£20 x £20 = £400
£ s d
400 0 0
¼d x ¼d = 1/16 less 1/16
----------------
£399 19 11-15/16 Ans.
It would be possible to adopt other methods, each of which would give
a different result.
Properly speaking, _this sum cannot be done_.
Multiplication is merely a contracted form of addition: it means
taking a number or quantity a certain number of times. Every
multiplication can be proved by addition. All numbers are _abstract_
or _concrete_--3 is abstract, £3 is concrete.
Two abstract numbers can be multiplied together--as, 4 times 3 = 12.
Proof: 3
3
3
3
--
12
One abstract number and one concrete number can be multiplied
together--as 2s. multiplied by 3 = 6s.
Proof: 2s.
2s.
2s.
---
6s.
Two concrete numbers cannot be multiplied together.
In the example just given, 2s. multiplied by 3, we see it simply
means to write down 2s. three times, and by addition we discover the
answer to be 6s. Suppose the reader lent a friend 2s. on Monday, 2s.
on Tuesday, and 2s. on Wednesday, he has lent 2s. three times, making
6s. lent in all.
Now, we will attempt to multiply 2s. by 3s., but it is impossible
to comprehend how many times is 3s. times. The answer to 2s. x 3s.
usually given is 6s. On the same lines, we multiply 9d. by 10d., and
our answer is--90d., that is 7s. 6d.--a greater product than 2s.
multiplied by 3s.
Although it is stated that two concrete numbers cannot be multiplied
together, it should be borne in mind that we can multiply yards,
feet, and inches, by yards, feet, and inches (length by breadth),
which will result in square or cubic measure: 12 inches make 1 foot,
and 3 feet make one yard, 144 square inches make 1 square foot, &c.
12 pence make 1 shilling, but how many square pence make 1 square
shilling?
The argument generally brought forward in favour of the performance
of this problem is, that when the Rule of Three is applied to
financial questions (such as interests, &c.) money is multiplied by
money.
Example.--If the interest on £10 is 15s., what is the interest on £20?