cents for apples, 1 cent for a pear, 2 cents for an orange, and 1 cent for a peach; how many cents did he give for all? EXPLANATIONS. Place the figures in an upright row or column, as before directed. Then begin at the bottom and add thus; 1 and 2 are three, and 1 are four, and 2 are six, and 1 are seven, and 2 are nine, and 1 are ten, and 2 are 12. You will find he paid twelve cents for all which he bought. 2 1 2 t 2 1 2 1 12 PROOF. To prove that your work is right, you may commence adding at the top, by saying, 2 and 1 are three, and 2 are five, and 1 are six, and 2 are eight, and 1 are nine, and 2 are eleven, and 1 are 12. Thus you will find, that the last amount is the same as the first; and, therefore, the work is right according to the method of proof; and it is perfectly evident, that it will make no difference whether you begin at the top or at the bottom of the column to add the figures. Another method of proving Addition is, to cross off the upper line and add the remaining lines; and if this last amount added to the upper line be equal to the first amount, the work is right, as the sum of the parts must be equal to the whole. 2. George bought an apple for 2 cents, a peach for 2 cents, a pear for 2 cents, a marble for 2 cents, a top for 2 cents, and he paid 2 cents for chestnuts; how many cents did he pay for all that he bought? Ans. 12 3. A boy bought a penknife for 6 cents, a slate for 9 cents, a sheet of paper for 1 cent, a slate-pencil for 2 cents, and he paid 4 cents for quills; how many cents did he pay for all? Ans. 22 cents. 4. William paid 6 cents for one picture book, 4 cents for another, 5 cents for an orange, 9 cents for an inkstand, 8 cents for quills, 7 cents for writing paper, and 3 cents for ink; how many cents did he pay for all? Ans. 42 cents. 5. A man gave Richard 9 cents, William 7 cents, James 8 cents, John 6 cents, Rufus 4 cents, George 5 cents, Joseph 3 cents, Thomas 2 cents, and Peter 1 cent; how many did he give to all? Ans. 45 cents. 6. Rufus bought 8 oranges of an orange man, Lewis bought 5, Samuel bought 3, Daniel bought 6, Stephen bought 4, Reuben bought 7, and Levi bought 2; how many oranges did they all buy? Ans. 35 oranges. 7. A teacher had 5 scholars in one class, 7 in another class, 4 in another class, 6 in another class, and 8 in another class; how many scholars had he in his school? Ans. 30 scholars. 8. Eliza paid 8 cents for pins, 6 cents for needles, 9 cents for a yard of riband, 3 cents for a skein of silk, and 4 cents for a cotton ball; how many cents did she pay for all? Ans. 30 cents. 9. A man gave money to his children as follows: to George 6 dollars, to William 5 dollars, to Charles 4 dollars, to Jane 3 dollars, and to Mary 7 dollars; how many dollárs did he give in all? Ans. 25 dollars. 10. A man bought a hat for 5 dollars, a pair of boots for 4 dollars, and a watch for 9 dollars; how many dollars did he pay for the hat, boots, and watch? Ans. 18 dollars. Q. If the numbers or quantities to be added contain more than units, as, tens, hundreds, thousands, &c., how must the factors or sums be placed? A. Units directly under units, tens under tens, hundreds under hundreds, thousands under thousands, millions under millions, billions under billions, and so on. Q. If the factors or sums to be added make more than one column, where must you begin to add? A. At the place of units or right hand column. Q. Why do you begin to add at the right hand column? A. Because numbers increase from the right hand to the left. Q. If the amount in any one column is more than ten, what must you set down? A. All over tens must be set down under the column which is added. Q. What must you carry to the next column? Q. Why do you carry one for every ten to the next column? A. Because numbers increase in a tenfold proportion from the right hand to the left, and, consequently, ten in any one column are only equal to one in the next column at the left hand. EXAMPLES For Exercise on a Slate. 1. James paid 15 cents for a spelling-book, 25 cents for a slate, 31 cents for an arithmetick, 45 cents for a geography, and 75 cents for a dictionary; how much did he pay for all of them? EXPLANATIONS. Here, you perceive, are five sums to be added, 15 and you must observe that, in these five sums, 25 the first column of figures at the right hand 31 represents UNITS, and the other represents TENS. 45 Beginning at the right hand column you must 75 say, 5 and 5 are ten, and 1 make eleven, 5 make sixteen, and 5 make twenty-one units, that is, 191 two tens and one unit; so you must set down 1 under the column of units, and add, or carry, the 2 tens to the next column; thus, 2 and 7 are nine, 4 make thirteen, 3 make sixteen, 2 make eighteen, and 1 make nineteen tens; and this being the last column at the left hand, you must set down the whole number 19, which makes the whole amount 191 cents; that is, one dollar and ninety-one cents, as one hundred cents make a dollar. 2. Add 2831, 6405, 974, 8152, 5379. EXPLANATIONS. 2831 6405 974 8152 5379 This example is formed of larger sums, or factors, than the preceding one; that is, of UNITS, TENS, HUNDREDS, and THOUSANDS; and if you learn to add these sums understandingly, you will then be able to add any number of figures, however large, that may be placed before you. You will remember that the first thing to be done, in all cases, is to place the numbers to be added, units under units, tens under tens, hundreds under hundreds, thousands under thousands, and so on. You must begin, as before, with the column at the right hand, and say, 9 and 2 make eleven, 4 make fifteen, 5 make twenty, and 1 make twenty-one units, that is, two tens 23741 and 1 unit. You must set down the 1 in its proper place, that is, under the column of units, and add, or carry, the two tens to the next column, the place of tens. Thus, two tens added to the 7 in the second column make nine, 5 make fourteen, 7 make twentyone, (you need not mention the cipher in adding,) and 3 make twenty-four tens, that is, two hundreds and four tens. You must set down the 4, which is four tens, under the second column, the place of tens, and add, or carry, the two hundreds to the next column, the place of hundreds. Thus, two hundreds added to the 3, in the third column, make five, 1 make six, 9 make fifteen, 4 make nineteen, and 8 make twenty-seven; that is, two thousands and seven hundreds. You must set down the 7, which is seven hundreds, under the third column, the place of hundreds, and add, or carry, the two thousands |