FORM.-Multiplying or dividing both terms of a fraction by the same number does not change its value; hence if the terms of are multiplied by 4, and the terms of ¦ are multiplied by 3, the resulting fractions and will be equal to the original fractions, and, and have a common denominator. 12 (d.) Rule.-Multiply or divide the terms of the frac tion by any number that will make them of the same denomination. *NOTES.-1. When one denominator can be divided exactly by the other it is necessary to multiply only one of the fractions; thus, t, ; &, . 2. When both denominators cannot be divided exactly by any number, it is necessary only to write for the numerator of each fraction the product of the numerator and the denominator not its own, over the product of the denominators; thus, t, t; a and 꾾. 8. Reduce and .and.and. and . and 9. Reduce and 4.4 and 10. Reduce . and and. ‡ and . and . and §. and . and 1. 4.4 and 3. LESSON XLVIII. 1. What is of 3 inches? ANS.-One of the two equal parts into which 3 inches is divided. FORM.*-Since ONE-THIRD of 1 apple is; ONE-THIRD of 2 apples is 2 times, which is . 10. What is of 3 apples? 11. What is 3 of 4 apples? 12. What is of 5 apples? ANS.-1 apple. ANS.—11 apple. ANS.-1 apple. ANs.--2§ apples. 14. What is equal to 4 of 6 apples? 13. What is of 7 apples? FORM.* of 6 apples must equal 6 times of one apple: that is, of one apple. 15. What is of 7 pears? Of 3 pears? Of 9 pears? 16. What is of 5 pears? Of 7 apples? Of 9 oranges? FORM.-Since of 5 pears equals 5 pears equals 2 times, which are 1 17. What is 3 of 8 apples? apples? FORM.-3 of 8 apples equals 3 times 4 of 8 apples, which is 24=32 apples. *To make these formulas and questions plain to the pupils, it is necessary to illustrate them by the use of visible objects. 18. What is of 7 oranges? Of 12 oranges? Of 16 lemons? 19. What is of 3? Of 6? Of 9 of 8? Of 11? LESSON XLIX. To find the fractional part of a number. 1. What is equal to of a number? The number divided by 4. ANS. 2. What is of 8? Of 17? Of 19? Of 27 ? Of 6? 3. What is equal to of a number? . ANS.-3 times the number divided by 4. 4. What is of 7? Of 9? Of 8? Of 11? Of 13? 5. If a barrel of flour costs $6, what will 1⁄2 of a barrel cost? OPERATION. -$6×5÷7=30=$42. FORM.*— of a barrel will cost barrel; 1 barrel costs $6, therefore which is $30, equal to $43. of 5 times as much as 1· will cost ¦ of 5 times $6 6. If a box of raisins cost $5, what will of a box cost? of a box cost box? of a box? of a 7. If a pound of tea is worth 90 cents, what * A contracted formula is better after the pupil learns to understand it. will of a pound cost? of a pound? of a pound? 8. If a bushel of wheat is worth 95 cents, what is of a bushel worth? of a bushel? of a • bushel? of a bushel? SLATE AND BLACKBOARD EXERCISES. MODEL OPERATION.—3 of 9=9x3÷4=27=63 Ans. STUDY AND RECITATION.-The above exercises should be copied and completed on slate or on paper, and read as a class exercise. It should be then completed at sight from the book; after which the class should be thoroughly examined upon it. 13. What will of a barrel of flour cost, if a barrel costs $11? If a barrel costs $6? $13? $15? $9? 14. What will pound costs 20 cts.? 37 cts.? 25 cts. ? of a pound of coffee cost if a 15. If a bushel of oats is worth 72 cts., what is the worth of of a bushel? Of of a bu.? of of a bu.? of a bu.? a bu.? of a bu.? of a bu.? of a bu.? { M |