ADDITION. ADDITION is the next step, which is the art of collecting many given numbers into one, and of expressing the amount correctly. It is either simple or compound; simple when it relates only to figures, and compound when those figures have a reference to value, measure, &c. Thus in simple addition the following examples will serve as specimens. In casting up these sums begin with the column of units on the right. Thus, in No. 1, say 7 and 9 are 16, and 7 are 25, and 3 are 26;-then as there are 6 units and two tens over, place the 6 under the column of units, and carry 2 to that of the tens, and proceed thus; 2 and 4 are 6, and 3 are 9, and 5 are 14, and 4 are 18, and 1 are 19; which being the whole, place the 9 under the column of tens, it being 9 tens; and the 1 being 100 place next to it on the left. Thus the whole will be, one hundred and ninety-six. This general rule will serve for all the others, carrying all the Lens in one column to the other throughout the whole. COMPOUND ADDITION. BEFORE the learner proceeds in this part of Arithmetic, as it will be to money accounts chiefly to which she will wish to direct her attention, it is absolutely necessary to Jearn perfectly, the following Tables.-Note, a farthing, being one fourth of a penny, is written thus, ; a halfpenny thus, ; three farthings thus, 4. 4 Farthings make 12 Pence 20 Shillings One Penny. Note, the Column with an £. signifies Pounds, s. Shil-' lings, and d. Pence. 2 £1 4 6 £14 1 1 £1208 4 1 Thus, in the first example, begin with the farthings, and say:-1 and 3 are 4, and 2 are 6, and 1 are 7; which being 1 penny and 3 farthings write underneath, and carry 1 to the pence: then 1 and 6 are 7, and 5 are 12, and 7 are 19, and 3 are 22, and 4 are 26; then 26 pence being 2 shillings and twopence over, place 2 under the column of pence and 2 under that of shillings; the whole sum making, two shillings and twopence three farthings. In order to prove any sum in addition, cast it up again the reverse way, namely, from the top to the bottom. The other examples must be performed in the same manner, taking care to carry one pound for every 20 shillings; and one for every 10 in the pounds, as in simple addition. Compound Addition also includes Weights and Measures, but it is thought proper not to perplex the learner with them in this early stage of her progress, though correct tables will be given of them in the course of the work, which may be referred to as occasion may require. It is necessary however to observe here, that all sums in weights and measures are cast up in the same way as pounds, shillings, and pence; with this difference only, the proper number must be carried to each line, for example, as From the minutes every 60 is carried as 1 to the hours, and the remainder set down; from the next every 24; and from the last every 7: so that the above sum is 2 weeks, 1 day, 19 hours, and 23 minutes. SUBTRACTION. THIS rule teaches the art of taking one number from another in order to find what remains. In the example, No. 1, say, 7 from 6 I cannot, but 7 from 16 (for you must always borrow 10, in simple numbers, in such cases) and there remains 9, which you set down. Then say, I that I borrowed and 6 are 7; 7 from 7 and there remains 0; 3 from 8 and there remains 5; nothing from 9 and there remains 9. In order to prove it, work the two last sums by addition thus: 367 9509 9876 The other sums are worked and proved in the same manner, taking care, in compound numbers, to attend to the difference of the value of the figures. Thus, in No. 4, say 9 from 7 I cannot, but 9 from 19 (adding 12) and there remains 10: 1 that I borrowed and 12 are 13; 13 from 6 I cannot, but 13 from 26 (adding 20) and there remains 13: 1 that I borrowed and 5 are 6; 6 from 3 I cannot, but 6 from 13 (adding 10) and there remains 7: 1 that I borrowed and 2 are 3; 3 from 2 I cannot, but 3 from 12, and there remains 9: 1 that I borrowed from 4, and there remains S. Prove it as before by addition, thus: £. s. d. 25 12 9 997 13 10 £423 6 7 MULTIPLICATION. THIS, for general purposes, is the most useful rule in Arithmetic; and therefore particular attention should be paid to the following Table, which must be learned completely by heart before any thing can be done by the pupil to advantage. In order to understand this table the learner must multiply each figure of the first column by those of the upper row, looking for the product in that square which is in a line with the one, and underneath the other. Thus if the pupil wants to find the value of 6, multiplied by 5, by looking on the line where the 5 is placed in the first column, under the 6 in the top line, the product will be found to be 30. The way therefore to learn this table, which must be |