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

3

must be observed also in finding the difference of two sums of
money.'
The object of multiplication is to find the sum or product by a short
and simple process which will render repeated additions unnecessary.
The definition is strictly applicable to all abstract numbers, and to
concrete numbers when the multiplier is an abstract number. In all
other cases, the meaning of the product must be modified to suit
particular cases, and at the same time made to coincide with the definition in all points which the factors possess in common.
It has been seen (Sect. VI. Art. 2.) that the product of two abstract numbers, 3 and 5, is 15, an abstract number consisting of abstract
units. And conversely, if 15 be divided by 3, the quotient is 5, an
abstract number. If,. however, 5 denote 5s. a concrete number, then
the product 5s. x 3 = 15s. a concrete number; and conversely,
15s. - 3 = 5s. a concrete number.2 But 15s. - 5s. = 3, an abstract
number, denoting that 5s. is contained 3 times in 15s. Also if 3 denote
1 Ex. To find the difference between ~79 8s. 6 d. and ~53 12s. 91d.
~ s. d.
79 8 61
53 12 9 -~25 15 8. difference.
First. 2 farthings cannot be taken from 1 farthing: add 4 farthings to 1 farthing,
then 2 farthings taken from 5 farthings leave 3 farthings; reserve the id.
Secondly. 1 penny added to 9 pence make 10 pence; which cannot be taken from
6 pence: add 12 pence to 6 pence, then 10 pence taken from 18 pence leave 8 pence;
reserve the 8d.
Thirdly. 1 shilling added to 12 shillings make 13 shillings, but 13 shillings
cannot be taken from 8 shillings: add 20 shillings to 8 shillings, then 13 shillings
taken from 28 shillings leave 15 shillings; reserve the 15s.
Fourthly. 1 pound added to 3 pounds make 4 pounds, and 4 pounds taken from
9 pounds leave 5 pounds.
Lastly. 50 pounds taken from 70 pounds leave 20 pounds.
Hence the difference is 25 pounds 15 shillings 8 pence and 3 farthings.
The use of the addition and subtraction of money may be illustrated in various
ways. For example: In an account of the transactions in money between two
persons, where receipts and payments are made between them. Each person in
stating his account would consider himself debtor for what he receives from, and
creditor for what he pays to, the other. To ascertain at any time the real state
of the account between them, the sums received would be added together, and
also the sums paid, and the smaller sum taken from the larger leaves a remainder.
If the sum received as creditor be the greater, the difference is due to the debtor, so
as to make the balance of the two accounts equal. If the sum paid as debtor be the
greater, the difference is due to the creditor to make the balance of their accounts
equal.
2 If 120 shillings be divided by 20, an abstract number, the quotient is 6 shillings,
the twentieth part of 120 shillings. If 120 shillings be divided by 20 shillings, the
quotient is 6, a number indicating that 20 shillings is contained 6 times in 120
shillings. But as 20 shillings make the larger unit of 1 pound, the number 6 will
denote the number of pounds contained in 120 shillings.