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ADDITION.

29. Addition in arithmetic) is the process of combining two or more numbers into one number.

NOTE 1.—The word number, as here used, stands for measured magnitude, or number of things.

30. The sum is the number obtained by adding. 31. The addends are the numbers to be added..

32. The sign, t, which is read plus, indicates that the numbers between which it is placed are to be added; thus, 6 +4, means that 4 is to be added to 6.

33. The sign, =, which is read equal or equals, indicates that that which is on the left of the sign, equals that which is on the right of the sign; thus, 3+4 = 7. 5+4+2 = 6 +5.

34. PRINCIPLES.

1. Only like numbers can be added.

2. The denomination of the sum is the same as that of the addends.

35. PRIMARY FACTS OF ADDITION.

There are forty-five primary facts of addition. See Elementary Book, pp. 32 and 82. The nine which many pupils fail to memorize perfectly are given below. (Note 1, p. 443.)

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37. Observe that in written problems in addition the figures that stand for units of the same order are usually written in the same column.

1. In example 2, what figures represent units of the second decimal order? Of the third decimal order ?

2. In example 5, what figures represent units of the first integral order?

38. Observe that in written problems in addition of denominate numbers, the figures that stand for units of the same denomination and order are usually written in the same column.

1. In example 5, what figures represent units of gallons ? Of quarts?

2. In example 5, what figures represent tens of gallons ?

3. In example 4, what figures represent hundreds of acres ?

Addition—Simple Numbers.

39. Find the sum of 275, 436, and 821. Operation.

Explanation. The sum of the units of the first order is 12; this is 275 436

equal to one unit of the second order and 2 units of the 821

first order. Write the 2 units of the first order, and

add the 1 unit of the second order to the other units of 1532 the second order.

The sum of the units of the second order is 13; this is equal to 1 unit of the third order and 3 units of the second order. Write the 3 units of the second order, and add the 1 unit of the third order to the other units of the third order.

The sum of the units of the third order is 15; this is equal to 1 unit of the fourth order and 5 units of the third order, each of which is written in its place.

The sum of 275, 436, and 821 is 1532.

40. PROBLEMS.

1. Add 3465, 4268, 3279, 6534, 5731.
2. Add 5732, 6721, 3466, 4269, 6535.
3. Add 2768, 5329, 4685, 3752, 8467.
4. Add 4671, 5315, 6248, 1533, 7232.

5. Add 375, 506, 258, 327, 580, 648, 846.
6. Add 436, 307, 449, 498, 736, 274, 888.
7. Add 625, 494, 742, 673, 574, 654, 638.
8. Add 564, 693, 684, 502, 376, 726, 877.

(a) Find the sum of the eight sums.

TO THE TEACHER.—Impress upon the pupil the fact that in arithmetic nothing short of accuracy is commendable. One figure wrong in one problem in ten is failure. The young man or the young woman who cannot solve ten problems like those on this page without an error, is worthless as an accountant.

Addition-Decimals.

41. Find the sum of 4.327, 8.29 and .836. Operation.

Explanation. The sum of the units of the third decimal order is 4.327 8.29

13; this is equal to 1 unit of the second decimal order

and 3 units of the third decimal order. Write the 3 .836

units of the third decimal order and add the 1 unit of 13.453

the second decimal order to the other units of that

order. The sum of the units of the second decimal order is 15; this is equal to 1 unit of the first decimal order and 5 units of the second decimal order. Write the 5 units of the second decimal order and add the 1 unit of the first decimal order to the other units of that order.

The sum of the units of the first decimal order is 14; this is equal to 1 unit of the first integral order and 4 units of the first decimal order. Write the 4 units of the first decimal order and add the 1 unit of the first integral order to the other units of that order.

The sum of the units of the first integral order is 13; this is equal to 1 unit of the second integral order and 3 units of the first integral order, each of which is written in its place.

The sum of 4.327, 8.29, and .836 is 13.453.

42. PROBLEMS.

1. Add 474.36, 21.37, 38.007, and 487. 2. Add 78.63, 61.993, .725, and 724.64. 3. Add .7, .84, .375, .0275, and .25326. 4. Add 85.997, 47.9994, 72, and 53.93.

5. Find the sum of seven hundred ninety-eight and nine hundred ninety-four thousandths, and seven hundred ninetyfour thousandths.

(a) Find the sum of the five sums.

TO THE PUPIL.-Can you solve these five problems and find the sum of the five sums on first trial without an error ?

Addition-United States Money.

43. Find the sum of the money represented in the following columns : $324.45

Explanation. 28.47 Sums of the units of each order: 375.28

Second decimal order (cents) 81 6.94

First decimal order (dimes). 70
175.89
First integral order .

82
27.56
Second integral order

56
475.39
Third integral order

39 802.21 354.48

Observe that the 8 of the first sum is included in the 916.37 70 of the second sum; that the 7 of the second sum is 144.50 included in the 82 of the third sum; that the 8 of the 75.34 third sum is included in the 56 of the fourth sum, and

8.88 that the 5 of the fourth sum is included in the 39 of 246.25 the fifth sum. Hence the sum of the five sums is rep$3962.01

resented by the figures 3962.01.

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* TO THE PUPIL -Remember that nothing short of absolute accuracy is of any value in such work as this.

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