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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.

NOTE 2.-Addition (in general) is the process of finding the sum of two or more magnitudes.

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

32. The sign, +, 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. They are given in the Werner Arithmetic, Book II., p. 273. The nine primary facts which many pupils fail to memorize perfectly are given below.

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7. In each of the above examples, tell which are addends and which is the sum.

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 ?

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Addition—Simple Numbers. 39. Find the sum of 275, 436, and 821. Operation.

Explanation. 275 The sum of the units of the first order is 12; this is 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 the 1532.

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.

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(a) Find the sum of the eight sums.

TO THE TEACHER.—Imipress 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.

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Addition-Decimals.

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

Explanation. 4.327

The sum of the units of the third decimal order is 13; 8.29

this is equal to 1 unit of the second decimal order and 3 .836

units of the third decimal order. Write the 3 units of 13.453 the third decimal order and add the 1 unit of 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 274.36, 21.37, 38.007, and .275
2. Add 78.63, 61.993, .725, and 724.64
3. Add .7,.84, .375, 0275, and .25326
4. Add .16, .625, .9725, .74674, and .3
5. Add 46.07, 14.003, 52.0006, and 28

6. Add 85.997, 47.9994, 72, and 53.93 7. Find the sum of two hundred and six thousandths, and two hundred six thousandths.

8. 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 eight sums.

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

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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 6.94

Second decimal order (cents) 81 175.89

First decimal order (dimés). 70 27.56 First integral order

82 475.39

Second integral order. 56 802,21 Third integral order

39 354.48

Observe that the 8 of the first sum is included in 916.37 144.50

the 70 of the second sum; that the 7 of the second sum 75.34

is included in the 82 of the third sum; that the 8 of 8.88

the third sum is included in the 56 of the fourth sum,

and that the 5 of the fourth sum is included in the 39 246.25

of the fifth sum. Hence, the sum of the five sums will $3962.01

be represented by the figures 396201.

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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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