7. A man sold a cow for 21 dollars, which was only seven tenths of what she cost him; how much did she cost him? When he bought her, he paid for her with cloth at 8 dollars a yard; how many yards of cloth did he give? 8. 21 is 7 tenths of how many times 8? 9. A man, being asked the age of his youngest son, answered, that the age of his eldest son was 24 years, which was 3 fifths of his own age; and that his own age was 10 times as much as that of his youngest son; what was his age? and what was the age of his youngest son? 10. 24 is 3 fifths of how many times 10? ina 1. A boy gave away 4 cents, which was 1 79 all he had; how many had he at first? 80. boy gave 5 apples to one of his companion 76 ARITHMETIC. [PART which was 1 fourth of what he had; how ma 3. A man paid away 4 dollars, which was 2 thirds of all the money he had; how much had he? 4. A man sold a watch for 18 dollars, which was 3 fourths of what it cost him; how much did it cost? 5. A man sold a cow for 15 dollars, which was 3 fifths of what the cow cost; how much did he lose by his bargain? 6. A man bought 12 yards of cloth, and sold it for 54 dollars, which was 9 eighths of what it cost him; what did it cost him a yard? and how much did he gain by his bargain? 7. There is a pole standing in the water, so that 10 feet of it is above the water, which is 2 thirds of the whole length of the pole; how long is pole? 8. There is a pole two thirds under water, and 4 feet out; how long the pole? 9. There is a pole two fifths under water, and 6 feet out of the water; how long is the pole? 10. There is an orchard, in which 3 sevenths of the trees bear cherries, and 2 sevenths bear peaches, • and 10 trees bear plums; how many trees are there in the orchard? and how many of each sort? 11. There is a school, in which 2 ninths of the boys learn arithmetic, 3 ninths learn grammar, 1 ninth learn geography, 1 ninth learn geometry, and 12 learn to write; how many are there in the school? and how many attending to each study? 12. A man sold a watch 63 dollars, which was 7 fifths of what it cost him; how much did he gain by the bargain? 19. ninths of 36 is 8 tenths of how many times 20. 3 fourths of 40 is 5 sevenths of how many imes 8! 21. 6 ninths of 45 is 3 fifths of how many times 7? 22. 5 sixths of 48 is 10 sevenths of how many times 3? 23. 4 sevenths of 63 is 6 fifths of how many times 8? 24. 5 ninths of 72 is 4 sevenths of how many times 9? B. 1. 4 fifths of 15 is 6 tenths of how many thirds of 21? 2. 4 thirds of 18 is 8 ninths of how many sevenths of 35! 3.6 sevenths of 21 is 2 thirds of how many thirds of 24? 4. 5 fourths of 24 is 10 sevenths of how many fifths of 40 ? 5. 5 eighths of 32 is 2 fifths of how many fifths of 35? 6. 4 sevenths of 63 is 6 eighths of how many ninths of 45? 7.3 sevenths of 56 is 4 ninths of how many fourths of 28? 8. 3 eighths of 64 is 6 tenths of how many sixths of 30? 9. 2 eighths of 72 is 3 tenths of how many fifths of 40? . 1. Two times eleven are how many Two times twelve are how many? inate wo times thirteen are how many ? 79. Rtimes fourteen are how many? 80. Redues fifteen are how many? 76 whi had of 3 6. Two times sixteen are how many? 7. Two times seventeen are how many! 8. Two times eighteen are how many? 9. Two times nineteen are how many? 10. Two times twenty are how many? 11. Three times eleven are how many? 12. Three times twelve are how many? 13. Three times thirteen are how many? 14. Three times fourteen are how many? 15. Three times fifteen are how many? 16. Three times sixteen are how many? 17. Three times seventeen are how many? 18. Three times eighteen are how many? 19. Three times nineteen are how many? 20. Three times twenty are how many? 2. Four times eleven are how many? 22 Four times twelve are how many 8. Four times thirteen are how many? 24. Four times fourteen are how many? 25. Four times fifteen are how many? 26. Four times sixteen are how many? 27. Four times seventeen are how many? 28. Four times eighteen are how many? 29. Four times nineteen are how many? 30. Four times twenty are how many? 31. Five times eleven are 32. Five times twelve are how many? how many 33. Five times thirteen are how many? 34. Five times fourteen are how many? 35. Five times fifteen are how many? 36. Five times sixteen are how many? 37. Five times seventeen are how many? 38. Five times eighteen are how many? 39. Five times nineteen are how many? 40. Five times twenty are how many? 41. Six times eleven are how many? 42. Six times twelve are how many? ? 67. and 68. less 69. less less, are how many? are how many? 70. less are how many? 71. 1, and, and, and, less §, are how many 24? 72., and, and, and, and, less, are how many? 73. and & are how many? 74. and are how many? 75. and are how many? When the denominators in two or more rac tions are the same, the fractions are said to have a common denominator. Thus and g have a common denominator. We have seen that, when two or more fractions have a common denominator, they may be added and subtracted as well as whole numbers. We add or subtract the numerators, and write their sum or difference over the common denominator. The first part of the process in the above examples was to reduce them to a common denominator. 76. Reduce and to a common denominator. NOTE. They may be reduced to twelfths. If it cannot be immediately seen what number must be the common denominator, it may be found by multiplying all the denominators together; for that will always produce a number divisible by all the denominators. 77. Reduce and to a common denominator. 78. Reduce and 2 and to a common denominator. 79. Reduce and to a common denominator. 80. Reduce and to a common denominator. |