The pupil must carefully commit all the definitions on page 77, before he commences mental operations. 1. If an apple be divided into two equal parts, one of those parts is called a half, and is written thus, . 2. If an apple be divided into three equal parts, one of those parts is called a third, and is written thus, . 3. Two of those parts are called two thirds, and are written thus, . 4. If an orange is divided into four equal parts, one of those parts is called a quarter, and is written thus, . Two of those parts are called two fourths, and are written thus,, or thus, . 5. Three of those parts are called three quarters, and are written thus, 2. 6. One is what part of two? 7. One is what part of three? Ans.. Ans.. Ans.. 8. One is what part of four? Ans. . What part of 5? 9. Two is what part of 3? 10. What part of 5 is 2? Is 7? Is 3? Is 4? Is 6 ? 11. What part of 7 is 2? Is 3? Is 5? Is 6? 12. What part of 11 is 4? Is 5? Is 6? Is 7? 13. What part of 19 is 5? Is 11? Is 13? Is 17? 14. When corn is 7 shillings a bushel, what part of a bushel could you buy for 1s.? For 2s.? For 5s. ? 15. When flour is $9 per barrel, what part of a barrel could be bought for $2? For $3? For $7 ? 16. If of a barrel of flour cost $2, what will What will? What will? What will ? 17. If of a cwt. of sugar cost $14, what will cost ? 18. What will f cost? 우? ? 뭐? 우? 구? 19. If of a pound of tea cost 35 cents, what will cost??? $? ft ? ? 20. If 11 cost? of a yard of cloth cost 30 cents, what will cost?3? T3? 13? 73 ? t?? 21. If of an acre cost $28, what will cost? What will an acre cost? 22. If & of a share in a railroad be worth $ 36, what is worth? What is the value of a whole share? 23. When of a share in a factory cost $60, what is the value of? What is the value of a whole share? 24. Gave $21 for of a yard of broadcloth, what cost + of a yard? What cost a yard? 25. Webster paid $8 for & of a chest of tea what would of a chest cost? What would 1⁄2 of a cost? What of a cost? 26. When of a ton of iron is sold for $32; what is the cost of? Of of? Of of? 27. Peter Jones paid $16 for of an ox; what cost of the ox, and what did Richard Martin pay for of a? What did S. Ayer pay for a of a? 28. Paid John Atwood $ 128 for of his farm; what is the value of, and what must J. Kimball pay for ? What is the value of the whole farm? of a 29. D. Webster bought of a saw mill, for which he paid $300. What was the value of the whole mill ? What is the value of of the mill? of 4 of 4 ? Of of ? Of † 30. 15 is of what number? Is? Is? Is it? 31. 21 is 32. 30 is ? of what number? Is 3? Is? Is of what number? Is ? Is g? Is 6? of what number? Is ? Is ? Is ?? of what number? Is? Is? Is ? of what number? Is? Is? Is 2% ? 36. Samuel Page sold a pair of oxen for $48, which was of their cost. What did he lose? 33. 14 is 34. 12 is 35. 18 is 37. Bought a horse for $72, which was of his real value; what did I gain? 38. 72 is of what number? 39. Sold a quantity of depreciated money for $81, which was of its nominal value; what was the sum sold? 40. Having improved a chaise 15 years, it was sold for $25, which was only of what it cost. What was the original price? 41. A Loafer shot at a flock of pigeons on a tree, and killed 24, which was of the number. pigeons will remain on the tree? How many Section 20. VULGAR FRACTIONS. FRACTIONS are parts of an integer. VULGAR FRACTIONS are expressed by two terms, called the Numerator and Denominator; the former above, and the latter below a line. Thus ; Numerator. The Denominator shows into how many parts the integer, or whole number, is divided. The Numerator shows how many of those parts are taken. 1. A proper fraction is one whose numerator is less than the denominator, as §. 2. An improper fraction is one whose numerator exceeds, or is equal to, the denominator; as 1 or §. 3. A simple fraction has a numerator and denominator only; as, Y. 4. A compound fraction is a fraction of a fraction, connected by the word of; as of 3 of 8 of 2. 5. A mixed number is an integer with a fraction; as 7161, 58. 6. A compound mixed fraction is one whose numerator or denominator, or both, is a mixed number; as 7초 11' or 44 7 7. The greatest common measure of two or more numbers is the largest number, that will divide them without a remainder. 8. The least common multiple of two or more numbers is the least number, that may be divided by them without a remainder. 9. A fraction is in its lowest terms, when no number but a unit will measure both its terms. 10. A prime number is that which can be measured only by itself or a unit; as 7, 11, and 19. 11. A perfect number is equal to the sum of all its aliquot parts; as 6, 28, 496, &c. 12. A fraction is equal to the number of times the numerator will contain the denominator. 13. The value of a fraction depends on the proportion, which the numerator bears to the denominator. I. To find the greatest common measure of two or more numbers; that is, to find the greatest number that will divide two or more numbers. 1. What is the common measure of 84 and 132; that is, what is the largest number, that will divide both of these numbers without a remainder ? Ans. 12. vide 48 and 132 without a remainder. It is, therefore, its greatest common measure. Hence the following RULE. Divide the greater number by the less, and if there be a remainder, divide the last divisor by it, and so continue dividing the last divisor by the last remainder, until nothing remains, and the last divisor is the greatest common meas ure. If there be more than two numbers, find the greatest common measure of two of them, and then of that common measure and the other numbers. If it should happen, that 1a is the common measure, the numbers are prime to each other, and are incommensurable. 2. What is the greatest common measure of 85 and 95 ? 3. What is the greatest common measure 168 ? 4. What is the greatest common measure 121? 5. What is the largest number that will 586 ? 6. What is the largest number that will 684 ? 7. What is the greatest common measure Ans. 5. of 72 and Ans. 24. of 119 and Ans. 1. divide 324 and Ans. 2. divide 582 and Ans. 6. of 32 and 172 ? Ans. 4. 8. What is the largest number that will divide 84 and 1728 ? Ans. 12. 9. What is the greatest common measure of 16, 20, and 26 ? Ans. 2. 10. What is the greatest common measure of 12, 18, 24, and 30? II. To reduce fractions to their lowest terms. Ans. 6. NOTE. A fraction is said to be in its lowest terms, when no number but a unit will divide its numerator and denominator. 1. Reduce to its lowest terms. OPERATION. We find by the last Rule, that 5 is 5) Ans. the largest number, that will divide both the numerator and denominator of the fraction; and having divided them both by it, we |