19. Forty-seven millions, two hundred and four thousands, eight hundred and fifty-one.

20. Six quadrillions, forty-nine trillions, seventy-two billions, four hundred and seven thousands, eight hundred and sixty-one.

21. Eight hundred and ninety-nine quadrillions, four hundred and sixty trillions, eight hundred and fifty billions, two hundred millions, five hundred and six thousands, four hundred and ninety-nine.

22. Fifty-nine trillions, fifty-nine billions, fifty-nine millions, fifty-nine thousands, nine hundred and fifty-nine.

23. Eleven thousands, eleven hundred and eleven. 24. Nine billions and sixty-five.

25. Write three hundred and four trillions, one million, three hundred and twentv-one thousands, nine hundred and forty-one.

26. Write nine trillions, six hundred and forty billions, with 7 units of the ninth order, 6 of the seventh order, 8 of the fifth, 2 of the third, 1 of the second, and 3 of the first.

27. Write three hundred and five trillions, one hundred and four billions, one million, with 4 units of the fifth order, 5 of the fourth, 7 of the second, and 4 of the first.

28. Write three hundred and one billions, six millions, four thousands, with 8 units of the fourteenth order. 6 of the third, and two of the second.

29. Write nine hundred and four trillions six hundred and six, with 4 units of the eighteenth order, five of the sixteenth, four of the twelfth, seven of the ninth, and 6 of the fifth.

30. Write sixty-seven quadrillions, six hundred and fortyone billions, eight hundred and four millions, six hundred and forty-four.

31. Write eight hundred and three quintillions, sixty-nine billions, four hundred and forty millions, nine hundred thousand and three.

32. Write one hundred and fifty-nine sextillions, four hundred and five billions, two hundred and one millions, three thousand and six.

33. Write four hundred and four septillions, nine hundred and three sextillions, two hundred and one quintillions, forty quadrillions, and three hundred and four.

ADDITION.

30. 1. John has two apples and Charles has three: how many have both?

ANALYSIS.-If John's apples be placed with Charles's, there will be five apples.

The operation of finding how many apples both have is called Addition.

2. James has 5 marbles and William 7? how many have both?

3. Mary has 6 pins and Jane 9: how many have both? 4. How many are 4 and 5 and 3?

5. How many are 6 and 4 and 9?

6. How many are 3 and 7? 4 and 6? 2 and 8? 5 and 5? 9 and 1? 10 and 0? 0 and 10?

7. How many are 6 and 3 and 9? How many are 18 and 2? 18 and 3? 18 and 5?

8. James had 9 cents and Henry gave him eight more: how many had he in all?

PRINCIPLES AND EXAMPLES.

31. James has 3 apples and John 4: how many have both? Seven is called the sum of the numbers 3 and 4.

The sum of two or more numbers is a number which contains as many units as all the numbers taken together.

ADDITION is the operation of finding the sum of two or more numbers.

OF THE SIGNS.

32. The sign is called plus, which signifies more. When placed between two numbers it denotes that they are to be added together.

The sign is called the sign of equality. When placed between two numbers it denotes that they are equal; that is, that they contain the same number of units. 3+2=5

Thus :

2+3

how many?

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

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

OPERATION. 14

21

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

35 cents.

The first number contains four units and 1 ten, the second 1 unit and two tens. We write the units in one column and the tens in the column of tens.

31. What is the sum of two or more numbers? What is addition? 32. What is the sign of addition? What is it called? What does it signify? Express the sign of equality? When placed between two numbers what does it show? When is a number cqual to the sum of other numbers? Give an example.

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 add the tens, and write the sum in the tens' place. Hence, the sum is 3 tens and 5 units, or 35 cents.

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

3. A farmer has 160 sheep in one field, 20 in another, and 16 in another: how many has he in all?

OPERATION.

24

62

86 OPERATION.

160

20

16

196

9. What is the sum of 304 and 273?

10. What is the sum of 3607 and 4082 ?
11. What is the sum of 30704 and 471912?

12. What is the sum of 398463 and 401536?

13. If a top costs 6 cents, a knife 25 cents, a slate 12 cents: what does the whole amount to?

14. John gave 30 cents for a bunch of quills, 18 cents for an inkstand, 25 cents for a quire of paper: what did the whole cost him?

15. If 2 cows cost 143 dollars, 5 horses 621 dollars, and 2 yoke of oxen 124 dollars: what will be the cost of them all! 16. Add 5 units, 6 tens, and 7 hundreds.

ANALYSIS.-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 up, and find the sum to be 765.

We must observe, that in all cases, units of the same order are written in the same column.

hundreds.

tens.

crunits.

77

765

17. What is the sum of 3 units, 8 tens, and 4 thousands?

18. What is the sum of 8 hundreds, 4 tens, 6 units, and 6 thousands?

19. What is the sum of 3 units, 5 units, 6 tens, 3 tens, 4 hundreds, 3 hundreds, 5 thousands, and 4 thousands?

20. What is the sum of five units of the 4th order, 1 of the 3d, three of the 4th, five of the 3d, and one of the 1st?

21. What is the sum of six units of the 2d order, five of the 3d, six of the 4th, three of the 2d, four of the 3d, two of the 1st, and four of the 2d?

22. What is the sum of 3 and 6, 5 tens and 2 tens, and 3 hundreds and 6 hundreds?

23. What is the sum of 4 and 5, 5 tens, 3 hundreds and 2 hundreds ?

GENERAL METHOD.

33. 1. A farmer paid 898 dollars for one piece of land, and 637 dollars for another; how many dollars did

he

pay for both?

ANALYSIS.-Write the numbers thus, and draw a line beneath them.

sum of the units,

sum of the tens,

sum of the hundreds,

OPERATION.

898

637

15

12

14

OPERATION.

898

637

1. The example may be done in another way, thus: Having set down the numbers, as before, say, 7 units and 8 units are 15 units, equal to 1 ten and 5 units: set the 5 in the units' place, and the 1 ten in the column of tens. Then say, 1 ten and 3 tens are 4 tens, and 9 tens are 13 tens, equal to 1 hundred and 3 tens. Set the 3 in the tens' place and the 1 hundred in the column of

11

1535

33. How do you set down the numbers for addition? Where do you begin to add? If the sum of any 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 to the next column, what is it called? What do you set down when you come to the last column?