148. Fractional units are named from the number of parts into which the unit is divided. Thus, is read one-sixth; +, one-seventh. Fractions are read by naming the number and kind of fractional units. Thus, is read five-sixths;, five twenty-firsts; 18, thirteen thirty-fifths. 1. Three elevenths. Five thirteenths. Eight twentyfirsts. 2. Forty-eight fiftieths. Twenty-seven eighty-fifths. 3. Sixty forty-eighths. Fifty-seven ninety-ninths. 4. Forty-two eighty-sevenths. Thirty-nine ninety-thirds. 5. Seventy-four one-hundredths. Ninety-seven one-hundred-fifths. 6. Fifty-two seventy-eighths. Thirty-six eighty-fourths. 7. Two hundred three-hundred-ninetieths. 8. Seven hundred seventy-one eight-hundred-sixtieths. 12. Four thousand six hundred thirty five-thousandths. Fractions are classified with reference to the relation of numerator and denominator thus: 150. A Proper Fraction is one in which the numerator is less than the denominator. Thus, &, §, 1, etc., are proper fractions. The value of a proper fraction is therefore less than 1. 151. An Improper Fraction is a fraction in which the numerator equals or exceeds the denominator. Thus, 1, 3, 14, are improper fractions. The value of an improper fraction is therefore 1 or more than 1. 152. A Mixed Number is a number expressed by an integer and a fraction. Thus, 23, 51, are mixed numbers. Mixed numbers are read by naming the fraction after the whole number. Thus, 23 is read two and three-fourths. Fractions may be regarded as expressing unexecuted division. Thus, 16 is equal to 168; 15 is read 15÷3. 153. 1. Interpret the expression 4. ANALYSIS.- represents 5 of 7 equal parts into which any thing is divided. It also represents one-seventh of five, and 5 divided by 7. It is read five-sevenths. 154. To reduce fractions to larger, or higher terms. 1. In of an apple how many fourths are there? How many eighths? 2. How many sixths are there in How are the terms of the fraction ? from ? ? How many ninths? obtained from those of 3. How many eighths are there in 4? How many twelfths? 4. How do the terms of the fraction compare with the terms of the fraction 1? 5. In what equivalent fraction can be expressed? 6. How do the terms of the fraction compare with those of?? 16 7. How are the terms of the fraction obtained from those of? 8. How are the terms of the fraction 9. How are the terms of the fraction obtained from ? obtained from ? 10. What then may be done to the terms of a fraction without changing the value of the fraction ? 155. Reduction of Fractions is the process of changing their form without changing their value. 156. A fraction is expressed in Larger or Higher Terms when its numerator and denominator are expressed by larger numbers. 157. PRINCIPLE.-Multiplying both terms of a fraction by the same number, does not change the value of the fraction. WRITTEN EXERCISES. 1. Change to forty-fifths. PROCESS. 45÷15-3 7 X3 21 15 X 3=45 ANALYSIS. Since there are 45 forty-fifths in 1, in there are 3 forty-fifths; and in there are 7 times, or 2; or, Since the denominator of the required fraction is 3 times that of the given fraction, we must multiply the terms of the fraction by 3. RULE.-Multiply the terms of the fraction by such a number as will change the given denominator to the required denominator. 158. To reduce fractions to smaller, or lower terms. 1. How many fourths are there in ? How many in ? 2. How many thirds are there in ? How many in? 3. How does the number of eighths of any thing compare with the fourths? Thirds with sixths? Halves with eights? 4. How do the terms of the fraction compare with those of? How with those of 4? 5. How do the terms of the fraction compare with those of? How with those of? 6. How are the terms of the fraction obtained from those of the fraction? How from those of 4? 7. How are the terms of the faction obtained from ? 8. What then may be done to the terms of a fraction without changing the value of the fraction? 9. Express,,, in smaller or lower terms. 159. A fraction is expressed in Smaller, or Lower Terms when its numerator and denominator are expressed in smaller numbers. 160. A fraction is expressed in the Smallest, or Lowest Terms when its numerator and denominator have no common divisor. 161. PRINCIPLE.-Dividing both terms of a fraction by the same number does not change the value of the fraction. Since fractions are in their smallest terms when their numerator and denominator have no common divisor, to reduce them to their smallest terms we may divide both terms by their greatest common divisor. RULE.-Divide the numerator and denominator by any common divisor, and continue to divide thus until the terms have no common divisor, Or, \ Divide both terms by their greatest common divisor. 2. Reduce 16 40 24 64 30' 809 to their smallest terms. 120, to their smallest terms. 3. Reduce 32. 96 21 33,108, 23, 144, |