219. When any quantity is made up of several others, expressed in different units, such as £1. 14. 6, or 2cwt. 1qr. 3lbs., it is called a compound quantity. From these tables it is evident that any compound quantity of any substance can be measured in several different ways. For example, the sum of money which we call five pounds four shillings is also 104 shillings, or 1248 pence, or 4992 farthings. It is easy to reduce any quantity from one of these measurements to another; and the following examples will be sufficient to shew how to apply the same process, usually called Reduction, to all sorts of quantities.
I. How many farthings are there in £18. 12. 6¾?[44]
Since there are 20 shillings in a pound, there are, in £18, 18 × 20, or 360 shillings; therefore, £18. 12 is 360 + 12, or 372 shillings. Since there are 12 pence in a shilling, in 372 shillings there are 372 × 12, or 4464 pence; and, therefore, in £18. 12. 6 there are 4464 + 6, or 4470 pence.
Since there are 4 farthings in a penny, in 4470 pence there are 4470 × 4, or 17880 farthings; and, therefore, in £18. 12. 6¾ there are 17880 + 3, or 17883 farthings. The whole of this process may be written as follows:
- £18 . 12 . 6¾
- 20
- 360 + 12 = 372
- 12
- 4464 + 6 = 4470
- 4
- 17880 + 3 = 17883
II. In 17883 farthings, how many pounds, shillings, pence, and farthings are there?
Since 17883, divided by 4, gives the quotient 4470, and the remainder 3, 17883 farthings are 4470 pence and 3 farthings (218).
Since 4470, divided by 12, gives the quotient 372, and the remainder 6, 4470 pence is 372 shillings and 6 pence.
Since 372, divided by 20, gives the quotient 18, and the remainder 12, 372 shillings is 18 pounds and 12 shillings.
Therefore, 17883 farthings is 4470¾d., which is 372s. 6¾d., which is £18. 12. 6¾.