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that units may stand under units, tens under tens, hundreds under hundreds, and so on for the higher orders.

II. Commencing at the right, find the sum of the numbers in the column of units; if this sum is less than ten, place it immediately under the unit column; but if it equals or exceeds ten, see how many tens it contains, and how many units over ; write down the units under the units' column, and carry the tens to the next, or tens' column. In this way proceed with each column, observing to carry for every ten contained in such column, one to the column of the next higher denomination. When we reach the last column, its whole amount must be set down.

How do you write the numbers for addition? Where do you commence to add ? If the sum is expressed by a single digit, how do you dispose of it? When it equals or exceeds ten, how do you proceed? What is the rule with regard to carrying? How do you proceed when you come to the last column ?

EXAMPLES.

(1.) 56430 12798 34457 21325

(2.) 7921341 82345768 79013265

7890275 177170649 amount.

125010 amount.

PROOF OF ADDITION.

11. The method of proving, or testing the work of addition, is generally to commence at the top of the respective columns and add downwards, carrying one for every ten as before ; if the sum is the same as when the columns were added upwards, the work is then supposed to be correct. This proof is not infallible, since mistakes

may occur in both operations, which shall balance each other.

How is the work of addition generally proved? Is this method of proof infallible 1 Why not?

(5.) 34567890 2357911 234567 24897

64

(6.) 43345678 21123355

27893 54689 734321

(7.) 123423434 23785432 9876543 751002 10200

37185329

65285936

157846611

8. Add 123405, 2354210, 794327, and 36547, together.

Ans. 3308489. 9. Add 275602, 345607, 4567801, and 365, together.

Ans. 5189375. 10. Add 100375, 406780, 4673005, 4112, and 2478, together.

Ans. 5186750. 11. Add 1034001, 78954, 379205, 367001, and 45637, together.

Ans. 1904798. 12. What is the sum of the following numbers: Three thousand six hundred and fifty, seven thousand eight hundred and thirty-two, eleven thousand five hundred and sixty-seven, ten thousand and fifty-six, four hundred and seventy-two?

Ans. 33577. 13. What is the sum of the numbers, four thousand three hundred and seventy-three, three thousand one hundred and fourteen, one thousand two hundred and twentythree, six hundred and fifty-four?

Ans. 9364,

14. Find the number of days in a year, the days of the respective months being as follows: January,31, February, 28, March, 31, April, 30, May, 31, June, 30, July, 31, August, 31, September 30, October, 31, November, 30, December, 31.

Ans. 365 days. 15. A man drew five loads of bricks; in the first load he had 1209, in the second load 1453, in the third load 1101, in the fourth load 1212, and in the fifth load 1303. How many bricks were there in all ?

Ans. 6278 bricks. 16. If there are shipped from the United States, 15624 barrels of flour to Sweden, 250 barrels to Holland, 205154 barrels to England, 6401 to Texas, 19602 to Mexico, what is the whole amount ?

Ans. 247031 barrels. 17. In 1837 the United States exported 100232 hogsheads of tobacco; in 1838 they exported 100592; in 1839 they exported 78995; in 1840 they exported 119484; in 1841 they exported 147828. How many hogsheads of tobacco were exported during these five years?

Ans. 547131 hogsheads. 18. If the cotton crop of the United States is estimated at 1360532 bales for the year 1839, 2177835 bales for the year 1840, 1634945 bales for the year 1841, and 1683574 bales for the year 1842, how many bales will the four years' crops amount to? Ans. 6856886 bales.

19. In 1839 the Onondaga Springs produced 2864718 bushels of salt; in 1840 they produced 2622305 bushels ;. in 1841 they produced 3340769 bushels; in 1842 they produced 2291903 bushels. What is the whole number of bushels during the above four years ?

Ans. 11119695 bushels.

20. The United States exported in bullion and specie, in 1838, 3508046 dollars; in 1839, 8776743 dollars ; in 1840, 8417014 dollars ; in 1841, 10034332 dollars. How much was exported during these four years ?

Ans. 30736135 dollars. 21. Amount of tea consumed in the United States, during 1842, was 13482645 pounds; during 1843, it was 12785748 pounds; in 1844, it was 13054327 pounds; in 1845, it was 17162550 pounds; and in 1846 it was 16891020 pounds. What was the whole number of pounds during these five years ?

Ans. 73376290 pounds. 22. The amount of coffee consumed in the United States, during the year 1842, was 107383567 pounds; in 1843, it was 85916666 pounds; in 1844, it was 149711820 pounds; in 1845, it was 94358939 pounds, and in 1846 it was 124336054 pounds. What was the whole number of pounds during these five years ?

Ans. 561707046 pounds. 23. The number of acres of public land sold by the United States government, in the year 1841, was 1164796 acres; in the year 1842, it was 1129217 acres; in 1843, it was 1605264 acres; in 1844, it was 1754763 acres; and in 1845 it was 1843527 acres. What was the whole number of acres sold during these five years ?

Ans. 7497567 acres. 24. The United States revenue for letter postage, under the new law, was as follows: for the year 1842, it was 3953315 dollars; for 1843, it was 3738307 dollars; for 1844, it was 3676162 dollars; and for 1845 it was 3660231 dollars. What was the whole number of dollars during these four years ? Ans. 15028015 dollars.

25. In 1843, the amount of gold coined at the United States mint and branches, was as follows : At Philadelphia, 4062010 dollars; at the branch at New Orleans, 3177000 dollars; at the branch at Dahlonega, 582782 dollars; at the branch at Charlotte, 287005 dollars. How many dollars of gold coined in all ?

Ans. 8108797 dollars. The sum of the numbers in each row of the following table, whether taken vertically or horizontally, or from corner to corner, is 24156. Let the pupil be required to make these 24 distinct additions. *

TABLE

2016 4212 1656 3852 1296 3492 936 3132 576 2772 216
252 20524248 1692 3888 1332 3528 9723168 612 2412

2448 288 2088 4284 1728 3924 1368 3564 1008 2808 648

684 2484 324 2124 4320 1764 3960 1404 3204 1044 2844

2880 720 2520 360 2160 4356 1800 3600 1440 3240 1080

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3744 1584 3384 828 3024 468 2664 108 2304 4104 1944

1980 3780 1224 3420 864 3060 5042700 144 2340 4140
41761620 3816 1260 3456 900 3096 540 2736 180 2376

* This table is formed by multiplying the numbers in the magic square of 11, by 36.

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