4. A cask of wine cost 67 dollars; what is 5 eighths of it worth ? 5. A man bought 9 oranges for 6 cents and 2 sevenths apiece, and sold them for 67 cents; what did he gain by the bargain ? 6. A man bought 10 yards of broadcloth for 70 dollars; how must he sell it per yard in order to gain 14 dollars ? 7. If when the days are 12 hours long, a man perform a journey in 3 days, how many hours is he in performing it? 8. If a man perform a journey in 36 hours, how many days would he be in performing it when the days are nine hours long? 9. If when the days are 11 hours long, a man can perform a journey in 5 days, in how many hours will he perform it? In how many days when the days are 9 hours long? 10. What number added to 2 fifths of 33, will make the number 17? 11. How many yards of cloth, that is 1 quarter of a yard wide, will line 10 yards, that is 3 quarters wide? 12. 8 yards of cloth that is 1 quarter wide are equal to how many yards that is 4 quarters wide? 13. How many yards of cloth, that is 3 quarters wide, are equal to 7 yards that is 5 quarters wide? 14. How many yards of cloth, that is 6 quarters wide, are equal to 37 that is 4 quarters wide ? 15. If a piece of cloth. 5 quarters wide, be worth 37 dollars, what is a piece of the same length, 3 quarters wide, worth? 16. If cloth 4 quarters wide is worth 8 dollars a yard, what is 1 yard of the same kind of cloth, that is 5 quarters wide, worth? SECTION XII. PARTS of one are called fractions. Fractions may be expressed by figures, as well as whole numbers. It requires two numbers to express a fraction; one to show into how many parts one is divided, and the other to show how many of those parts are used. For example, if we wish to express one half, (which means that one is divided into two equal parts, and that one part is used,) we must use the figure 2 to express that one is divided into two equal parts, and the figure 1 to show that one part is used. And these must be written in such a manner that we may always know what each of them is intended to express. One half is usually written thus, ; one number above a line, and the other below it. The number below the line shows into how many parts one is divided, and the number above the line shows how many parts are used. Example. of an apple signifies that the apple is to be cut into 7 equal parts, and that 3 parts are to be used. Illustrate by a line, divided into 7 equal parts, and three of the parts taken.. In the same way illustrate the meaning of the fractions, †, %. We may observe, that, when one is divided into 3 parts, the parts are called thirds; when one is divided into 4 parts, the parts are called fourths, &c. that is, the fraction takes its name from the number of parts into which one is divided. The number under the line is called the denominator, because it gives name to the fraction; and the number above the line is called the numerator, because it shows the number of parts used. Thus, 10 is the denominator and 3 the numerator. N. B. The pupil must be made familiar with this mode of expressing fractions, and must be able to apply it to any familiar objects; as apples, oranges, &c.; or by blackboard, before he is allowed to proceed any farther. Particular care must be taken to make him understand what the denominator signifies, and what the numerator, as explained above. The denominator should always be explained first. The following examples are a recapitulation of some of the foregoing sections, for the purpose of showing the application of the above method of writing fraction Having analyzed the question, the pupil may write the required fraction on the blackboard. See Section VIII. A. A. 1. In 2 how many times?* 2. In 3 how many times? 3. In 2 how many times? 4. In 4 how many times? 5. In 6 how many times 6. In 7 how many times? 7. In 8 how many times? 8. In 2† how many times ? 9. In 3 how many times ? 10. Reduce 4 to an improper fraction. 11. Reduce 34 to an improper fraction. 12. Reduce 5 to an improper fraction. When the numerator is larger than the denominator, the fraction is ealled an improper fraction. See Key. t2% is read two and 1 half. It is called a mixed number. That is, to find how many fifths there are in four and 1 fifth. First and how many fifths there are in 4. |