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103.

CHAPTER VIII.

COMMON FRACTIONS.

What is the name of one of the parts when a unit

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When a unit is divided into twelve equal parts, what is

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Express in figures: 1. Three-sevenths.

2. Five-ninths.

3. Seven-eighths.

4. Five-twelfths.

5. Seven-sixteenths.

6. Five-eighteenths.

7. Four-elevenths.

8. Nine-twentieths.

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Read: 1, 2, 2, 11, 78%, 24, 11, 13, 28, 28.

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104. The expression

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means:

I. Seven of the parts when a unit has been divided into nine equal parts.

II. One-ninth of seven units; for, if seven units be divided into nine equal parts, one of these parts will be seven times as great as one of the parts obtained by dividing one unit into nine equal parts.

III. The quotient of seven divided by nine.

105. In the fraction, the lower figure shows the number of equal parts into which the whole has been divided, and is therefore a divisor; but, since it shows the number of parts into which the whole has been divided, it shows the name of each part, and is therefore called the denominator.

The upper figure shows the number of these parts taken, and is therefore called the numerator.

The figure, then, above the line denotes number, the figure below the line name.

106.

The numerator and denominator are called the terms of a fraction.

107. A proper fraction is one of which the numerator is less than the denominator; as J.

108. An improper fraction is one of which the numerator equals or exceeds the denominator; as, 17:

When the numerator is greater than the denominator, more than one unit must be regarded as divided into equal parts; thus,

means that three units have been divided each into four equal parts, and that all the parts of two units and one part of the third unit are taken.

109. A mixed number is an expression consisting of a whole number and a fraction; as 4, 5.35. These expressions are read four and three-sevenths, five and thirty-five hundredths.

Every mixed number means that some entire units are taken, and the fraction of another unit.

Select the proper fractions, the improper fractions, and mixed numbers from the following expressions:

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8, 21 3, 94, 125, 7, 14, 47, 64, 15, 187, 1, 1, 51, 25. Change, 17, 63, 25, 183, §.

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14 to proper fraction represents a quantity which resented by a whole number or else by a mixed number. Thus, 224.

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For, if we suppose several units to be divided each into seven equal parts, and we take 19 of these parts, 14 (that is, 2 × 7) will make 2 units, and the five remaining parts will be five-sevenths of another unit.

111. To reduce an improper fraction to a whole or mixed number,

Divide the numerator by the denominator.

The quotient will be the whole number, and the remainder, if any, will be the numerator of the fractional part, of which the denominator is the same as the denominator of the improper fraction.

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112. A whole number or a mixed number represents a quantity which can also be represented by an improper fraction. Thus, $33 $15.

For each dollar contains 4 fourths; therefore 3 dollars contain 3 × 4 fourths or 12 fourths; which, together with the 3 fourths, make 15 fourths. Hence,

113. To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.

114. A whole number may be expressed as a fraction with any given denominator. Thus, 963.

For, as 1 unit contains 7 sevenths, 9 units contain 9 x 7 sevenths, or 63 sevenths.

A whole number may be written in the form of a fraction with 1 for a denominator. Thus, 9.

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25. Change 12 to thirds; 8 to fourths; 7 to fifths; 9 to halves; 12 to ninths; 13 to sixths; 11 to sevenths; 14 to eighths.

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21. Change 25 to 94ths; 218 to 23ds; 375 to 87ths.

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