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ARITHMETIC.

ARTICLE 1. ARITHMETIC is the science of numbers, and the art of computing by them.

2. A Unit is one.

3. A Number is a unit, or a combination of units.

4. A Concrete, or Denominate Number, is a number which is applied to some object or objects; as, one boy, two apples, three slate pencils, four sounds.

5. An Abstract Number is a number which is not applied to any object; as, one, two, three.

6. EXERCISE.

Name the concrete numbers in the following list:

:

Four girls; seven swans; two; ten; nine chairs; five knives; eight; twelve horses; six mules; two oxen; four; eleven; seven pond lilies; one; ten; thirteen; nine days; fifteen lessons; two rabbits; six bushels.

Name the abstract numbers in the above.

7. The fundamental operations of written Arithmetic are based upon NOTATION, and consist of ADDITION, SUBTRACTION, MULTIPLICATION, and DIVISION.

NOTATION AND NUMERATION.

8. Notation is the art of writing numbers.
Numeration is the art of reading numbers.

9. Besides being expressed in words, numbers are repre、

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sented by letters and figures. The method of representing them by letters is called the ROMAN method, because it was used by the ancient Romans. The method of representing them by figures is called the ARABIC method, because our first knowledge of it was obtained from the Arabs.

ROMAN Method.

10. The Roman Method is principally used in writing dates, and in numbering chapters and sections of books.

11. It employs seven capital letters; I representing one; V, five; X, ten; L, fifty; C, one hundred; D, five hundred; M, one thousand.

12. By combining these letters in various ways, all numbers may be expressed, the following principles being observed:

(1.) When a letter is repeated, its value is repeated.

(2.) When a letter is placed before another of greater value, its value is to be taken from that of the greater; thus, IV

denotes four.

(3.) When a letter is placed after another of greater value, its value is to be added to that of the greater; thus, VI denotes six.

(4.) When a letter is placed between two of greater value, its value is to be taken from their united value; thus, XIX denotes

nineteen.

(5.) Any letter may be made to express thousands instead of units by placing a dash over it. Thus X denotes ten thousand; D, five hundred thousand; M, one thousand thousand, or one million.

13. TABLE OF ROMAN NOTATION.

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15. Write the following in Roman characters:

1. All the numbers from one to twenty, inclusive.

2. All the numbers from thirty to forty, inclusive.
3. All the numbers from ninety to one hundred, inclusive.
4. One hundred thirty-eight.

*VIIII is sometimes used for nine.

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