Ans.

15. A farmer bought 25 cows, 4 horses, 70 hogs, and 200 sheep: how many did he buy in all? 16. Add 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 that in all cases, units of the same order fall under each other.

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?

20. What is the sum of five units of the 4th order, one of the 3d, 3 of the 4th, five of the 3d, and one of the 1st?

21. What is the sum of six units of the 2d order, five of the third, six of the 4th, three of the 2d, four of the 3d, two of the 1st, and four of the 2d?

22. 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. 23. 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.

In this example, the sum of the units of the first order is 11. 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 units of the second order is 12. But 12 tens are equal to 1 hundred, and 2. tens; so that 1 is set down in the hundreds' place, and 2 in the tens' place. The sum of the units of the third order 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, viz. 1531, is the sum sought.

OPERATION.

894

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 the 3 in the tens' place, and write

637

11

1531

the 1 hundred under the 6 in the column of hundreds. We 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 cannot be expressed by a single figure, write down the excess over exact tens, and then add to the next left hand column as many units of its own order as there were tens in the sum. 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.

14. Hence, for the addition of simple numbers, we have the following

RULE.

I. Write down the numbers to be added, so that units of the same order shall fall directly under each other, and draw a line beneath them.

II. Beginning at the foot of the units' column, add up each column in succession, and write the sum under the column when it can be expressed by a single figure.

III. When the sum in any column cannot be expressed by a single figure, write down the excess over exact tens, and then add to the next left hand column as many units of its own order as there are tens in the sum; observing to set down the entire sum of the last column.

EXAMPLES.

1. What is the sum of the numbers 375, 6321 and 598 ?

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

Also, in the examples below, the small figure under each column, shows how many are to be carried to the next column to the left. Beginners should set down the numbers to be carried as in the examples.

(2.) 96972

(3.) 9841672

(4.)

81325

14. How do you set down the numbers for addition? Where do you begin to add? If the sum of any 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 to the next column, what is it called? What do you set down when you come to the last column?

PROOF OF ADDITION.

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.

15. How do you prove addition by the first method? How de

you prove addition by the second method?

7. Add 8635, 2194, 7421, 5063, 2196, and 1245 together. Ans. 26754. 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. 7047897. 10. Add 1, 37, 39504, 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 sixtyseven thousand; one thousand four hundred and fiftyfive; twenty-seven millions and eighteen; two hundred and seventy millions and twenty-seven thousand ?

Ans. 297303078.

13. Add together fifty-eight billions, nine hundred and eighty-two millions, four hundred and eighty-seven thousand, six hundred and fifty-four; seven hundred and forty billions, three hundred and fifty millions, five hundred and forty thousand, seven hundred and sixty; four hundred and twenty-five billions, seven hundred and three millions, four hundred and two thousand six hundred and three; thirty-four billions, twenty millions, forty thousand and twenty; five hundred and sixty billions, eight hundred millions, seven hundred thousand and five hundred.

APPLICATIONS.

1. How many days are there in the twelve calendar months? January has 31, February 28, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, and December 31. Ans. 365 days.

2. What is the total weight of seven casks of merchandise; viz. No. 1, weighing 960 pounds, No. 2, 725 pounds, No. 3, 830 pounds, No. 4, 798 pounds, No. 5, 698 pounds, No. 6, 569 pounds, No. 7, 987 pounds? Ans, 5567 pounds.