will cost ¼ of what the same number costs at 6d. 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 cost at | |||
|---|---|---|---|
| £153 0 0 | £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 | |
| 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 | 0 0 1½ |
ANOTHER EXAMPLE.
What do 1735 lbs. cost at 9s. 10¾d. per lb.? The price 9s. 10¾d. is made up of 5s., 4s., 10d., ½d., and ¼d.; of which 5s. is ¼ of £1, 4s. is ⅕ of £1, 10d. is ⅙ of 5s., ½d. is ¹/₂₀ of 10d., and ¼d. is ½ of ½d. Follow the same method as in the last example, which gives the following:
| or what 1735 tons would cost at | |||
|---|---|---|---|
| £1735 0 0 | £1 per ton. | ||
| 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 fraction12 of some one which goes before. No rule can be given