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149. A Fraction is a number expressing one or more of the equal parts of a unit.

150. A Fractional Unit is one of the equal parts into which a unit is divided.

The number of these parts indicates their name. Thus,
One divided into two equal parts = 2 halves. One half is written.

One divided into three equal parts = 3 thirds.
One divided into four equal parts = 4 fourths.
One divided into five equal parts = 5 fifths.
One divided into six equal parts = 6 sixths.
One divided into seven equal parts = 7 sevenths.
One divided into eight equal parts = 8 eighths.
One divided into nine equal parts = 9 ninths.
One divided into ten equal parts = 10 tenths.

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When we express nine tenths thus, 10, it is called a Common Fraction; but when thus, .9, it is called a Decimal Fraction. Hence,

With reference to the mode of expressing them, Fractions are of two kinds, namely: Common and Decimal. (See page 81.)

A fraction is expressed by two numbers, one written under the other, with a horizontal line between them.

151. The Terms of a fraction are the two numbers used to express it, and are called the Denominator and the Numerator.

152. The Denominator is that term of the fraction which indicates the number of equal parts into which the unit is divided, and is written below the horizontal line.

153. The Numerator is that term which indicates the number of equal parts taken, and is written above the horizontal line. Thus, in the fraction, the 3 is the denominator, and signifies that a unit is divided into three equal parts; the 2 is the numerator, and signifies that two of these parts (thirds) are taken, or expressed.

Fractions are read by first pronouncing the number in the numerator, and then the parts of the unit expressed by the denominator. Thus is one half;, two thirds; 1, four twenty-firsts; 2, seven thirty-seconds.

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1. Four ninths.

2. Six twenty-firsts.

3. Five eighteenths.

4. Seven thirty-seconds.
5. Eight twelfths.
6. Nine twenty-fifths.
7. Two nineteenths.
8. Eight elevenths.

9. Eleven fifteenths.

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숲, 춤, 중, 흉, 8, 꿍,

10, 11, 12, 18, 14, 18,

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| 10. Nine one-hundred-thirds.
11. Two three-hundred-fortieths.
12. Five two-hundredths.

13. One four-hundred-thirteenth.
14. Three three-hundred-firsts.

15. Seventy eightieths.
16. Nineteen ninetieths.
17. Four ten-thousandths.
18. Two hundred-thousandths.

In reference to their value, fractions are of two kinds, namely: Proper and Improper.

154. A Proper Fraction is one whose numerator is less than its denominator; as, है, .

Such a fraction is called proper because its value is less than a unit, and is, therefore, properly expressed in a fractional form.

155. An Improper Fraction is one whose numerator equals or exceeds its denominator; as, 물, 은.

Such a fraction is called improper because its value equals or exceeds a unit, and, therefore, the proper expression for its value would be an integer or a mixed number.

EXERCISES.

Of the following fractions, name the class to which each belongs.

춤,,,목, 꽃, 목, 103, 수분, 183, 10,

13,1층, 위, 113, 14, 19, 14, 18, 1876

A Mixed Number is one expressed by an integer and a fraction; as, 4,9.

In reading a mixed number, and belongs between the integer and fraction. Thus, 41 is read 4 and.

In reference to their form, fractions are of three kinds, namely, Simple, Complex, and Compound.

156. A Simple Fraction is one whose terms are whole numbers; as, 8, 1.

157. A Complex Fraction is one which has a fraction in one or both of its terms; as,

158. A Compound Fraction is a fraction of a fraction; as, & of, which may also be written thus, & × 1.

In reference to their fractional unit, fractions are of two kinds, namely: Similar and Dissimilar.

159. Similar Fractions are those that have like fractional units; as, &, ;

160. Dissimilar Fractions are those that have

unlike fractional units; as, &, ;,, 8.

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If we multiply the numerator of tional unit in and is the same, 4. units as . x 2 = . Again,

If we divide the denominator of by 2, we obtain. The number of fractional units in and is the same, 2. But the value of the

by 2, we obtain . The frachas 2 times as many fractional

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