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Art. 59. RULES.-1. To reduce an integer to a fraction, Multiply the integer by the given le. nominator, and write the denominator under the product.

2. To reduce a mixed number to a fraction, Multiply the integer by the denominator of the fraction, to the product add the numerator, and write the denominator under the result.

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SOLUTION.-In 11 half-days there are as many days as two half-days are contained times in 11 half-days, which is 5 times. There are 5 days in 11 half-days.

3. How many pints in 14 half-pints? In 17 half-pints? In 21 half-pints?

4. How many yards in 18 thirds of a yard? In 19 thirds of a yard? In 22 thirds of a yard? 5. How many weeks in 28 sevenths of a week? 30 sevenths of a week?

6. A mason was 17 half-days in building a wall how many days did he work?

7. A boy earned 25 fourths of a dollar by selling papers: how many dollars did he earn?

8. A man walked 25 eighths of a mile in an hour: how many miles did he walk?

9. How many ones in 45? 56? 75? 84? 10. How many ones in 8? 95? 77? 98?

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Art. 60. A Proper Fraction is one whose numerator is less than its denominator; 1, ... 8

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as,

An Improper Fraction is one whose numerator is equal to or greater than the denom

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The value of a proper fraction is less than one; and the value of an improper fraction is equal to or greater than one

Art. 61. RULE.-To reduce an improper fraction to an integer or mixed number, Divide the numerator of the fraction by the denominator.

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SOLUTION.-In 2 eighths there is 1 fourth, and in 6 eighths there are as many fourths as 2 eighths are contained times in 6 eighths, which is 3. There are 3 fourths in 6 eighths.

4. How many fifths in 2 tenths? 4 tenths? 6 tenths? 8 tenths? 12 tenths?

5. How many fifths in 6 fifteenths? 9 fifteenths? 12 fifteenths? 18 fifteenths?

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7. How many eighths in 8? 19? 34?

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8. Reduce 12, 1%, and 18 each to fourths.
9. Reduce, 3, and

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each to sevenths.

each to eighths.

each to sixths.

each to tenths.

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duce to by dividing both terms by 21, the greatest number which will exactly divide each term.

NOTE. The teacher should show that the value of a fraction is not changed by dividing both of its terms by the same number.

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Art. 62. When a fraction fraction is reduced to an

equivalent fraction with smaller terms, it is reduced to lower terms.

A fraction is in its Lowest Terms when no integer except 1 will exactly divide both numerator and denominator.

Art. 63. PRINCIPLE.-The division of both terms of a fraction by the same number does not change its value.

Art. 64. RULE. -To reduce a fraction to its lowest terms, Divide both terms of the fraction by any common divisor; then diviac both terms of the resulting fraction by any common divisor; and so on, until the terms of the resulting fraction have no common divisor except 1. Or:

Divide both terms of the fraction by their greatest common divisor.

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1. How many fourths of an or

ange in 1 half? In 2 halves?

2. How many

eighths of an orange in 1 fourth? In 3 fourths?

SOLUTION.-In one fourth there are 2 eighths, and in 3 fourths there are 3 times 2 eighths, which are 6 eighths. There are 6 eighths in 3 fourths.

3. How many ninths in 1 third? In 2 thirds? 3 thirds? 4 thirds?

4. How many tenths in ? ? ?

5. How many twelfths in ? ? ? 6. Change and each to twelfths. 7. Change,, and 8. Change, 7, and 1 9. Change, 6, and 10. Change, 14, and

each to eighteenths. each to twenty-fourths.

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each to thirtieths. each to twenty-eighths.

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