These numbers are not, it is true, the same as those given at the beginning of this article, but their difference is the same, by (40). With the last-mentioned numbers proceed in the same way as in (42), which will give, as their difference, 2 ten-thous. 1 thous. 6 hund. 4 tens, and 6 units, which is 21646. 44. From this we deduce the following rules for subtraction: I. Write the number which is _to be subtracted_ (which is, of course, the lesser of the two, and is called the _subtrahend_) under the other, so that its units shall fall under the units of the other, and so on. II. Subtract each figure of the lower line from the one above it, if that can be done. Where that cannot be done, add ten to the upper figure, and then subtract the lower figure; but recollect in this case always to increase the next figure in the lower line by 1, before you begin to subtract it from the upper one. 45. If there should not be as many figures in the lower line as in the upper one, proceed as if there were as many ciphers at the beginning of the lower line as will make the number of figures equal. You do not alter a number by placing ciphers at the beginning of it. For example, 00818 is the same number as 818, for it means 0 ten-thous. 0 thous. 8 hunds. 1 ten and 8 units; the first two signs are nothing, and the rest is 8 hundreds, 1 ten, and 8 units, or 818. The second does not differ from the first, except in its being said that there are no thousands and no tens of thousands in the number, which may be known without their being mentioned at all. You may ask, perhaps, why this does not apply to a cipher placed in the middle of a number, or at the right of it, as, for example, in 28007 and 39700? But you must recollect, that if it were not for the two ciphers in the first, the 8 would be taken for 8 tens, instead of 8 thousands; and if it were not for the ciphers in the second, the 7 would be taken for 7 units, instead of 7 hundreds. 46. EXAMPLE. What is the difference between 3708291640030174 and 30813649276188 ---------------- Difference 3677477990753986 EXERCISES. I. What is 18337 + 149263200 - 6472902?--_Answer_ 142808635. What is 1000 - 464 + 3279 - 646?--_Ans._ 3169. II. Subtract 64 + 76 + 144 - 18 from 33 - 2 + 100037.--_Ans._ 99802. III. What shorter rule might be made for subtraction when all the figures in the upper line are ciphers except the first? for example, in finding 10000000 - 2731634. IV. Find 18362 + 2469 and 18362-2469, add the second result to the first, and then subtract 18362; subtract the second from the first, and then subtract 2469.--_Answer_ 18362 and 2469.