8. A man had 3 calves worth 2 dollars each, 4 calves worth 3 dollars each, and 7 calves worth 5 dollars each; how many calves had he?

9. A man sold a cow for 16 dollars, some corn for 20 dollars, wheat for 25 dollars, and butter for 5 dollars; how many dollars must he receive?

The putting together two or more numbers, (as in the foregoing examples,) so as to make one whole number, is called Addition, and the whole number is called the sum, or

amount.

10. One man owes me 5 dollars, another owes me 6 dollars, another 8 dollars, another 14 dollars, and another 3 dollars; what is the amount due to me?

11. What is the amount of 4, 3, 7, 2, 8, and 9 dollars? 12. In a certain school 9 study grammar, 15 study arithmetic, 20 attend to writing, and 12 study geography; what is the whole number of scholars?

SIGNS. A cross, +, one line horizontal and the other perpendicular, is the sign of addition. It shows that numbers, with this sign between them, are to be added together. It is sometimes read plus, which is a Latin word signifying'

more.

Two parallel, horizontal lines,=, are the sign of equality. It signifies that the number before it is equal to the number after it. Thus, 5+3= 8 is read 5 and 3 are 8; or, 5 plus (that is, more) 3 is equal to 8.

In this manner let the pupil be instructed to commit the following

ADDITION TABLE.

3+0= 314+0 = 415+0= 5 3+1 4 4+1= 5 5+1 6

2+0= 2

2+1=3

2+2 4 3+2

354+2 6

5+2=7

ADDITION TABLE-CONTINUED.

7+0= 78+0= 890 9 7+1 8 8+1= 9 9+1=10

7+2=9

7+3=10

8+2 1092=11 8+3 =11 9+3=12 8+4 12 9+4 13 8+5=13 9+5=14

86149+6=15

8+7=15 9+7=16 8 +8 = 16 9 +8=17 8917 9+9=18

4+3+2 how many?

6+4+5= how many?

¶ 5. When the numbers to be added are small, the addition is readily performed in the mind; but it will frequently be more convenient, and even necessary, to write the numbers down before adding them,

13. Harry had 43 cents, his father gave him 25 cents more; how many cents had he then?

One of these numbers contains 4 tens and 3 units. The other number contains 2 tens and 5 units. To unite these two numbers together into one, write then down one under the other, placing the units of one number directly under units of the other, and the tens of one number directly under tens of the other, thus:

43 cents. Having written the numbers in this man25 cents. ner, draw a line underneath.

43 cents.
25 cents.

8

43 cents.

25 cents.

Ans. 68 cents.

We then begin at the right hand, and add the 5 units of the lower number to the 3 units of the upper, number, making 8 units, which we set down in unit's place.

We then proceed to the next column, and add the 2 tens of the lower number to the 4 tens of the upper number, making 6 tens, or 60, which we set down in ten's place, and the work is done.

It now appears that Harry's whole number of cents is 6 tens and 8 units, or 68 cents; that is, 43 +25=68.

14. A farmer bought a chaise for 210 dollars, a horse for 70 dollars, and a saddle for 9 dollars; what was the whole amount?

Write the numbers as before directed, with units under units, tens under tens, &c.

After the same manner are performed the following examples:

15. A man had 15 sheep in one pasture, 20 in another pasture, and 143 in another; how many sheep had he in the three pastures? 15 +20 + 143 how many?

16. A man has three farms, one containing 500 acres, another 213 acres, and another 76 acres; how many acres in the three farms? 500+213 +76 how many?

17. Bought a farm for 2316 dollars, and afterwards sold it so as to gain 550 dollars; what did I sell the farm for? 2316+550 how many?

Hitherto the amount of any one column, when added up, has not exceeded 9; consequently has been expressed by a single figure. But it will frequently happen that the amount of a single column will exceed 9, requiring two or more figures to express it.

18. There are three bags of money. The first contains 876 dollars, the second, 653 dollars, the third, 524 dollars, what is the amount contained in all the bags ?

OPERATION.

First bag,

876

Second bag,

653

Third bag,
Amount,

524

2053

Writing down the numbers as already directed, we begin with the right hand, or unit column, and find the amount to be 13, that is, 3 units and 1 ten. Setting down the 3 units, or right hand figure, in unit's place, directly under the column, we reserve the 1 ten, or left hand figure, to be added with the other tens, in the next column, saying, 1, which we reserved, to 2 makes 3, and 5 are 8, and 7 are 15, which is 5 units of its own order, and 1 unit of the next higher order, that is, 5 tens and 1 hundred. Setting down the 5 tens, or right hand figure, directly under the column of tens, we reserve the left hand figure, or 1 hundred, to be added in the column of hundreds, saying, 1 to 5 is 6, and 6 are 12, and 8 are 20, which being the last column, we set down the whole number, writing the 0, or right hand figure, directly under the column, and carrying forward the 2, or left hand figure, to the next place, or place of thousands. Wherefore, we find the whole amount of money contained in the three bags to be 2053 dollars, the answer.

PROOF. We may reverse the order, and, beginning at the top, add the figures downward. If the two results are alike, the work is supposed to be right.

From the examples and illustrations now given, we de◄ rive the following

RULE.

I. Write the numbers to be added, one under another, placing units under units, tens under tens, &c., and draw a line underneath.

II. Begin at the right hand or unit column, and add together all the figures contained in that column: if the amount does not exceed 9, write it under the column; but if the amount exceed 9, so that it shall require two or more figures to express it, write down the unit figure only under the column; the figure or figures to the left hand of units, being tens, are so many units of the next higher order, which, being reserved, must be carried forward, and added to the first figure in the next column.

III. Add each succeeding column in the same manner, and set down the whole amount at the last column

EXAMPLES FOR PRACTICE.

19. A man bought four loads of hay; one load weighed 1817 pounds, another weighed 1950 pounds, another 2156 pounds, and another 2210 pounds; what was the amount of hay purchased?

20. A person owes A 100 dollars, B 2160 dollars, C 785 dollars, D 92 dollars; what is the amount of his debts?

21. A farmer raised in one year 1200 bushels of wheat, 850 bushels of Indian corn, 1000 bushels of oats, 1086 bushels of barley, and 74 bushels of pease; what was the whole Ans. 4210.

amount?

22. St. Paul's Cathedral, in London, cost 800,000 pounds sterling; the Royal Exchange 80,000 pounds; the MansionHouse 40,000 pounds; Black Friars Bridge 152,840 pounds; Westminster Bridge 389,000 pounds, and the Monument 13,000 pounds; what is the amount of these sums?

Ans. 1,474,840 pounds.

23. At the census in 1820, the number of inhabitants in the New England States was as follows:-Maine, 298,335; New Hampshire, 244,161; Vermont, 235,764; Massachusetts, 253,287; Rhode Island, 83,059; Connecticut, 275,248; what was the whole number of inhabitants, at that time, in those States ? Ans. 1,389,854.

24. From the creation to the departure of the Israelites from Egypt was 2513 years; to the siege of Troy, 307 years more; to the building of Solomon's Temple, 180 years; to the building of Rome, 251 years; to the expulsion of the kings from Rome, 244 years; to the destruction of Carthage, 363 years; to the death of Julius Cæsar, 102 years; to the Christian era, 44 years; required the time from the Creation to the Christian era. Ans. 4004 years.

25.

2 8 6 3 7 0 5 4 2 1 0 6 1 3107429 3 1 5 6 3 8 6 2 5 3 0 34792 247135 8673

26.

43 675 8 3 0 2 1 4 6 3 17 5 2 3 4 9 7 1 3 6 20 608127 5 3 0 6 217 56 5 2 17 4 6 3 0 1 28 870 3 26 3 47 2013

B