Elementary arithmetic, with brief notices of its history... by Robert Potts.

10
Conversely, to reduce any concrete quantity cr fraction to the
fraction of any other unit.1
First: Any fraction of a less unit is reduced to the fraction of a
greater unit by dividing the fraction of the less unit by the number of
less units which make one of the greater units.
Secondly: A fraction of a greater unit is reduced to one of a less
unit by multiplying the fraction by the number of less units in the
greater unit.
18. PROP. To find the sumn or difference of concrete fractions.
The sum or difference of any concrete fractions can be found by
reducing the given fractions to fractions of the same unit, and then
finding their sum or difference.
Or the value of each of the concrete fractions may be first found in
smaller units of the same kind, and then the sum or difference may be
found of these units.
19. PPoOP. To find the product or quotient of concrete fractions.
The method of multiplication and division of concrete fractions
differs not from that of abstract fractions.
If a concrete fraction be multipliel or divided by an abstract
fraction, the product or quotient will be parts of the same concrete
unit as the multiplicand or dividend.
If both fractions be concrete, the nature of the product or quotient
-will be determined by the consideration, whether the results of these
operations do, or do not admit of any rational interpretation.
are to be taken; it will then be clear that 5 shillings is y- of the unit, or of 12
shillings.
Find the value of of one pound sterling.
S'. d.
8) 20 0 = ~1
2 6 = - of ~1
5
12 6 = of l1.
1 Conversely, what fraction of ~1 is 12s. 6d.?
Here 12s. 6d. = 25 sixpences,
and ~1 = 20s. = 40,,
It is obvious that 12s. 6d. will be the same part of ~1
as 25 sixpences is of 40 sixpences,
that is, 12s. 6d. = 40 or 5 of ~1.
Reduce -5 of one pound to the fraction of a shilling.
Here 20 of the smaller units make one of the larger.
Thus,7 of 1 = - x 20 = 2 of 1 shilling.
Conversely, Reduce 2 of 1 shilling to the fraction of a pound.
Here 1 larger unit is equal to 20 of the smaller,
And -~ of 1 shilling = 0 - '2 = 0 x - = rof.1
27 2 97 2!3U l