29. Add these rows of figures, from left to right, and write down the amount of each row.

2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 999999999999

2 2 3 3 4 4 5 5 6 6 7 7 3 3 3 5 5 5 7 7 7 9 9 9 1 11 1 2 2 2 2 8 8 8 8 5 5 5 5 5 7 7 7 7 7 4 4 6 6 6 6 4 4 4 4 2 3 4 5 9 1 8 2 7 3 6 4 5 5 5 5 2 3 1 5 6 9 2 5 5 4 8 9 3 5 2 7 6 3 9 5 4 8 6 2

§ VIII. 1. Copy these rows of figures on your slate. add them up, and set down the amount in flgures.

2. In the last example you added rows of units, and set down the amount. Add, now, these rows of tens. and hundreds, and thousands, &c., in the same manner.

50

500

6000
7000

80000

900000

4000000

70000

60 600 8000 50000 600000 6000000

3. Here are some simple examples, containing different orders.

1 2 3 600 6000 900

8000 90000

5. The following are larger, but are to be added in the

[The learner will readily understand and perform the above examples. If, however, he should hesitate, let him study, or let the teacher repeat to him, the following explanation.]

In the third row of examples above, 1 ten is added to 1 unit. The ten is a unit of the second order, and should therefore stand in the second place, and the unit is a unit of the first order, and ought to be written in the first place. We will take away, therefore, the cypher on the right of the ten, and in its place will put the unit.

All of the first row of examples are performed in this way, and the same explanation will apply to them.

In the fourth row of examples, 70 or 7 tens are added to 6 units, and 1 unit. The 6 units, and 1 unit, make 7 units, which are written, as before, in place of the 0 in 70. The others are all similar.

[The teacher will perceive, that, thus far in the examples containing several columns, no one column added up, has exceeded 9. He should require his pupils to explain the addition of every column, in the manner given above, using the name of the order he is adding. Thus, in the last example, he should begin I unit and 8 units are 9 units, which are to be written in the units' place, in the answer. 1 ten and 1 ten are two tens; 2 tens and 7 tens are 9 tens, to be written in the tens' place in the answer, &c.]

It is plainly of no consequence on which side you begin to add the examples above, since each column is added separately. It is better, however, to begin on the right hand, as will presently be seen. It is, also, very manifest, that as all the units are to be added together, all the tens together, &c., it is most convenient to write the numbers so that units shall stand under units, and tens under tens, &c.

The pupil should be very careful never to add the figures of different orders together; for 3 units and 2 tens, are neither 5 units, nor 5 tens. But 3 units and 2 units are 5 units; and 3 tens and 2 tens are 5 tens.

6. Write down 15 and 6, and add them.

15

Set this down. Bring it down 1 ten and 1 ten

First, add the units together. 5 units and 6 units are 11 units; that is, 1 ten and 1 unit, written 11. There is one ten in the upper number. under the tens' place. Now add the tens. are 2 tens, or twenty.

Join this to the 1 unit, and it is 21.

7. Write 17 and 26, and add them.

17

26

13

3

43

First, add the units. 7 units and 6 units are 13 units; equal to 1 ten and 3 units. Set this down. Now add the tens. 1 ten and 2 tens are 3 tens. Set these under the tens. Now add again. 3 tens and 1 ten are 4 tens; which, joined with the 3 units, make 43.

8. Let the following examples be performed and explained in the same way.

37 65 39 44 37 28 76 52 67 56
54 27 27 46 55 39 18 28 19 25

The learner will see, that, when his units are more than 9, it is impossible to write them in the units' place; because there are no characters to express them. Every even ten, therefore, he is obliged to add with the tens. And if there are any units over, he sets them down in the units' place. Of course, after he has added his units column, a part of the amount goes to the units' place, and a part to the tens' place. In the examples above, these two parts are both set down. But this is inconvenient, because it renders, at least, two additions necessary. The following process is better.

10. Add 54 and 39.

54 9 units and 4 units are 13 units; that is, I ten and 3 units. 39 The 1, is the part that belongs to the tens' place. Therefore, in mind, add it with the tens' column. Thus, 1 ten and 3 tens 93 are four tens; 4 tens and 5 tens are 9 tens. The answer is 93. In the same manner, we add 1 to the hundreds' column, for every ten tens, 1 to the thousands' column for every ten hundreds, and 1

to any column, or order of figures, for every ten of the next lower order.

THIS ADDITION of one foR EVERY TEN TO THE NEXT HIGHER ORDER IS CALLED CARRYING.

If we were to write down the whole amount of any column, whose sum is more than 9, as in the examples above, it would take at least two figures, and sometimes more. Of these, it is plain, that the one on the right hand is the one to be set down, and the other, or others, the number to be carried. Thus :

11. Add 375, and 463, and 999, and 888.

375

999

The amount of the

463 5, and carry the 2. down 2, and carry 3. set down 7, and carry

888

2725

units is 25; of course, we set down the There are 32 tens. Therefore, we set There are 27 hundreds. We therefore 2. As there is nothing to add it to, we put it in the next place, by itself.

[The pupil should, frequently, be exercised in explaining operations in addition, in the manner of the preceding illustrations.]

The following are to be performed, in the manner of the preceding.

12. In an orchard, 19 trees bear cherries, 28 bear peaches, 8 bear plums, and 58 apples. How many trees in all ?

Ans. 113. 13. Four men purchased a field. The first gave 74 dollars; the second, 67; the third, 41; and the fourth, 27. How much did all give?

Ans. 209.

14. How many times does the hammer of a clock strike in 24 hours, if it strikes regularly from 1 to 12, and then from 1 to 12 again?

Ans. 156.

15. How many days in the Spring months, containing March, 31 days; April, 30; and May 31?

Ans. 92.

16. How many in the Winter months, containing December, 31; January, 31; February, 28?

Ans. 90.

17. How many in the Summer and Autumn months, containing June, 30; July, 31; August, 31; September, 30; October, 31; November, 30?

18. Then, how many days in the year ?

Ans. 183.

Ans. 365.

19. If it require 650 men to man a 74 gun ship; 475, to man a 44; 350, to man a 36; 275, to man a 32; 200, to man a 20; and 180, to man an 18; how many men will it require to man the whole ?

Ans. 2,130.

20. A man spent 30 years in the United States, 5 years in France, 12 years in Italy, 7 years in Germany, 4 years in the Netherlands, and afterwards returned to the United States, where he lived 26 years. How old was he at his death? Ans. 84.

The pupil is now prepared to understand the following rule. 1. WRITE DOWN THE NUMbers to be aDDED, SO THAT THE SAME ORDERS IN EACH, MAY STAND IN THE SAME COLUMN, UNDER EACH OTHER,

II. BEGIN WITH THE FIRST ORDER, ADD EACH COLUMN BY ITSELF, AND, IF THE amount be not more than 9, set it dowN UNDER THAT

COLUMN.

III. IF THE AMOUNT BE MORE THAN 9, THINK WHAT FIGURES YOU WOULD USE TO WRITE THAT AMOUNT. OF THOSE FIGURES, SET DOWN THE RIGHT HAND ONE, UNDER THE ORDER ADDed. CARRY ALL TO THE

LEFT OF THIS, TO THE NEXT HIGHer order.

You have now been learning to perform ADDITION. You find it is a process, which makes one number out of several. For brevity's sake,

THE SINGLE NUMBER, THUS found, is called AMOUNT OR SUM. Then,

ADDITION IS FINDING A SINGLE NUMBER, WHICH SHALL EXPRESS THE AMOUNT OF TWO OR MORE NUMBERS.

+between two numbers, or sets of numbers, signifies that they are to be added.

This sign is commonly called plus, which is a Latin word, meaning more.

= between two numbers, or sets of numbers, signifies that they are equal to each other. Thus, 6+8=14 signifies that 6 and 8 equal 14.

EXAMPLES FOR PRACTICE.

1. A man bought 4 pieces of cloth, containing, the first, 60 yards; the second, 97; the third, 82; and the fourth, 112. How many yards in all?

Ans. 351. 2. For the cloth, he paid as follows: for the first piece, 235 dollars; for the second, 384; for the third, 327; and for the fourth, 486 dollars. How much did he give for all? Ans. 1,432.

3. A man had a sum of money to pay. He paid at one time, 693 dollars; at another, 75; at another, 1,421; at another, 1,652; and at another, 542. There were 964 dollars left unpaid. What was the whole sum?

Ans. 5,347. dollars, and sold Ans. 531. 275 dollars; the How many dolAns. 878.

4. A merchant bought wine to the amount of 437 it so as to gain 94 dollars. What did he sell it for? 5. There are four bags, containing, the first, second, 178; the third, 356; and the fourth, 69. lars in all ? 6. A merchant bought at one time, 543 barrels of beef; at another, 407; at another, 152; and at another, 414. How many did he buy in all ? Ans. 1,516.

7. From the creation of the world to the food, were 1,656 years; thence, to the building of Solomon's temple, 1,344 years; thence, to the birth of our Saviour, 1,004; thence, to the present time, 1,830. How old is the world? Ans. 5,834 years.

8. A man left his estate, at his death, to four children. They paid debts to the amount of 1,476 dollars, and then had 4,768 dollars each. How much was the whole estate ? Ans. 20,548 dollars.