The trouble is that when the poor fellow came to multiply by the “naught” he forgot in the first instance that it was nothing, and that the biggest number in the world multiplied by nothing will produce nothing. He knew that something ought to go down there, and so in sheer desperation he wrote down the number he was multiplying. In the second instance, while he recognized that nothing is nothing, he forgot that all our figuring is done by columns, as we saw in our last lesson; so that when we are multiplying by tens we must put our first figure down in the hundreds column, and so on. By forgetting this he multiplied his number by two hundreds, but put his first figure down in the tens columns, and thus he really multiplied by only 28 instead of 208. Now, the very simplest way to avoid this sort of mistake is to “go through the motions” of multiplying by the “naught” or “zero.” Thus: The Right Way. 3,125 208 ------ 25000 0000 6250 ------- 650,000 This looks a little clumsy, perhaps, but it is the logical way--to go through the process of saying naught times 5 is naught, naught times 2 is naught, etc., putting down the results in the proper columns. It is the safest way, if you are the least bit weak on the principles of numbers, to do even the process of multiplying by whole hundreds. Thus: 3,125 200 ------ 0000 0000 6250 ------- 625,000 By writing his example in the “short cut” style I have seen many a man make this mistake: Wrong. 3,125 200 ----- 62500 That is, after setting down his two surplus ciphers, when he obtained another in multiplying 5 by 2, he forgot that it was a new one and went right on to the next process. If you are in that position that you must really learn your arithmetic all over again, stick to the logical method of showing every process and learn the “short cuts” afterward. Now, when the reverse situation arises in division, a similar error is of frequent occurrence. Suppose we are to divide 650,000 by 3,125. This sometimes results: The Wrong Way. 3,125)650,000(28 625 0 ----- 25,000 25,000 That is, the figurer, when he came to try to divide 2,500 by 3,125, realizing that it would not “go,” simply “brought down” another figure. He forgot that the real mental process was 3,125 goes into 2,500 no times, or produces “naught,” and that “naught,” or “cipher,” must be set down in the proper tens column. The only safe way, again, is to indicate every process; to “bring down” but one figure at a time and to set down every result, even the “nothings,” in its proper place. That will make our example look like this: