1. Units of the same order are written in the same column; and when the sum in any column is 10 or more than 10, it produces one or more units of a higher order, which must be added to the next column. This process is sometimes called "carrying the tens."

2. In adding, learn to pronounce the partial results without naming the numbers separately; thus, instead of saying 7 and 5 are 12, and 5 are 17, simply pronounce the results, 7, 12, 17, etc.

From the preceding examples and illustrations we deduce the following rules:

RULE. - I. Write the numbers to be added so that the units of the same order stand in the same column; that is, units under units, tens under tens, etc.

II. Commencing with units, add each column separately, and write the sum underneath, if it is less than ten.

III. If the sum of any column is ten or more than ten, write the unit figure only, and add the ten or tens to the next column.

IV. Write the entire sum of the last column.

PROOF. -I. Begin with the right hand or unit column, and add the figures in each column in an opposite direction to that in which they were first added; if the two results agree, the work is probably correct. Or,

II. Separate the numbers added into two sets by a horizontal line; find the sum of each set separately; add these sums, and if the amount is the same as that first obtained, the work may be presumed to be correct.

42. By the methods of proof here given, the numbers are united in new combinations, which render it almost impossible for two precisely similar mistakes

to occur.

The first method is the one commonly used in business.

14. 37042 + 1379 + 809 + 127 + 40 = ? Ans. 39397. 15. What is the sum of one thousand six hundred fifty-six, eight hundred nine, three hundred ten, and ninety-four? Ans. 2869. 16. Add forty-two thousand two hundred twenty, thousand one hundred five, four thousand seventy five, and five hundred seven. Ans. 56907.

ten

17. Add two hundred ten thousand four hundred, one hundred thousand five hundred ten, ninety thousand six hundred eleven, forty-two hundred twenty-five, and eight hundred ten. Ans. 406556.

18. What is the sum of the following numbers: seventy-five, one thousand ninety-five, six thousand four hundred thirty-five, two hundred sixty-seven thousand, one thousand four hundred fifty-five, twenty-seven mil

lion eighteen, two hundred seventy million twenty-seven thousand? Ans. 297303078. 19. A man on a journey traveled 37 miles the first day, 33 miles the second, 40 miles the third, and 35 miles the fourth. How far did he travel in the four days?

20. A merchant has in one cask 75 gallons of oil, in another 65, in a third 57, in a fourth 83, in a fifth 74, and in a sixth 67. How many gallons has he in all?

Ans. 421.

21. An estate is to be shared equally by four heirs, and the portion given to each heir is to be $3754. What is the amount of the estate? Ans. $15016.

22. How many men are there in an army consisting of 52714 infantry, 5110 cavalry, 6250 dragoons, 3927 light-horse, 928 artillery, 250 sappers, and 406 miners?

23. A merchant deposited $ 56 in a bank on Monday, $74 on Tuesday, $120 on Wednesday, $96 on Thursday, $170 on Friday, and $ 50 on Saturday. How much did he deposit during the week?

24. A merchant bought at public sale 746 yards of broadcloth, 650 yards of muslin, 2100 yards of flannel, and 250 yards of silk. How many yards did he buy in all?

25. Five persons deposited money in the same bank; the first, $5897; the second, $12980; the third, $ 65973; the fourth, $37345; and the fifth as much as the first and second together. How many dollars did they all deposit? Ans. $141072.

26. A man willed his estate to his wife, two sons, and four daughters; to his daughters he gave $2630 apiece, to his sons, each $4647, and to his wife $3595. was the value of his estate?

What Ans. $23409.

27. A man commenced farming in the west, and raised, the first year, 724 bushels of corn; the second

year, 3498 bushels; the third year, 9872 bushels; the fourth year, 9964 bushels; and the fifth year, 11078 How many bushels did he raise in the five

bushels.

33. A has $3648, B has $7035, C has $429 more than A and B together, and D has as many dollars as all

the rest. How many dollars has D? they all?

Ans. D has $21795.

How many have All have $43590.

34. A man bought three houses and lots for $15780, and sold them so as to gain $695 on each lot. For how much did he sell them? Ans. $17865.

35. At the battle of Waterloo, which took place June 18, 1815, the estimated loss of the French was 40000 men; of the Prussians, 38000; of the Belgians, 8000; of the Hanoverians, 3500; and of the English, 12000. What was the entire loss of life in this battle?

36. The expenditures for certain purposes in New England for a certain year were as follows: Maine, $380623; New Hampshire, $221146; Vermont, $246604; Massachusetts, $1424873; Rhode Island, $136729; and Connecticut, $430826. What was the total expenditure?

Ans. $2840801.

37. The eastern continent contains 35413799 square miles; the western continent, 16237535; Australia, Polynesia, and other islands, 3709781. What is the entire area of the land surface of the globe?

38. The population of New York in 1890 was 1515301; of Boston, 448447; of Philadelphia, 1046964; of Chicago, 1099850; of St. Louis, 451770; of New Orleans, 242039. What was the entire population of these cities?

39. The population of the globe is estimated as follows: North America, 88005695; South America, 33565882; Europe, 360580788; Asia, 823155251; Africa, 168497091; Australia and Polynesia, 5683968. What is the total population of the globe according to this estimate?

Ans. 1479488675.

40. The railroad distance from New York to Albany is 143 miles; from Albany to Buffalo, 297; from Buffalo to Cleveland, 183; from Cleveland to Toledo, 113; from Toledo to Decatur, 323; and from Decatur to St. Louis, 113 miles. What is the distance from New York to St. Louis? Ans. 1172 miles. 41. A man owns farms valued at $56800; city lots valued at $86760; a house worth property to the amount of $6785. value of his property?

$12500, and other What is the entire

Ans. $162845. The first agreed

42. Three persons bought a hotel. to pay $7375, the second agreed to pay twice as much, and the third, $13555. What was the value of the hotel? Ans. $35680.

43. In January, 1876, a merchant bought goods to the amount of $2675; in February, $4375; and in March, $1897. How much did he owe for the goods?

44. I owe three notes, one note being for $2509, another for $6563, and a third for $3925. How much do I owe for the three notes ?