[Let the answers be given in dollars and cents, or in shillings. 1 dollar is 100 cents. 7. If 5 bushels of corn cost 7 dollars, what is that a bushel ? 8. If a man receive 8 dollars for 6 days' work, what is that per day? 9. If 3 bushels of wheat cost 8 dollars, what will 2 bushels cost? 10. A man had 30 dollars, and gave away 3 sevenths of it; how much did he give away? 11. If 4 yards of cloth cost 10 dollars, what will 3 yards cost ? 12. If 3 barrels of cider cost 8 dollars, what will 10 barrels cost ? 13. If 7 pounds of flour cost 40 cents, what will 10 pounds cost ? 14. If 4 firkins of butter cost 26 dollars, what will 7 firkins cost? 15. If 3 men can do a piece of work in 7 days, how long will it take 1 man to do it? How long would it take 4 men ? 16. If 2 cocks will empty a cistern in 3 hours, in how long a time would l empty it? In how long a time would 7 cocks empty it? SECTION XI. A. 1. Bougit 1 half of a yard of cloth for 1 dollar and 1 half; what was that a yard ? 2. 1 and 1 half is the half of what number ?* 3. If 1 third of a yard of cloth cost 1 dollar and 3 fourths of a dollar, how much does a yard cost? * See Sect. VI. Art. A., and Sect. IX Ari. B. 4. 2 and 3 fourths is 1 third of what number? 5. If i half of a barrel of beer cost 2 dollars and I fourth of a dollar, how much will a barrel cost? 6. 2 and 3 fourths is one half of what number? 7. If 1 fourth of a box of lemons cost 3 dollars and 2 thirds of a dollar, what will a box cost ? 8. 2 and 2 thirds is 1 fourth of what number? 9. 3 and 1 half is 1 fourth of what number? 10. If i third of a barrel of pork cost 4 dollars and 1 third of a dollar, what will i barrel cost ? 11. 4 and 2 thirds is I third of what number? 12. If 1 sixth of a barrel of fish cost 2 dollars and 1 fifth of a dollar, what will a barrel cost ? 13. 3 and 2 fifths is 1 sixth of what number? 14. If 1 fifth of a barrel of salmon cost 3 dollars and 2 sevenths of a dollar, what is that a barrel ? 15. 4 and 3 sevenths is 1 fifth of what number? 16. If a man can travel 4 miles and 3 sevenths of a mile in 1 ninth of a day, how far will he travel in a whole day? 17. 5 and 3 sevenths is 1 ninth of what number? 18. 2 and 4 fifths is 1 seventh of what number? 19. 6 and 3 eighths is 1 eighth of what number? 20. 7 and 5 sixths is 1 third of what number? 21. 8 and 3 sevenths is 1 fourth of what number? 22. 5 and 3 tenths is 1 seventh of what number? 23. 8 and 5 ninths is 1 fifth of what number? 24. 9 and 4 fifths is 1 eighth of what number? 25. 6 and 4 tenths is 1 tenth of what number? 26. m and 4 ninths is 1 fifth of what number? 27. 8 and 7 tenths is 1 seventh of what number? B. 1. If 2 thirds of a barrel of beef cost 3 dollars, what does 1 third of a barrel cost? 2. 3 is 2 times what number ? * * See Sect. VI., Art. B. 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 9 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, t; 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. One third is written .. ........ Example of an apple signifies that the apple is to be cut into 7 equal parts, and that 3 parts are to be used. Let us apply an example to Plate II. refers to a square divided into 8 parts, and signifies that 5 parts are to be used. 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., and to the table, 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 fractions. See Section VIII. A. | A. 1. In 2 how many times 1 ? Ans. 4.* 3. In 2 how many times ļ? Ans. . In 6 how many times < ? 31 how many times 1 ? je 55 to an improper fraction. crator is larger than the denominator, the fraction 2. 6 is fraction. 3. 8 is 1 half. It is called a mixed number. many fifths there are in four aud 1 fifth. |