nfused ("Yes, sir"), or you omit
something in your work, and consequently it is incorrect.

(c.) If nines occur, you sometimes add ten, and then take off one, for
it is very easy to add ten.

(d.) Another method of calculating, which is, however, not very common,
is this: to take our old case, adding eight to seven, you take as much
from the eight to add to the seven as will be sufficient to make ten,
and then it will be easy to add the rest. Thus you think in a minute
that three from the eight will make the seven a ten, and then there will
be five more to add, which will make fifteen. If the next number was
seven, you would say five of it will make twenty, and then there will be
two left, which will make twenty-two.' This mode, though it may seem
more intricate than any of the others, is, in fact, more rapid than any
of them, when one is a little accustomed to it.

"These are the four principal modes of calculating which occur to me.
Pupils do not generally practice any of them exclusively, but
occasionally resort to each, according to the circumstances of the
particular case."

The teacher here stopped to inquire how many of the class were
accustomed to add by calculating in either of these ways or in any
simpler ways.

3. "There is one more mode which I shall describe: it is by _memory_.
Before I explain this mode, I wish to ask you some questions, which I
should like to have you answer as quick as you can.

"How much is four times five? Four _and_ five?

"How much is seven times nine? Seven _and_ nine?

"Eight times six? Eight _and_ six?

"Nine times seven? Nine _and_ seven?"

After asking a few questions of this kind, it was perceived that the
pupils could tell much more readily what was the result when the
numbers were to be multiplied than when they were to be added.

"The reason is," said the teacher, "because you committed the
multiplication table to memory, and have not committed the addition
table. Now many persons have committed the addition table, so that it is
perfectly familiar to them, and when they see any two numbers, the
amount which is produced when they are added together comes to mind in
an instant. Adding in this way is the last of the three modes I was to
describe.

"Now of these three methods the last is undoubtedly the best. If you
once commit the addition table thoroughly, you have it fixed for life;
whereas if you do not, you have to make the calculation over again every
time,