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.

(2.)

96972

(3.) 9841672

(4.) 81325

§ 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; twenty seven millions and eighteen; two hundred and seventy millions and twenty-seven thousand. Ans. 297303078.

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. A merchant on settling his accounts finds that he owes A 60 dollars, B 150 dollars, C 240 dollars, and to D 100 dollars. How much does he owe in all?

Ans.

3. 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.

4. A man borrowed a sum of money and paid in part 267 dollars, and afterwards paid the remainder 325 dollars: How much did he borrow?

Ans.

dollars.

5. At the Custom House, on the first day of June, there were entered 1800 yards of linen; on the 10th, 2500 yards; on the 25th, 600 yards; on the day following, 7500 yards; and on the three last days of the month, 1325, yards each day: What was the whole amount entered during the month?

Ans.

yards 6. A farmer has his live stock distributed in the following manner: in pasture No. 1, there are 5 horses, 14 cows, 8 oxen, and 6 colts; in pasture No. 2, 3 horses, 4 colts, 6 cows, 20 calves, and 12 head of young cattle; in pasture No. 4, 320 sheep, 16 calves, 2 colts, and 5 head of young cattle. How much live stock had he of each kind, and how many head had he altogether?

Ans. 8 horses, 20 cows, 8 oxen, 12 colts, 36

calves, 17 head of young cattle, and 320 sheep. Total live stock, 421 head.

7. What is the interval of time between a transaction which happened 125 years ago, and one that will happen 267 years hence?

Ans.

years.

8. An army consists of 4000 foot soldiers, 4006 cavalry or horse, 3093 artillery-men, 1224 riflemen, 1400 pioneers

and 200 miners: What is the whole number of men in the army? Ans. 13923. 9. The mail route from Albany to New-York is 144 miles, from New-York to Philadelphia 90 miles, from Philadelphia to Baltimore 98 miles, and from Baltimore to Washington City 38 miles: What is the distance from Ans. miles. 10. Suppose a man was born on the 1st of January, 1795: When will he be 85 years old?

Albany to Washington?

Ans. In 1880.

11. A man dying leaves his only daughter nine hundred and ninety-nine dollars, and to each of three sons two hundred dollars more than he left the daughter. What was each son's portion, and what the amount of the whole estate? Each son's part Ans. Whole estate

dollars.

dollars.

12. What was the whole number of inhabitants in the United States in 1840; there being in Maine 501,793'; New Hampshire 284,574; Vermont 291,948; Massachusetts 737,699; Rhode Island 108,830; Connecticut 309,978; New-York 2,428,921; New-Jersey 373,306; Pennsylvania 1,724,033; Delaware 78,085; Maryland 469,232, Virginia 1,239,797; North Carolina 753,419; South Carolina 594,398; Georgia 691,392; Alabama 590,756; Mississippi 375,651; Louisiana 352,411; Tennessee 829,210; Kentucky 779,828; Ohio 1,519,467; Indiana 685,866; Illinois 476,183; Missouri 383,702; Arkansas 97,574; Michigan 212,267; Florida 54,477; Wisconsin Territory 30,945; lowa Territory 43,112; District of Columbia 43,712; Naval Service 6,100 ? Ans. 17,068,666.

SUBTRACTION OF SIMPLE NUMBERS.

§ 16. John has 6 apples and Charles has 4. How many more apples has John than Charles?

Ans. 2. Two is called the difference between the number of apples which John has, and the number of apples which Charles bas.

SUBTRACTION is finding the difference between two

numbers.

The larger of the two numbers is called the minuend, the lesser is called the subtrahend, and their difference is called the remainder.

Q. What is Subtraction? What is the larger number called? What As the smaller number called? What is the difference called?

§ 17. James has 8 pears and gives 5 to William: how many has he left? Ans. 3.

Q. Which number is the minuend? Which the subtrahend? Which the remainder?

§ 18. The sign, is called minus, a term signifying less. When placed between two numbers it denotes that the one on the right is to be taken from the one on the left.

Thus, 6-4-2, denotes that 4 is to be taken from 6. Here 6 is the minuend, 4 the subtrahend, and 2 the remainder.

When the numbers are small, their difference is apparent, and instead of saying, 6 minus 4 equals 2, we say, 4 from 6 leaves 2.

Q. What is the sign of subtraction? What is it called? What does the term signify? When placed between two numbers what does it denote? When the numbers are small how do you read them, as 6—4 ?

19. The following table should be committed to memory, and read, two from two naught remains; two from three, one remains, &c.