To prove Subtraction. Cast the 9's out of the minuend ; then cast them out of the subtrahend and remainder together, and if the same result is obtained in both cases, the operation may be regarded as accurate.
Example. 59876 34959 24917 In casting out the 9's of the upper row, I find the remainder 8 ; the same is found in casting out the 9's of the two lower lines.
To prove Multiplication. Cast the 9's out of the multiplicand, and put the re mainder on one side of a cross, then do the same with the multiplier, and put the remainder on the other side of the cross; multiply these remainders together, and cast the 9's out of the product ; the re mainder place at the top of the cross; cast the 9's out of the product, and the remainder place at the bottom of the cross, which, if the operation be correct, will be the same as that at the top.
Example. 5943 26 25658/ ' 11886 3 8 154518 / 6 To prove Division. Cast the 9's out of the divisor, and also out of the quotient, the remainder of the former place on the side of the cross; that of the latter on the other ; multiply them together, and take in the remainder, if any ; cast out the 9's, and the remainder put at the top of the cross ; this, if the operation be correct, will agree with the remainder of the di vidend obtained from the dividend after the 9's are cast out.
Er. 264)87655(332 792 . 845 3/41/* 792 .535 / 528 7 This method of proving sums lies u.n fler disadvantages. 1. If an error of 9, or any of its multiples, be committed, the results will nevertheless agree, and so the error will remain undiscovered. This will be the case, when a figure is placed or reckoned in a wrong column, which is a frequent cause of mistake. 2. When it is known that an error has been committed, it is not pointed out where the error lies, and of course not easily corrected.
Having given a full account of the fun damental rules of Arithmetic, we shall re fer our readers to the several articles in alphabetical order, for rules depending on the four already treated on. See AL LOCATION, ANNUITIES, EXCHANGE, INTE REST, &C. &c.