. Answer: £40. 4s. 2d., and £1. 10s. 1 d. f. 3 4 (10) Find the value of of a guinea + 99. We shall here shew how the primitive fractions, as defined in Article (69), may be applied to the practical calculation of prices, when the price of an unit of any denomination is supposed to be given: and the tediousness of the enunciations of the rules at length, will be a sufficient excuse for the mere indications of the processes to be employed, by means of examples. |