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 writ ing fractions 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 called an improper fraction. See Key. 2% 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. 13. Reduce 63 to an improper fraction. 14. Reduce 8,3 to an improper fraction. 15. Reduce 94 to an improper fraction. 1. A man sold 8 yards of cloth for 3 dollars à yard; what did it come to ? 2. A man sold a horse for 76 dollars, which was g of what it cost him; how much did it cost him? 3. A man sold of a gallon of wine for 40 cents; what was that a gallon? 4. If it will take 17 yards of cloth to make a coat, how many yards will it take to make 7 coats? 5. If 1 horse consume 34 bushels of oats in 2 days, how much would 2 horses in 5 days? 6. If when the days are 94 hours long a man perform a journey in 10 days, in how many days would he perform it when the days are 12 hours long? 7. A man sold 8 yards of cloth for 73 dollars a yard, and received 8 firkins of butter at 63 dollars a firkin; how much was then due to him? 8. Two men are 38 miles apart, and are travel ing towards each other, one at the rate of 3 miles an hour, the other 2 miles; how much do they approach each other in an hour? How much in 2 hours? In how many hours will they meet? At what distance from each place from which they set out? SECTION XIII. A. 1. If you give of an orange to one boy, and to another, how much more do you give the first, than the second? 2. of an orange is how many of an orange? 3. If you give of an orange to one boy, and to another, how many would you give away How many would you have left? 4. and are how many? ? 5. A man gave to one labourer of a bushel of wheat, and to another; how many of a bushel did he give to both? How many bushels? 6. and are how many? How many times 1? 7. A man gave of a barrel of flour to one man, and of a barrel to another; to which did he give the most? 8. is how many ? 9. A man bought time, and of a bushel of wheat at one of a bushel at another; at which time did he buy the most? 10. is how many? 11. A man bought of a yard of cloth at one time, and of a yard at another; at which time did he buy the most? 12. are how many? 13. A man wished to give of a bushel of wheat |