Now, here is where you forget something. When you started out to “borrow” you had to go away over to the 2 in the fifth column; that made your 0 in the fourth column a 10, but you immediately passed this one on to the third column, which left only 9; again you passed it on from the third to the second column, which left only a 9 in the third column. Hence you have now a 9 in the third and in the fourth columns, and your results there will be in each case 9 from 9 leaves 0. Coming to the fifth you have a 1 instead of a 2, having borrowed 1; and you have to borrow again from the 3 to make your 1 into an 11, obtaining 9 from 11 leaves 2; and your sixth and last figure, being reduced from 3 to 2, your last result is 1 from 2 leaves 1. This last part is easy, but one out of practice is almost certain to forget that his 0’s in the third and fourth columns became 9’s. If you have any difficulty with subtraction, study out the processes in this example until you understand them and you will never make a mistake again. Now, as to the shape in which the examples will be given: The plain problems in addition will be unmistakable. You will be told that a concern sold 27,356 barrels of flour in one month, 38,452 the next, etc., and you cannot well run off the track. But you may find both processes involved in one “problem,” and you must then be careful to understand just what is meant by the question, so that you will know what you are expected to do with the figures. Take this, for example: “A had $3,465 and B $4,895. A gained $1,146 and B lost $602. Which then had the more, and how much?” Here you must add A’s gain to his principal--that is, the sum he had to start with--and subtract B’s loss from his principal; then subtract the smaller result from the larger, stating which is the “winner.” Thus: $3,465 $4,895 $4,611 1,146 602 4,293 ------ ------ ------ $4,611 $4,293 $318 Answer.--A has $318 more. When it comes to multiplication and division, there is just one “catch,” so it might appear to the untrained mind of some poor candidate, which is made to play a part in nearly every problem. It is safe to say that 90 per cent. of the failures on these two processes turn on this one point. It is a very simple one and really the same in both processes. It arises in the handling of the “naught” or “cipher,” as we used to call it, the “zero”--call it what you like, it is nothing, anyhow. And that’s the point to be remembered. Here is an example: Multiply 3,125 by 208. Now it seems almost incredible, but I have seen literally hundreds of papers, it seems to me, where this very simple problem was worked out this way: The Wrong Way. 3,125 208 ------ 25000 3125 6250 ------ 681250 Or else this: Another Wrong Way. 3125 208 ----- 25000 6250 ----- 87500