Note. In solving the foregoing questions, the pupil should not be permitted to ask the question the second time. After the solution is commenced, it should not be interrupted. 76. If of an orange cost 4 cents, what will SOLUTION.-If cost 4 cents, will cost cents; of 4 cents is 2 cents. Therefore, if orange cost 4 cents, will cost 2 cents. cost? of 4 of an 77. 6 is 2 of some number; what is of the same number? 78. 20 is of some number; what is of the same number? 79. 24 is 3 times what number? 4 times what number? 80. If a man can earn 60 cents a day by working of the time, how much could he earn by working all the time? 60 is of what number? 81. There is a pole in the mud, in the water, and 6 feet out of the water; how long is the pole? How much in the water, and how much in the mud? 82. A farmer sold a horse for 63 dollars, which was of what it cost him; how much did he gain by the bargain? 1 1 51 SOLUTION. He gained. If 63 dollars are 7, of 63 dollars is of 63 dollars is 9 dollars; if 9 dollars is, 2 times 9 dollars are; 2 times 9 dollars are 18 dollars. Therefore, he gained 18 dollars. 83. A man sold a village lot for 84 dollars, by which he lost of what it cost him; how much did it cost, and how much did he lose by the sale ? 84. A man sold a cow for 27 dollars, and gained by the sale; what did the cow cost him? 85. A lady lost of her money, and then had 27 dollars remaining in her purse; how much did she lose? 6* CHAPTER VII. § 28.-1. A man being asked the age of his wife, answered, that his eldest daughter was 6 years old, and that of her age was just of the age of his wife; what was her age? of 6 is of what number? 77 7 is 2 times 2; 2 times 2 7 times 4 is 28. There 6 2. Two men, talking of their sheep, one said he had 18. Then, said the other, of mine is exactly of yours; how many had he? of 18 is of what number? 6 6 3. A drover bought a sheep for 16 dollars, and sold it again for of of the first cost; did he gain or lose by the bargain, and how much? of 16 is of what number? SOLUTION.― of 32 is 4; & is 3 times 4; 3 times 4 is 12; if 12 is 3, of 12 is; of 12 is 6; if 6 is , nine times 6 is; 9 times 6 is 54; as many times 6 as the number of times that 6 is contained in 54; 6 in 54, 9 times. Therefore, & of 32 is of 9 times 6. 12. § of 32 is § of how many times 4? 5?3? § 29.-1. 2 thirds of 9 is of how many fifths of 20 ? SOLUTION. 3 1 of 9 is 3; is 2 times 3; 2 times 3 is 6; if 6 is 3, of 6 is ; of 6 is 2; if 2 is 4, 7 times 2 is; 7 times 2 is 14; as many fifths of 20 as the number of times that of 20 is contained in of 20 is 4; 4 in 14, 32 times. Therefore, of of 32 fifths of 20. 14; 9 is Note.-3 and 2 fifths, is called a complex fraction, and is 2. of 20 is of 25 is 3. 4. 5. of 36 is 6. 7. 8. 9. of 40 is 11 of 42 is 6 3 of 50 is 10 of 60 is 0 of how many sevenths of 35? of how many ninths of 54? 45? 7 12 10. of 63 is of 4 times 64 is of how many times of of 5 times 82? 11 CHAPTER VIII. § 30.-The relative value of one part to another may, more readily, be explained by some visible representation as by means of an apple, or as represented below by lines, which may be drawn on the blackboard, and fully explained by the teacher. Note.-A whole line may be drawn on the board; underneath draw lines one half the length, and under the lines representing halves draw lines representing eighths, and sixths, &c. It would be well also for the teacher to prepare small pieces of wood, of lengths, varying to represent the different parts of a unit. 1. If you divide an apple into 2 equal parts, and take away 1 of those parts, how much of the apple will you take away ? How many halves in 1? in 11⁄2? in 2? 2 3 3! 5? 7? 81? 10? 11? 12? 2. If a yard of cloth is divided into 3 equal parts, what is one of those parts called? How many thirds in 1? 2?5? 7 } ? 12 } ? 3. If you divide an apple into 4 equal parts, and take away one of those parts, how many will be left? What part of the whole apple? How How many fourths in 1 in 3? 8? 94? 101? 112? Note. The number of parts should be written by the pupils on the black-board, so as to be seen by the entire class. Two parallel horizontal lines are the sign of equality; thus. It shows that the numbers between which it is placed are equal to each other; as 3 12, and is read 3 is equal to 12, or 3 equals 12. 4 4. If a piece of cloth be divided into 5 equal parts, what will Î of those parts be called? 2 parts? 3 parts? How many are equal to a unit? 5. If a number, or an apple, be divided into 6 equal parts, what will one of those parts be called? How many sixths 1 ? 1/1/144 6. If you had of an apple, and should divide it into 2 equal parts, what would 1 of those parts be called? What is of 7. When the numerator and denominator (see § 20) are equal, what is the value of the fraction? Answer, 1. 8. When the numerator is greater than the denom |