86. RULES.-1. To reduce a fraction to higher terms, Divide the given denominator by the denominator of the fraction, and multiply both terms by the quotient. 2. To reduce fractions to the least common denominator, Divide the least common multiple of the denominators by the denominator of each fraction, and multiply both terms by the quotient. Case V. Compound Fractions reduced to Simple Fractions. 93. How much is 1 half of 1 third of a pear? 1 half of 1 fourth of a pear? 94. A father divided 1⁄2 of a pine-apple equally between 3 boys: what part of the pine-apple did each boy receive? 95. What is of ? of? of !? 106. Reduce of of 71⁄2 to a simple fraction. 87. RULES.-To reduce a compound fraction to a simple fraction, 1. Multiply the numerators together for a numerator, and the denominators together for a denominator. Or, 2. Indicate the continued multiplication of the numerators, and also of the denominators, and reduce the resulting fraction to its lowest terms by cancellation. REVIEW PROBLEMS. 115. Reduce 16 to a fraction having 8 for a denominator. 116. Change 35÷21 to a fraction in its lowest terms. 117. How many 15ths of a gallon in 33 gallons? 118. Reduce 304 to a mixed number with the fraction in its lowest terms. 119. Reduce $19, $137, $455, and $100 each to whole or mixed numbers. 120. Reduce, 7%, and 1 each to 30ths. 121. Reduce 12, 183, and 33 5 each to 12ths. 122. Reduces of of 2 of 24 to a simple fraction. 123. Reduce, , and to a common denominator; to the least common denominator. 124. Reduce, 5, and of to their least common denominator. SUGGESTION.-First reduce 5 and of to simple fractions. 125. Reduce, of, and 4 of 63 to their least common denominator. 126. Reduce of 21, of 3, and of of 64 to their least common denominator. 127. Reduce of 3, 5 of 2%, and of 13! to their least common denominator. 128. Reduce, 4 of 54, 24 of 3, and 2 to their least common denominator. ADDITION OF FRACTIONS. 1. A clerk spends of his salary for board, of it for clothing, and for other expenses: what part of his salary does he spend? 2. How many ninths in 3, 5, and †? 3. A man traveled of his journey the first day, and of it the second day: what part of the journey did he travel in the two days? 4. How many twelfths in and ? and ? 5. A owns of a vessel, and B 3 of it: what part of the vessel do both own? 6. What is the sum of and ? and ? SUGGESTION.-First add the fractions and then the integers. 10. Show that fractions having a common denominator, express like fractional units, and that only like fractional units can be added. WRITTEN PROBLEMS. 11. What is the sum of 3, 28, and ? 16 23' 23' 14. What is the sum of 141 23 45 160 97 160, 160, and 138? 15. What is the sum of 12, and 11? 8, Since unlike fractional units can not be added, reduce the fractions, 2, and to a common denominator, and then add the resulting fractions. 27. Add of, 3 of 5 of 21, and 7. 28. Add of 21, 2 of 3, and 3 of 3 of 6. 4 29. Add of 5, and of of §. 3 30. Add of 2, 3 of §, 1⁄2 of ‡ of 11⁄2, and 31⁄2. 31. Add 33, 371⁄2, 554, and 663. The sum of 331, 371, 55, and 663, equals the sum of } + + + added to the sum of 33 +37+55+66. +++3=212 or 24. Write the under the fractions and add the 2 with the integers. The sum is 1931 32. Add 391, 563, 88, and 104,. 33. Add 45, 87, 66, and 75. 34. Add 12, 163, 183, 301, 331, and 62. 35. Add, of 3, 163, and 48. 36. Add $5.121, $3.183, $8.25, and $3.811. 37. Add, 4, 4 of 54, and 65. 3 3 7 38. Add ,,,, and of 2%. 3, PRINCIPLES AND RULES. 88. PRINCIPLES.-1. Only like fractional units can be added. Hence, 2. Fractions must have a common denominator before they can be added. 89. RULES.-1. To add fractions, Reduce the fractions to a common denominator, add the numerators of the new fractions, and under the sum write the common denominator. 2. To add mixed numbers, Add the fractions and the integers separately, and combine the results. NOTES.-1. Compound fractions must be reduced to simple fractions before they can be added. 2. When mixed numbers are small they may be reduced to improper fractions and then added. SUBTRACTION OF FRACTIONS. 1. A boy spent of his money for a slate: what part of his money has he left? 2. How much is 3. How much is 4. A bought less? 11 less? less 12? of a bushel of clover seed and sold of a bushel to B: what part of a bushel has A left? 10. 51 less 31? 11. Why can not less? less? 63 less 4? 93 less 7? 121 less 61? be subtracted from without first re ducing the fractions to a common denominator? less g? 49 13. Subtract 37 from 6; 33 from ; 42 from 909 14. Subtract from 13. 85 PROCESS: -788-1343, Ans. |