In , seven is the denominator, six is the numerator, and 6 and 7 are the terms of the fraction. Can the division be performed? 7. In a Proper Fraction the numerator is less than the denominator. ,,, are proper fractions. The value of a proper fraction is less than 1. Why? 8. In an Improper Fraction the numerator either equals or exceeds the denominator. 45 7, 1, 15, are improper fractions. 231 The value of an improper fraction equals 1 or is greater than 1. Why? 9. A Mixed Number consists of an integer and a fraction. 59, 20, 311, are mixed numbers. ORAL EXERCISES. 1. Analyze the fraction Explanation. 1. The denominator shows that the unit has been divided into 12 equal parts. 2. The numerator shows that 11 of those equal parts form the fraction. 3. The fraction is read "eleven-twelfths." 4. 11 and 12 are the terms of the fraction. 5. As dividend and divisor they denote of 11. 2. Analyze in like manner the following: 7 9 14 6 1 9 9 36 1. 3, 24, 16, 33, 8, 15, 50, 100, 10, 18, 15, 18, 44, 39. 2. 6 4 9 6 7 11 2 7 16 26 11, 20, 27, 8, 10, 31, 80, 3, 11, 11, 18, 18, 18, 20. 17 8 8 3. 11 9 2 3 7 15 15 19 24 18 35 13' 19' 43' 12' 21' 3' 91' 12' 23' 42, 40' 32' 37' 6 0 0· 3. Express by Arabic numerals: 1. Sixteen twenty-sevenths. 2. Thirteen twenty-ninths. 18, 34, 4. Twelve twenty-thirds. 8. One and 12 twentieths. 9. Two and three-ninths. 10. Nineteen and three fortieths. 11. Six sevenths. 12. Five ninths. 13. Ten fifteenths. 26. Eight twenty-firsts. 27. Eleven twentieths. 28. Five twenty-seconds. 14. Eight twenty-thirds. 29. Eight thirty-sixths. 17. Fifteen thirtieths. 32. Seven fourteenths. 21. Seven elevenths. 24. Eight twentieths. 35. Eighteen fortieths. 36. Sixteen seventeenths. 37. Seven twenty-firsts. 38. 212 tenths. 39. 101 hundredths. 25. Five thirteenths. 40. Nine and five-sixths. 4. What kind of numbers and fractions are: REDUCTION OF FRACTIONS. INDUCTIVE STEPS. 1. Express as a fraction one fourth of a dollar. 4. Write the equation, one half a dollar equal to two fourths. 5. Since, how can the terms of the fraction be changed to the terms of the fraction ? 6. How can the terms of be changed to the terms of ? 7. Multiplying in like manner by 2, what does become? 8. How can be changed back to ? 9. How can become? How can become? 2. A Common Divisor of two or more numbers exactly divides each of them. becomes by dividing both terms by their common divisor 3. 3. The Greatest Common Divisor of two or more numbers is the greatest number that exactly divides each of them. becomes } by dividing both terms by their greatest common divisor, 6. 4. When terms have no common divisor, the fraction is said to be in its Lowest Terms. ,,, are fractions in their lowest terms. PRINCIPLE. Multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction. Reduction to Lowest Terms. EXERCISES. 1. Reduce & to its lowest terms. Process. 6)36 3+% Explanation. 1. According to the principle, we must divide both terms. 2. Dividing by 6, we obtain ; dividing by 2, we obtain 3. The terms 3 and 5, having no common divisor, are the lowest terms of the fraction 36. How can be obtained from 36 by one division? What, then, is the Greatest Common Divisor of 36 and RULE. 1. Divide both terms of the given fraction, and also resulting terms, by any common divisor. 2. Continue thus to divide resulting terms until terms are found that have no common divisor; or, 3. Make a single division by using the Greatest Common Divisor of the given terms. 3. Multiplying both terms of by 8, we obtain #8, a fraction in higher terms. Hence, 좋음. |