ADDITION of SIMPLE QUANTITIES. ADdition of fimple quantities teacheth to collect feveral numbers, of the fame denomination, into one number called the fum. R U L E. Write the numbers to be added underneath each other, their units being in one column, their tens in another, their hundreds in a third, and fo on. Draw a line under them all, and then add up each column feparately, beginning with the column of units; obferving, for every ten in the fum of any column, to add one to the fum of the next, fetting down only the excess above the tens under each column; but for the last column write down the whole fum. P R O O F. Begin at the top of the queftion, and reckon the figures downwards, in the fame manner as you added them upwards, and if the fum be the fame as that before found, the work is supposed to be right. Or rather thus. Add the figures in the uppermost row together, and find how many nines are contained in their fum. Then, reject the nines, and fet down the remainder even with the figures in the row. Do in the fame manner with every other row in the question, and find the fum of thefe remainders, out of which fum you must also reject the nines. If this last remainder be equal to the excess of nines in the total fum, the queftion is fupposed to be right. OBSERVE. To the above ingenious method of proving addition of fimple quantities, there is one objection, and that is, it fometimes makes a wrong operation appear right; but it never makes a right operation appear wrong. A 3 TABLE The teacher will find it advantageous to make fome of EXAMPLE S. (1) 41010816 (2) 371214 (3) 714121 1210108 1381014 0. ΙΟΙΟΙΟ8 4032 + 3 200 7101012 3 Sum 26324654 5 Proof 26324654 Second methodof proof. 192108 101018 |