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§ II. ADDITION.

MENTAL EXERCISES. Art. 17. When it is required to find a single number to express the sum of the units contained in several smaller numbers, the process is called Addition. Ex. 1. James has 3 pears and his

younger brother has 4, how many have both ?

ILLUSTRATION. - To solve this question, the 3 pears and 4 pears must be added together; thus, 3 added to 4 makes 7. Therefore James and his brother have 7

pears.

ADDITION TABLE.

2 and ( are 2 2 and 1 are 3 2 and 2 are 4 2 and 3 are 5 2 and 4 are 6 2 and 5 are 7 2 and 6 are 8 2 and 7 are 9 2 and 8 are 10 2 and 9 are 11 2 and 10 are 12 2 and 11 are 13 2 and 12 are 14

3 and ( are 3
3 and I are 4
3 and 2 are 5
3 and 3 are 6
3 and 4 are 7
3 and 5 are 8
3 and 6 are 9
3 and 7 are 10
3 and 8 are 11
3 and 9 are 12
3 and 10 are 13
3 and 11 are 14
3 and 12 are 15

4 and 0 are 4
4 and I are 5
4 and 2 are

6
4 and 3 are 7
4 and 4 are 8
4 and 5 are 9
4 and 6 are 10
4 and 7 are 11
4 and 8 are 12
4 and 9 are 13
4 and 10 are 14
4 and 11 are 15
4 and 12 are 16

5 and 0 are 5
5 and I are 6
5 and 2 are 7
5 and 3 are 8
5 and 4 are 9
5 and 5 are 10
5 and 6 are 11
5 and 7 are 12
5 and 8 are 13
5 and 9 are 14
5 and 10 are 15
5 and 11 are 16
5 and 12 are 17

6

9 and Oare 9 9 and I are 10 9 and 2 are 11 9 and 3 are 12 9 and 4 are 13 9 and 5 are 14 9 and 6 are 15 9 and 7 are 16 9 and 8 are 17 9 and 9 are 18 9 and 10 are 19 9 and 11 are 20 9 and 12 are 21

6 and I are 7 6 and 2 are 8 6 and 3 are 9 6 and 4 are 10 6 and 5 are 11 6 and 6 are 12 6 and 7 are 13 6 and 8 are 14 6 and 9 are 15 6 and 10 are 16 6 and 11 are 17 6 and 12 are 18

7 and 0 are 7
7 and I are 8
7 and 2 are 9
7 and 3 are 10
7 and 4 are 11
7 an 5 are 12
7 and 6 are 13
7 and 7 are 14
7 and 8 are 15
7 and 9 are 16
7 and 10 are 17
7 and 11 are 18
7 and 12 are 19

8 and Oare 8
8 and 1 are 9
8 and 2 are 10
8 and 3 are 11
8 and 4 are 12
8 and 5 are 13
8 and 6 are 14
8 and 7 are 15
8 and 8 are 16
8 and 9 are 17
8 and 10 are 18
8 and il are 19
8 and 12 are 20

10 and 0 are 10
10 and 1 are 11
10 and 2 are 12
10 and 3 are 13
10 and 4 are 14
10 and 5 are 15
10 and 6 are 16
10 and 7 are 17
10 and 8 are 18
10 and 9 are 19
10 and 10 are 20
10 and 11 are 21
10 and 12 are 22

11 and 0 are 11
11 and 1 are 12
11 and 2 are 13
11 and 3 are 14
11 and 4 are 15
ll and 5 are 16
11 and 6 are 17
11 and 7 are 18
11 and 8 are 19
11 and 9 are 20
11 and 10 are 21
11 and il are 22
11 and 12 are 23

12 and 0 are 12
12 and I are 13
12 and 2 are 14
12 and 3 are 15
12 and 4 are 16
12 and 5 are 17
12 and 6 are 18
12 and 7 are 19
12 and 8 are 20
12 and 9 are 21
12 and 10 are 22
12 and 11 are 23
12 and 12 are 24

13 and 0 are 13 13 and I are 14 13 and 2 are 15 13 and 3 are 16 13 and 4 are 17 13 and 5 are 18 13 and 6 are 19 13 and 7 are 20 13 and 8 are 21 13 and 9 are 22 13 and 10 are 23 13 and 11 are 24 13 and 12 are 25

QUESTION. - Art. 17. What does addition teach ?

2. Thomas had three nuts, and James gave him two more; how many had he then ?

3. A boy had four apples, and he found two more ; how

many in all ?

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4. I have six dollars, and a man has paid me three more; how many have I?

5. Enoch had seven marbles, and John gave him two more ; how many had he then?

6. Benjamin has four dollars, and his sister has three; how many have both?

7. Paid five dollars for a barrel of flour, and seven dollars for sugar; how much for both ?

8. James had two cents, and Samuel gave him six more ; how many had he in all ?

9. How many are five apples and six apples ?
10. How many are four dollars and eight dollars ?

11. How many are 2 and 3? 2 and 5 ? 2 and 7 ? 2 and 9? 2 and 4? 2 and 2 ? 2 and 8 ? 2 and 6?

12. How many are 3 and 3? 3 and 5 ? 3 and 7 ? 3 and 9?

3 and 4? 3 and 6? 3 and 8? 3 and 3? 13. How many are 4 and 3? 4 and 5 ? 4 and 8? 4 and 9? 4 and 1? 4 and 2 ? 4 and 4 ? 4 and 7 ?

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

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

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

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

18. How many are 9 and 1 ? 9 and 3? 9 and 5 ? 9 and 4? 9 and 6? 9 and 8? 9 and 9: 9 and 2 ?

19. How many are 11 and 3 ? 11 and 2 ? 11 and 4 ? 11 and 6 ? 11 and 7 ? 11 and 9? 11 and 11? 11 and 13 ? 11 and 12 ? 11 and 2 and 3: 11 and 4 and 4? 11 and 15? 12 and 7 and 3 ? 12 and 6 and 3? 8 and 8 and 4? 9 and 5 and 6 ? 9 and 8 and 8 ?

20. Gave nine cents for a pound of cheese, and seven cents for a quart of molasses; what did I give for both ?

21. If you buy a picture-book for eleven cents, and a knise for nine cents, what is the cost of both ?

22. John paid Luke seven cents for marbles, and twelve cents for gingerbread; how much money was received ?

23. Thomas paid twelve cents for a top, and eight cents for cherries; what did both cost ?

24. A merchant sold three barrels of flour to one man, and thirteen to another; what was the quantity sold ?

25. I have two apple-trees; one bears twelve bushels of apples, and the other eleven; how many bushels do both trees produce ?

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

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

28. How many are 3 and 2 and 2? 3 and 3 and 2? 3 and 5 and 5? 3 and 4 and 7? 3 and 6 and 7 ? 3 and 7 and 10 ? 3 and 8 and 9? 3 and 9 and 9 ? 9 and 12 ?

29. How many are 4 and 2 and 2? 4 and 3 and 3? 4 and 4 and 5 ? 4 and 6 and 7 ? 4 and 7 and 7 ? 4 and 8 and 3? 4 and 9 and 3 ? 4 and 8 and 8 ? 12 and 12?

30. How many are 5 and 3 and 3? 5 and 4 and 4? 5 and 5 and 1 : 5 and 6 and 7? - 5 and 7 and 8 ? 5 and 8 and 7 ? 5 and 9 and 9? 5 and 10 and 3 ? 3 and 11:

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

32. How many are 7 and 2 and 3? 7 and 3 and 3? 7 and 5 and 9? 7 and 6 and 6 ? 7 and 8 and 8? 7 and 9 and 8? 7 and 10 and 11 ? 8 and 11 and 7 ?

33. How many are 8 and 2 and 9 ? 8 and 4 and 3? 8 and 7 and 7 ? 8 and 9 and 10? 8 and 7 and 9? 8 and 10 and 10? 8 and 9 and 12 ? 7 and 7 and 11 ?

34. How many are 9 and 5 and 2 ? 9 and 4 and 3? 9 and 9 and 6 ? 9 and 10 and 3? 9 and 8 and 8? 9 and 4 and 9 ? 9 and 9 and 9 ? 8 and 8 and 12 ?

35. How many are 2 and 2 and 4 and 5 ? 3 and 4 and 5 and 6 ? 4 and 5 and 6 and 7 ? 5 and 5 and 4 and 42 9 and 1 and 2 and 3 and 5? 7 and 7 and 9 and 7 ? 36. James had 4 apples, Samuel gave him 5 more,

and John gave him 6; how many had he in all ?

37. Gave 7 dollars for a barrel of flour, 5 dollars for a hundred weight of sugar, and 8 dollars for a tub of butter; what did I give for the whole ?

38. Paid 5 dollars for a pair of boots, 12 dollars for a coat, and 6 dollars for a vest; what was the whole cost ?

39. I have 7 apple-trees, 9 cherry-trees, 6 pear-trees, and 8 plum-trees; how

many

in all ? 40. Paid 50 dollars for a horse and 70 dollars for a chaise ; what was the cost of both ?

ILLUSTRATION. - We may first divide the dollars into tens, and then add them together. Thus, 50 equals 5 tens, and 70 equals 7 tens; 5 tens and 7 tens are 12 tens or 120 units. Therefore the cost of the horse and chaise was 120 dollars.

41. A man performed a journey in 4 days; the first day he travelled 10 miles, the second day 20, the third day 30, and the fourth day 40 miles; what was the whole distance ?

42. Gave 10 cents for an almanac, 30 cents for paper, 50 cents for quills, and 80 cents for a penknife; what did I give for the whole ?

43. Gave 75 cents for an arithmetic and 67 for a geography ; what was the cost of both ?

ILLUSTRATION. We may divide the cents into tens and units. Thus, 75 equals 7 tens and 5 units ; 67 equals 6 tens and 7 units; 7 tens and 6 tens are 13 tens; and 5 units and 7 units are 12 units or 1 ten and 2 units; 1 ten and 2 units added to 13 tens make 14 tens and 2 units, or 142. Therefore the arithmetic and geography cost 142 cents, or 1 dollar and 42 cents.

44. Bought eight yards of broadcloth for 32 dollars, and forty yards of carpeting for 46 dollars; what did they both cost?

45. In a certain school 9 scholars study grammar, 12 arithmetic, 7 logic, 2 rhetoric, and 17 punctuation ; how many are there in the school ?

46. Paid 2 dollars for a cap, 3 dollars for shoes, 7 dollars for pantaloons, 6 dollars for a vest, and 22 dollars for a coat; what was the cost of the whole?

47. On the fourth of July 20 cents were given to Emily, 15 cents to Betsey, 10 cents to Benjamin, and none to Lydia what did they all receive ?

48. Bought four loads of hay; the first cost 15 dollars, the second 12 dollars, the third 20 dollars, and the fourth 17 dollars; what was the price of the whole ?

49. Gave 55 dollars for a horse, 42 dollars for a wagon, and 17 dollars for a harness; what did they all cost ?

50. Sold 3 loads of wood for 17 dollars, 6 tons of timber for 19 dollars, and a pair of oxen for 67 dollars; what sum did I receive ?

Art. 18. From the solution of the preceding questions, the learner will perceive, that

Addition is the process of collecting several numbers into one sum, which is called their amount.

Art. 19. Signs. - Addition is commonly represented by this character, t, which signifies plus, or added to. The expression 7 +5 is read, 7 plus 5, or 7 added to 5.

This character, =, is called the sign of equality, and sig. nifies equal to. The expression 7+ 5 = 12 is read, 7 plus 5, or 7 added to 5, is equal to 12.

OPERATION.

Dollars.

EXERCISES FOR THE SLATE. Art. 20. The method of operation, when the numbers are large, and the sum of each column is less than 10.

Ex. 1. A man bought a watch for 42 dollars, a coat for 16 dollars, and a set of maps for 21 dollars; what did he pay for the whole ?

Ans. 79 dollars.
In this example, having arranged the

numbers, units under units, and tens un-
42

der tens, in regular columns, we first add 16

the column of units; thus, I and 6 are 7 21

and 2 are 9 (units), and set down the

amount under the column of units. We Amount 79

then add the column of tens; thus, 2 and

1 are 3 and 4 are 7 (tens), which we set under the column of tens, and thus find the amount of the whole to be 79 dollars.

ART. 21. First Method of Proof. Begin at the top and add the columns downward in the same manner as they were before added upward ; and if the two sums agree, the work is presumed to be right.

The reason of this proof is, that, by adding downward, the order of the figures is inverted ; and, therefore, any error made in the first addition would probably be detected in the second.

Note. — This method of proof is generally used in business.

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QUESTIONS. - Art. 18. What is addition ? — Art. 19. What is the sign of addition, and what does it signify ? What is the sign of equality, and what does it signify? - Art. 20. How are numbers arranged for addition? Which column must first be added? Why? Where do you place its sum? Where must the sum of each column be placed ? What is the whole bum called ?

Art. 21. How is addition proved? What is the reason for this method of proof? Is this method in common use?

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