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. 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? 10 Art. 60. A Proper Fraction is one whose numerator is less than its denominator; 1, ... 8 5 as, An Improper Fraction is one whose numerator is equal to or greater than the denom 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. 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? 7. How many eighths in 8? 19? 34? 8 32 2 8. Reduce 12, 1%, and 18 each to fourths. 25 each to sevenths. each to eighths. each to sixths. each to tenths. 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. 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. 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. 11 each to thirtieths. each to twenty-eighths. |