are to be added together. Thus, 3+2 denotes that 3 and 2 are to be added together.

The sign, is called the sign of equality. When placed between two numbers it denotes that they are equal to each other.

Thus, 3+2=5.

When the numbers are small we generally read them, by saying, 3 and 2 are 5.

Q. What is the sign of addition? What is it called? What does it signify? When placed between two numbers what does it express? Express the sign of equality. When placed between two numbers what does it show? Give an example.

§ 13. Before adding large numbers the pupil should be able to add, in his mind, any two of the ten figures. Let him commit to memory the following table, which is read, two and 0 are two; two and one are three; two and two are four, &c.

how many?

1+2+3+4+5+6+7+8+9= how many?

1. What is the sum of 3 and 3 tens?

2. What is the sum of 8 tens and 9?

Ans.

3. What is the sum of 4, 5, and 4 tens?

Ans. 89.

Ans.

4. What is the sum of 1, 2, 3, 4, and 9 tens? Ans. 100. 5. What is the sum of 1, 2, 3, 4, 5, and 6 tens? Ans.

6. What is the sum of 1, 4, 9, and 5 tens? Ans. 64. 7. What is the sum of 4, 8, 3, and 7 tens? Ans. 8. What is the sum of 1, 2, 4, and one hundred.

9. What is the sum of 1, 3, 4, and 4 units of the second order.

10. What is the sum of 4 and 5, and 4 units of the third order.

11. What is the sum of 6 and 2, and 5 units of the third order.

12. James has 14 cents, and John gives him 21: how many will he then have?

Having written the numbers, as at the right of the page, draw a line beneath them.

14

21

35

The first number contains 1 ten and 4 units, the second 2 tens and 1 unit. We write the units under the units, and the tens under the tens.

We then begin at the right hand, and say 1 and 4 are 5, which we set down below the line in the units' place. We then proceed to the next column, and add the tens, by saying 2 and 1 are 3, which we write in the tens' place. Hence, the sum is 35: that is, James will have 35 cents.

13. John has 24 cents, and William 62: how many have both of them?

We write the numbers as before, and draw a line beneath them. We then add the units to the units, and the tens to the tens.

24

62

86

14. A farmer has 160 sheep, 20 cows, and 16 head of young cattle: How many has he in all?

We write the numbers so that units shall stand under units, tens under tens, and hundreds under hundreds. By adding, we find the sum of the units to be 6, the sum of the tens 9, and the sum of the hundreds 1: and the entire sum 196.

Add together the following numbers:

160

20

16

196

15. A farmer bought 25 cows, 4 horses, 70 hogs, and 200 sheep: How many did he buy in all? Ans.

16. What is the sum of 5 units, 6 tens, and 7 hundreds?

We set down the 5 units in the place of units, the 6 tens in the place of tens, and the 7 hundreds in the place of hundreds. We then add them up, and find the sum to be 765. We must observe in all cases, that units fall under units, tens under tens, &c.

17. What is the sum of 3 units, 8 tens, and 4 thousands? Ans. 4083. 18. What is the sum of 8 hundreds, 4 tens, 6 units, and 6 thousands? Ans. 6846. 19. What is the sum of 3 units, 5 uniis, 6 tens, 3 tens, 4 hundreds, 3 hundreds, 5 thousands, and 4 thousands? Ans. 9798.

20. If a top costs 6 cents, a knife 25 cents, a slate pencil 1 cent, and a slate 12 cents, what does the whole amount to? Ans. 44 cts.

21. John gives 30 cents for a bunch of quills, 18 cents for an inkstand, 25 cents for a quire of paper: what did they all cost him? Ans. 73 cts.

Thus far, the amount of any one column, when added up, has not exceeded 9; and therefore its sum could be expressed by a single figure. But the sum of a single column will often exceed 9, and we will now show what is to be done in that case.

22. Add together the numbers 894 and 637.

In this example, the sum of the units is 11, which cannot be expressed by a single figure. But 11 units are equal to 1 ten and 1 unit; therefore, we set down 1 in the place of units, and 1 in the place of tens. The sum of the tens is 12. But 12 tens are equal to 1 hundred, and 2 tens; so that 1 is set down in the hundred's place, and 2 in the ten's place. The sum of the hundreds is 14. The 14 hundreds are equal to 1 thousand, and 4 hundreds; so that 4 is set down in the place of hundreds, and 1 in the place of thousands. The sum of these numbers, 1531, is the sum sought.

OPERATION.

894

The example may be done in another way, thus: Having set down the numbers, as before, we say, 7 and 4 are 11: we set down 1 in the units place, and write the 1 ten under the 3 in the column of tens.

1 to 3 is four, and 9 are 13.

We then say,

We set down

the three in the tens place, and write the 1

637

11

1531

We

hundred under the 6 in the column of hundreds. then add the 1, 6, and 8 together, for the hundreds, and find the entire sum 1531, as before.

When the sum in any one of the columns exceeds 10, or an exact number of tens, the excess must be written down, and a number equal to the number of tens, added to the next left hand column.

This is called carrying to the next column. The number to be carried may be written under the column or remembered and added in the mind. From these illustrations we deduce the following general

RULE.

§ 14. I. Set down the numbers to be added, units under units, tens under tens, hundreds under hundreds, &c., and draw a line beneath them.

II. Begin at the foot of the unit's column, and add up the figures of that column. If the sum can be expressed by a single figure, write it beneath the line, in the unil's place. But if it cannot, see how many tens and how many units it contains. Write down the units in the unit's place, and carry as many to the bottom figure of the second column as there were tens in the sum. Add up that column: set down the sum and carry to the third column as before.

III. Add each column in the same way, and set down the entire sum of the last column.

Q. How do you set down the numbers for addition? Where do you begin to add? If the sum of the first column can be expressed by a single figure, what do you do with it? When it cannot what do you write down? What do you then add to the next column? When you add the tens to the next column, what is it called? What do you set down when you come to the last column?