two _are_ four?"--"Thrice one _is_ or _are_,
three?"--"Three times one _is_, or _are_, three?"--"Three times naught
_is_, or _are_, naught?"--"Thrice three _is_, or _are_, nine?"--"Three
times four _is_, or _are_, twelve?"--"Seven times three _make_, or _makes_,
twenty-one?"--"Three times his age _do_ not, or _does_ not, equal
mine?"--"Three times the quantity _is_ not, or _are_ not,
sufficient?"--"Three quarters of the men were discharged; and three
quarters of the money _was_, or _were_, sent back?"--"As 2 _is_ to 4, so
_is_ 6 to 12;" or, "As two _are_ to four, so _are_ six to twelve?"

OBS. 15.--Most of the foregoing expressions, though all are perhaps
intelligible enough in common practice, are, in some respect, difficult of
analysis, or grammatical resolution. I think it possible, however, to frame
an argument of some plausibility in favour of every one of them. Yet it is
hardly to be supposed, that any _teacher_ will judge them all to be alike
justifiable, or feel no interest in the questions which have been raised
about them. That the language of arithmetic is often defective or
questionable in respect to grammar, may be seen not only in many an ill
choice between the foregoing variant and contrasted modes of expression,
but in sundry other examples, of a somewhat similar character, for which it
may be less easy to find advocates and published arguments. What critic
will not judge the following phraseology to be faulty? "4 times two units
_is_ 8 units, and 4 times 5 tens _is_ twenty tens."--_Chase's Common School
Arithmetic_, 1848, p. 42. Or this? "1 time 1 is l. 2 times 1 are 2; 1 time
4 is 4, 2 times 4 are 8."--_Ray's Arithmetic_, 1853. Or this? "8 and 7 _is_
15, 9's out leaves 6; 3 and 8 _is_ 11, 9's out leaves 2."--_Babcock's
Practical Arithmetic_, 1829, p. 22. Or this again? "3 times 3 _is_ 9, and 2
we had to carry _is_ 11."--_Ib._, p. 20.

OBS. 16.--There are several different opinions as to what constitutes the
grammatical subject of the verb in any ordinary English expression of
multiplication. Besides this, we have some variety in the phraseology which
precedes the verb; so that it is by no means certain, either that the
multiplying terms are always of the same part of speech, or that the true
nominative to the verb is not essentially different in different examples.
Some absurdly teach, that an abstract number is necessarily expressed by
"_a singular noun_," with only a singular meaning; that such a numb