t Write down in figures, at length, the following sums: Eleven, twenty-nine, forty-one, sixty-eight, ninety. One hundred and one, one hundred and ninety-two, four hundred and sixty-five, nine hundred and ninety-nine. One thousand two hundred and four, six thousand seven hundred and twenty-nine, nineteen thousand seven hundred and ninety-two, four hundred and twenty-seven thousand two hundred and ninety-six, nine hundred and forty-two thousand seven hundred. Two millions six hundred and forty-two thousand two hundred and forty-nine, one hundred and ninety-seven millions three hundred and forty-two thousand six hundred and ninety-two. Write down in words, at length, the following: 7, 14, 20, 29, 38, 56, 89, 102, 169, 374, 4762, 19872, 87634, 765432, 9876543, 98765432, 987654321. SIMPLE ADDITION Is the adding of two or more numbers together, (of the same denomination.) to make them one total sum, or number. Some authors affirm, that there are two sorts of Addition, Subtraction, Multiplication and Division, simple and compound; but I am not of that opinion. As, for instance, compound is a mixture of many particulars, of divers denominations, how can 24 dollars be added to 6 pounds of iron ? or how can 20 yards of cloth be taken from 100 pounds of sugar? In Addition, you must place your figures in such a manner, that units will stand under units, tens under tens, hundreds under hundreds, &c. Begin at the units on the lowest line, and add upwards each column, carrying the number of tens contained in each column to the next, putting down the remainder; and the sum of the last, or left-hand column, you will put down in full. RULES for proving Addition. After you add up all, begin at the top, and add downwards; and if that sum and the former agrees, you are right in the work. I prefer the following method; to cast the 9's out of each line, and put the excess in the upper fork of a cross, and cast the 9's out of the sum total, and put the excess in the under fork of the same cross; and if they be alike, the question is right. 753274 In casting out the 9's, begin at 8 on the bottom 597487 row, or units' place of that row, and say, 8 and 5 875675 is 13, that is, 4 above 9, which 4 you carry to 7, 516358 (in the same row, or right-hand line of figures,) making 11, that is, 2 above 9, which 2 you carry 2742794 to 4, which make 6; then carry that 6 to the next top or bottom figure of the next left-hand line, or row of figures, and proceed throughout. Thus, 6 and 7 is 13, that is, 4 above 9; that 4 and 8 make 12, that is, 3 above 9; that 3 and 7 is 10, that is, 1 above 9; that 1 and 5 is 6, and 3, (the first figure in the next row,) is 9, that is, 0, or nothing; then 6 and 4 is 10, that is, 1 above 9; that 1 and 2 is 3, and 3 in the next left-hand row is 6, and 7 is 13, that is, 4 above 9, that 0 or nothing; then 6 and 1 in the next left-hand row is 7, and 7 is 14, that is, 5 above 9; then that 5, and the 5 above the 9, (you must not count 9's in a row of figures, when proving by the cross,) is 10, that is, 1 above 9; that 1 and the next 7 in the left-hand row is 8, and 5 is 13, that is, 4 above 9; that 4 and 8 is 12, that is, 3 above 9; that S and 5 is 8. This 8 is set in the upper part of the cross, thus: RULE. Place the numbers, according to their respective value, under each other, dollars under dollars, dimes under dimes. cents under cents, and mills under mills, and proceed exactly as in whole numbers; then place the separatrix in the sum total, directly under the separatrix points above. NOTE. As accounts are kept throughout the United States in dollars and cents, and parts of a cent, instead of mills, I will give examples here in that way, for the scholar to practise. I always teach scholars under my tuition, to add and subtract the fractional parts of cents, with very little trouble. The American youths certainly can be taught the fractional parts of a cent, as easy as the English, Irish and Scotch, are taught the fractional parts of a penny. RULE. If halves and quarters are required to be added, call a half 2, as two quarters are equal to a half of any number; and the quarters will always read one-fourth, thus, 4, and three-quarters thus, . Therefore, in adding halves and quarters, count the figure over the 4 for so many quarters, and the 2's in the halves for so many quarters; then |