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Copy the numbers in lines 13 to 22 inclusive and add; then add the columns numbered 23 to 30 inclusive:

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Proceed in the same way for lines numbered 31 to 45 inclusive, and for columns numbered 46 to 53 inclusive:

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25. Addition of Larger Numbers. You have learned how to add numbers of more than two figures, and the directions given on page 12 for adding two-figure numbers apply to all cases.

2936 8798

14 sum of units

12 sum of tens

Thus, to add 2936 and 8798 we might proceed as shown in the left-hand solution, but the process shown in the right-hand solution is bet

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ter because it is shorter and
allows the work to be per-
formed more rapidly.

2936

8798

11734

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21. Recently we had 9196 steamers and 12,831 other American vessels engaged in trade along our coast. What was the total number?

22. In our country there were reported as built recently in one year 147 sailing vessels, 674 steam vessels, 62 canal boats, and 274 barges, not counting many smaller boats. What was the total of those reported?

23. In a recent year our country sold abroad $32,305,412 worth of manufactured cotton, and $2,287,936 worth of manufactured wool. What was the total value?

The following table shows certain statistics relating to our country in 1800, and the increase in 100 years. Add the increase to the column for 1800 and find the statistics for 1900.

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26. Addition of United States Money. In adding United States money simply proceed as with ordinary integers, keeping units of the same order in the same column as here shown.

$12.50 0.75

23.

1.05

$37.30

We can easily keep the units of the same order in the same column by placing the decimal points under one another.

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CHAPTER III

SUBTRACTION OF INTEGERS

27. Subtraction. The process of finding what number must be added to one of two numbers to make the other, or of taking one number from another, is called subtraction.

28. Symbol. The symbol of subtraction is a short horizontal line,. It is read minus, a word meaning less.

Thus 17-98 is read " 17 minus 9 equals 8."

29. Terms. The smaller of the two given numbers in subtraction is called the subtrahend; the larger one is called the minuend; the result of the subtraction is called the remainder or difference. To check the result, add the subtrahend and remainder; the result should be the minuend.

468 minuend 143 subtrahend 325 remainder

30. The Addition Method of Subtraction. This method, also called the Austrian or making-change method, is recommended in the New York State Syllabus. It consists simply in finding, in the case of 468 - 143, what must be added to 143 to make 468. We proceed as follows: 3+5=8; 4+2 = 6; 1+ 3 = 4.

31. The Taking-away Method. familiar method of subtraction. 4 from 6, 2; 1 from 4, 3.

This is, at present, a more
Here we say: 3 from 8, 5;

Of the two methods the first is always used in making change, it is the more rapid when thoroughly learned, and it is growing in favor. When a pupil has already acquired one method, however, and works rapidly and accurately, it is not good policy to attempt to change it.

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