OF THE SIGNS.

14. The sign +, is called plus, which signifies more. When placed between two numbers it denotes that they 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. 15. 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.

1

6+5=11 7+5=12 8+5=13

9+5=14

6+8=14 7+8=15 8+8=16

6+9=15 7+9=16 8+9=17

9+8=17

949

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 hundreds place, and 2 in the tens 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.

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. We then say, 1 to 3 is four, and 9 are 13.

We set

637

11

1531

the three in the tens place, and write the 1 der the 6 in the column of hundreds.

We 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.

16. I. Set down the numbers to be added so that units shall be under units, tens under tens, hundreds under hundreds, &c. and draw a line beneath them.

Write

II. Begin at the foot of the units 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 units place. But if it cannot, see how many tens and how many units it contains. down the units in the units 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.

EXAMPLES.

1. What is the sum of the numbers 375, 6321

In the 1st, 2d and 3d examples, the small figu

written under the sums express the numbers to be carried from one column to the other. Thus, in the 3d example, 1 is to be carried from the 1st column to the 2d 1 from the 2d to the 3d: 1 from the 3d to the 4th: 1 from the 4th to the 5th: 2 from the 5th to the 6th: and 2 from the 6th to the 7th. Beginners had better set down the numbers to be carried, as in the 3d example.

PROOF OF ADDITION.

17. 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.

§ 18. 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.

QUESTIONS.

§ 13. What is addition? What is the single number call. ed?

§ 14. 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.

§ 16. How do you set down the numbers for addition? Where do you begin to add? When the sum of a column can be expressed by a single figure what do you do? When it cannot, what do you add to the next column? When you add for the tens to the next column, what is it called? What do you set down when you come to the last column? €17. How do you prove addition?

do you prove addition by the 2d method?

7. Add 8635, 2194, 7421, 5063, 2196 and 1245 together. Ans. 26754.

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. 7047897.

10. Add 1, 37, 29504, 6790312, 18757421 and 265 together. Ans. 25577540.

11. Add 562163, 21964, 56321, 18536, 4340, 279 and 83 together.

Ans. 663686