We write the numbers as before, and draw a line beneath them. We then add the units to the units, and the tens to the tens. 24 62 86 14. A farmer has 160 sheep, 20 cows, and 16 head of young cattle: How many has he in all? We write the numbers so that units shall stand under units, tens under tens, and hundreds under hundreds. By adding, we find the sum of the units to be 6, the sum of the tens 9, and the sum of the hundreds 1 and the entire sum 196. Add together the following numbers: 160 20 16 196 15. A farmer bought 25 cows, 4 horses, 70 hogs, and 200 sheep: How many did he buy in all? Ans. 16. What is the sum of 5 units, 6 tens, and 7 hundreds ? We set down the 5 units in the place of units, the 6 tens in the place of tens, and the hundreds in the place of hundreds. We then add them up, and find the sum to be 765. We must observe in all cases, that units fall under units, tens under tens, &c. hundreds. units. 6 7 765 17. What is the sum of 3 units, 8 tens, and 4 thousands? Ans. 4083. 18. What is the sum of 8 hundreds, 4 tens, 6 units, and 6 thousands? Ans. 6846. 19. What is the sum of 3 units, 5 units, 6 tens, 3 tens, 4 hundreds, 3 hundreds, 5 thousands, and 4 thousands? Ans. 9798. 20. If a top costs 6 cents, a knife 25 cents, a slate pencil 1 cent, and a slate 12 cents, what does the whole amount to? Ans. 44 cts. 21. John gives 30 cents for a bunch of quills, 18 cents for an inkstand, 25 cents for a quire of paper: what did they all cost him? Ans. 73 cts. Thus far, the amount of any one column, when added up, has not exceeded 9; and therefore its sum could be expressed by a single figure. But the sum of a single column will often exceed 9, and we will now show what is to be done in that case. 22. Add together the numbers 894 and 637. In this example, the sum of the units is 11, which cannot be expressed by a single figure. But 11 units are equal to 1 ten and 1 unit; therefore, we set down 1 in the place of units, and 1 in the place of tens. The sum of the tens is 12. But 12 tens are equal to 1 hundred, and 2 tens; so that 1 is set down in the hundred's place, and 2 in the ten's place. The sum of the hundreds is 14. The 14 hundreds are equal to 1 thousand, and 4 hundreds; so that 4 is set down in the place of hundreds, and 1 in the place of thousands. The sum of these numbers, 1531, is the sum sought. OPERATION. The example may be done in another way, thus: Having set down the numbers, as before, we say, 7 and 4 are 11: we set down 1 in the units place, and write the 1 ten under the 3 in the column of tens. We then say, 1 to 3 is four, and 9 are 13. We set down 894 637 11 1531 We the three in the tens place, and write the 1 hundred under the 6 in the column of hundreds. then add the 1, 6, and 8 together, for the hundreds, and find the entire sum 1531, as before. When the sum in any one of the columns exceeds 10, or an exact number of tens, the excess must be written down, and a number equal to the number of tens, added to the next left hand column. This is called carrying to the next column. The number to be carried may be written under the column or remembered and added in the mind. From these illustrations we deduce the following general RULE. § 14. I. Set down the numbers to be added, units under units, tens under tens, hundreds under hundreds, &c., and draw a line beneath them. II. Begin at the foot of the unit's column, and add up the figures of that column. If the sum can be expressed by a single figure, write it beneath the line, in the unil's place. But if it cannot, see how many tens and how many units it contains. Write down the units in the unit's place, and carry as many to the bottom figure of the second column as there were tens in the sum. Add up that column: set down the sum and carry to the third column as before. III. Add each column in the same way, and set down the entire sum of the last column. Q. How do you set down the numbers for addition? Where do you begin to add? If the sum of the first column can be expressed by a single figure, what do you do with it? When it cannot what do you write down? What do you then add to the next column? When you add the tens to the next column, what is it called? What do you set down when you come to the last column? EXAMPLES. 1. What is the sum of the numbers 375, 6321 and 598. In this example, the small figure placed under the 4, shows how many are to be carried from the first column to the second, and the small figure under the 9, how many are to be carried from the second column to the third. OPERATION. 375 6321 598 7294 11 In like manner, in the examples below, the small figure under each column, shows how many are to be carried to the next column at the left. Beginners had better set down the numbers to be carried as in the examples. § 15. Begin at the right hand figure of the upper line, and add all the columns downwards, carrying from one column to the other, as before. If the two results agree the work is supposed right. SECOND PROOF. Draw a line under the upper number. Add the lower numbers together, and then add their sum to the upper number. If the last sum is the same as the sum total, first found, the work may be regarded as right. Q. What do the small figures under the columns denote? How do you prove addition by the first method? How do you prove addition by the second method? 7. Add 8635, 2194, 7421, 5063, 2196, and 1245 to gether. Ans. 8. Add 246034, 298765, 47321, 58653, 64218, 5376, 9821, and 340 together. Ans. 730528. 9. Add 27104, 32547, 10758, 6256, 704321, 730491, 2787316, and 2749104 together. Ans. 10. Add 1, 37, 29504, 6790312, 18757421, and 265 together. Ans. 25577540. 11. Add 562163, 21964, 56321, 18536, 4340, 279, and 83 together. Ans. 12. What is the sum of the following numbers: viz., Seventy-five; one thousand and ninety-five; six thousand four hundred and thirty-five; two hundred and sixty-seven thousand; one thousand four hundred and fifty-five; enty seven millions and eighteen; two hundred and Fenty millions and twenty-seven thousand. Ans. 297303078. |