EXAMPLES IN MULTIPLICATION OF COMPOUND QUANTITIES BY MIXED NUMBERS. Every line to be described in writing. 41. How much cheese would cost £4 1's. 8.d., if 1qr. 24 lb. cost £1? Multiply by 41. 42. How much beef will £3. 2.s. 6 d. buy, if 1'qr. 3·lb. 8 oz. cost £1.? Multiply by 31. 43. What quantity of beer is worth £7. 3's. 4.d., when 1'bar. 28'galls. cost £1? Multiply by 74. at 2. 16 4 8. 6 at 3 19. 7 at 5 17. 6. 44. If 23 yd. 2-qr. 1'na. of linen cost a sovereign, how much will cost five guineas? Multiply by 5. 45. Supposing the keep of a horse for 4 we. 5 da. to cost £2', how long could he be maintained for £3 10's.? Divide by 2. Multiply Quotient by 34. 46. What weight of goods will cost £9. 7's. 6 d., at the rate of 2. cwt. 1.qr. 24 lb. for £1.? 47. If 20's. will pay for manuring 3 r. 21 po. of ground, what extent will be manured for £8. 6's. 3.d.? 48 At the rate of 35 mi. 5 fur. 30 po. per hour, how far will a train travel in 4.ho. 20 min.? 49. If the fare for a distance of 41 mi. 7 fur. be £1, how far should one be conveyed for £2⋅ 8's. 9'd.? 50. If a man's wages be 17's. 6'd. per week, how much will he earn in 9 we. 4 da.? 51. If a man must work 11 da. 5 ho. to earn £2, in what time will he earn £7. 10's., counting 10 hours to the day? Multiply by 34. 52. If 13 yd. 3 qr. 1∙na. cost 16 s., how much will cost 40's.? Multiply by 21. To Divide a Compound Quantity by a Fraction. Multiply by Reciprocal of Divisor. (PRINCIPLE XVII.) This process is employed to ascertain the Quantity of which the given one is a certain Fraction. For example, if we wish to discover the amount of which £342 15′s. 21d. are, we must Divide £342. 15's. 2 d. by, the result of which operation will coincide with the Product of £342′ 15's. 2 d. ×%. For, ...of Required Amount = £342 15's. 2 d. .. Required Amount = £342 15's. 24d. Then, Dividing both sides of the Equation by Required Amount =£342 15's. 2d. .. Required Amount £342 15's. 21d. × (PR. IX.) (PRIN. XXIV.) (PR. xx.) (PR. XVII.) FIRST EXAMPLE WORKED OUT. Five-eighths of a certain sum of money amount to £342 15's. 24d.; what is that sum? By First Method. Example completed. £. By Second Method. £. 8. d. 342 15 2 of Reqd. Amt. 8. 5) 2742 1 840 of Reqd. Amt. 548 8 4 Required Amt. SECOND EXAMPLE WORKED OUT. If 2 qr. 24 lb. cost £1. 8's. 9 d., what is the price per cwt.? 2. qr. 24 lb. of 1 cwt. (EXERCISE LXXXIX.) .. £1 8's. 9 d. of cost of 1 cwt. .. cost of 1' cwt. = £1 8's. 9.d.§. (PRIN. XX.) £18's. 9.d. x . (PRIN. XVII.) To Divide a Compound Quantity by a Mixed Number. First. Reduce Divisor to its equivalent Improper Fraction in its lowest terms. Second. Multiply Given Quantity by Reciprocal of this Improper Fraction. THIRD EXAMPLE WORKED OUT. If 9'cwt. 3'qr. 14·lb. cost £26 9's. 11 d., what will 1 cwt. cost? = 9 cwt. 3 qr. 14·lb. 97 cwt.2 of 1.cwt. Example completed; except the work of the Long Division. EXAMPLES IN DIVISION OF COMPOUND QUANTITIES BY FRACTIONS OR MIXED NUMBERS. Describe every line in writing. 1. Of what sum are £1247 1's. Oąd. three fifths? 2. Of what amount are £2973′ 3′s. 10d. =? 3. If of a yd. cost 2's. 24d. what will 1-yd. cost? 4. If 7 articles cost £4 2's. 5d. what will 11. cost? What will 1·lb. Avoir, cost 5. If lb. cost 3's. 6d.? 6. If 1 lb. cost 16's. 11d.? 7. If 21 lb. cost 12's. 24d.? 8. If 24 lb. cost 19's. Od.? 9. If 4 lb. cost 8's. 10d.? 10. If 7 lb. cost 24's. 5ğd.? 11. If 3 lb. cost 17 s. 24d.? 12. If 5 lb. cost 14's. 6.d.? 13. If 11 oz. cost 8's. 8d.? 14. If 15 oz. cost 10:s. 74d.? 15. If 5 oz. cost 4's. 3d.? 16. If 6 oz. cost 2's. 11d.? 17. If 7 oz. cost 6's. 34d.? 18. If 9 oz. cost 15's. 6d. ? 19. If 13 oz. cost 3's. 94d.? 20. If 12. oz. cost 11's. 10 d. ? * Principle XIX. Cor. i. How much is cloth per yard 21. When 3 qr. cost 13's. 0ąd.? 22. When 3-na. cost 2's. 10d.? 23. When 5'na. cost 3's. 10d.? 24. When 7-na. cost 2's. 3d.? 25. When 9'na. cost 7's. 6d. What is the rent per acre 31. At £1. 17 s. 74d. for 3'r. 20°p.? 32. At £1 19 s. 6d. for 1'r. 20'p.? What is the price per cwt. £. 8. d. 35. At 5 1 11 36. At 1. 15. qr. lb. for 3. 14. ? 41 for 1 14·? At what rate per lb. Avoir. will The Compound Quantity may, sometimes, with advantage, be put into the form of a Vulgar or Decimal Fraction, previously to Multiplying or Dividing. This method is of especial utility when the Multiplier or Divisor is a Fraction or a Mixed Number. When the Multiplier or Divisor is large, the Compound Quantity may be turned into a Simple Quantity by Reducing it to the lowest denomination which it contains. The result* will, of course, come out in units of this denomination, and will require to be converted, by Ascending Reduction, into the Compound form. FIRST EXAMPLE WORKED OUT. What will 42% E. E. of cloth cost, at 5ğd. per yard? * In Division, the coincident result. (See pp. 218 and 224) Second. = 32 =2555d. = 2991d.; By Decimal Fractions. 42% E. E. = 42.6 times 1.25 yd. = 53.25 yd.; Cost of 53.25 yd. at 5ğd. = 5·625d. × 53·25 = = 299.53125d.; q. EXERCISES XLV. & XLVI. EXERCISE EXERCISE EXERCISES LXXII. & XLIII. EXERCISE XLIII. EXERCISES LXXXVI. & LXXXV. SECOND EXAMPLE WORKED OUT. Multiply £4· 11's. 6.d. by 9864. = = 40 = £225639 £451274 Third: By Decimal Fractions. £4 11 s. 6d. × 9864⋅ = £4·575 × 9864. = £45127.8 = £45127 16's. PROPOSED DECIMAL COINAGE. By far the greater part of the time, attention, and labour, expended on the explanations, tables, rules, and examples occupying pages 173 to 234 inclusive, has been exacted from us by the fact that our Concrete Units of Comparison do not proceed by regular Decimal gradations. That is to say, each such unit has not, exactly, one tenth of the value of the next greater, and, consequently, tenfold the value of the next smaller. If all our Measures, Weights, and Coins were thus decimally arranged, Concrete Quantities of every kind |