Subtraction, being an inverse operation, is more difficult than addition. The symbolism 32 15 17 may be taken to represent the answer to two questions (i) What number added to fifteen gives thirty-two? (ii) What will remain when fifteen is taken from thirty-two If the child is taught the former interpretation, subtraction will be to him complementary addition if he is taught the latter it will be subtraction in the obvious sense of the word. In Spite of good arguments on the other side, the latter should probably be preferred as representing a more vigorous and effective idea. The following method of dealing with carrying is recommended on the same ground of psychological efficiency. Five cannot be taken from two we borrow, therefore, one of the three tens represented by the 3, and take three from it to make the two up to five. The residue, seven, is set down in the units' place. We then take the one ten from the remaining two tens, and set it down in the tens' place. Division, another inverse process, again presents two meanings. The symbolism 20 4 5 may be regarded as stating either (i) that the number of fours in twenty is five, or (ii) that one quarter of twenty is five. The former interpretation should alone be used for some time after the formal introduction of the process. Divi sion should not be studied at all until the child has considerable familiarity with addition, multiplication, and subtraction.