5. Since 1½ or 3 halfpence is ¼ of 6_d._ or 12 halfpence, 153 tons, at 1½_d._ each, will cost ¼ of what the same number costs at 6_d._ each, that is, ¼ of£3 . 16 . 6, which is 0 19 1½ ----------- The sum of all these quantities is 425 10 7½ which is, therefore, £2 . 15 . 7½ × 153. The whole process may be written down as follows: or what 153 tons would | £153 0 0 cost at £1 per ton. | ----------- ----------- £2 is 2 × £1 | 306 0 0 2 0 0 10_s._ is ½ of £1 | 76 10 0 0 10 0 5_s._ is ½ of 10_s._ | 38 5 0 0 5 0 6_d._ is ⅒ of 5_s._ | 3 16 6 0 0 6 1½_d._ is ¼ of 6_d._ | 0 19 1½ 0 0 1½ | ------------ ---------- Sum | £425 10 7½ £2 15 7½ ANOTHER EXAMPLE. What do 1735 lbs. cost at 9_s._ 10¾_d._ per lb.? The price 9_s._ 10¾_d_. is made up of 5_s._, 4_s._, 10_d._, ½_d._, and ¼_d._; of which 5_s._ is ¼ of £1, 4_s._ is ⅕ of £1, 10_d._ is ⅙ of 5_s._, ½_d._ is ¹/₂₀ of 10_d._, and ¼_d._ is ½ of ½_d._ Follow the same method as in the last example, which gives the following: or what 1735 tons would | £1735 0 0 cost at £1 per lb. | ------------ ----------- 5_s._ is ¼ of £1 | 433 15 0 0 5 0 | 4_s._ is ⅕ of £1 | 347 0 0 0 4 0 | 10_d._ is ⅙ of 5_s._ | 72 5 10 0 0 10 | ½_d._ is ¹/₂₀ of 10_d._ | 3 12 3½ 0 0 0½ | ¼_d._ is ½ of ½_d._ | 1 16 1¾ 0 0 0¼ | ------------- ------------ by addition ... | £858 9 3¼ £0 9 10¾ In all cases, the price must first be divided into a number of parts, each of which is a simple fraction[47] of some one which goes before. No rule can be given for doing this, but practice will enable the student immediately to find out the best method for each case. When that is done, he must find how much the whole quantity would cost if each of these parts were the price, and then add the results together. [47] Any fraction of a unit, whose numerator is unity, is generally called an _aliquot part_ of that unit. Thus, 2_s._ and 10_s._ are both aliquot parts of a pound, being £⅒ and £½. EXERCISES. What is the cost of