RULE. Multiplying an integer by a fraction, consists in multiplying by the numerator, and dividing the product by the denominator. 7. Multiply 45 by §. 8. Multiply 68 by t. 10. Multiply 480 by g. Ans. 333. Ans. 54. Ans. 49. Ans. 300. 11. At 16 dollars a ton, what will be the cost of of a ton of hay? Ans. 12 dollars. 12. If a village lot is worth 340 dollars, what is of it worth? Ans. 255 dollars. 13. If a hogshead of sugar is worth 75 dollars, what is 11 of it worth? Ans. 683 dollars. 14. If an acre of land produce 114 bushels of oats, how many bushels will of an acre produce? Ans. 64 bushels. 15. If a man travel 47 miles in a day, how far does he travel in of a day? CASE III. Ans. 298 miles. 99. To multiply a fraction by a fraction. 1. If a bushel of apples is worth of a dollar, what is of a bushel worth? ANALYSIS. Since 1 bushel is worth of a dollar, 1⁄2 of a bushel is worth times of a dollar; Therefore of a bushel is worth equals, and a 1⁄2 of is. of a dollar. 2. If a yard of cloth cost a dollar, how much will of a yard cost? 18 3. When oats are worth of a dollar a bushel, what is of a bushel worth. 4. If a man own of a vessel, and he sells of his share what part of the vessel does he sell? 5. At of a dollar a bushel, what will of a bushel of corn cost? OPERATION. == Ans. ANALYSIS. Since 1 bushel cost of a dollar, of a bushel will cost times of a dollar. By multiplying the numerators 2 and 3 together, we obtain the numerator 6 of the product; and by multiplying the denominators 8 and 4 together, we obtain the denominator 12 of the product, and thus we have the required product. Hence we have the following for and RULE. Multiply together the numerators for a new numerator, and the denominators for a new denominator, reduce the result to its lowest terms. OPERATION. X11X5X1= XXX=10=5 Ans. 1, 5 and ? When integers or mix ed numbers occur among the given factors, they may be reduced to improper fractions before multiplying; and an integer may be reduced to the form of a fraction by writing 1 for its denominator; thus 5=5. 18. What is the product of, and ? Ans. 19. Find the value of of multiplied by ofr OPERATION. Ans. NOTES. 1. Fractions with the word of between them are sometimes called compound fractions. The word of is simply an equivalent for the sign of multiplication, and signifies that the numbers between which it is placed are to be multiplied together. 2. When the same factors occur in both numerator and denominator of fractions to be multiplied together, they may be omitted and the remaining factors only used; thus, 5 and 3 being found in both the numerators and denominators of the above example may be omitted in multiplying. 20. Multiply of 9 by Ans. 1 of. 21. Multiply of 3 by 7 of 21. Ans. 51. 22. What is the product of, of and 11? Ans. 1. 23. What is the product of of by 51? Ans. 3. Ans. 25. What is the value of of times of 3? Ans. 2. of a bushel of Ans. of a dollar. 26. At g of a dollar a bushel, what will corn cost? 27. When peaches are worth of a dollar a bushel, what is of a bushel worth? Ans. dollar. 28. Jane having of a yard of silk gave of it to her sister; what part of a yard did she give her sister? Ans. of a yard. 29. When pears are worth of a dollar a basket, what is of of a basket worth? Ans. 30. A man owning of a ship, sold what part of the whole ship did he sell? 31. A grocer having of a hogshead of molasses sold of it; what part of a hogshead remained? 32. At g of a dollar a yard, what will be the cost of of 4285 8 yards of cloth ? Ans. 14 dollars. DIVISION. CASE I. 100. To divide a fraction by an integer. 1. If 3 pounds of raisins cost of a dollar, how much will 1 pound cost? ANALYSIS. If 3 pounds cost of a dollar, 1 pound which is of 3 pounds, will cost of, or of a dollar. Therefore, 1 pound will cost of a dollar. 2. If 4 pounds of coffee cost of a dollar, how much will 1 pound cost? 3. If 5 marbles cost of a dollar, how much will 1 marble cost? 4. If of a barrel of flour be equally divided among persons, what part of a barrel will each have? 5. If of a box of tea be equally distributed among 8 persons, what part of a box will each have? 6. Paid of a dollar for 4 pounds of butter; what was the cost per pound? FIRST OPERATION. +4= Ans. SECOND OPERATION. ANALYSIS. In the first operation we divide the fraction by 4, by dividing its numerator by 4, obtaining 3. In this case the value of the fractional +4=8 Ans.. unit is unchanged, but we diminish the number taken, 4 times. In the second operation we divide the fraction by 4, by multiplying the denominator by 4, obtaining. In this case the value of the fractional unit is diminished 4 times, but the number taken is the same. Hence, Dividing a fraction consists in dividing its numerator, or multiplying its denominator. NOTE. We divide the numerator when it is exactly divisible by the divisore oth. erwise we multiply the denominator grapes, what part of a bushel will each have? Ans. . 23. If 5 yards of sheeting cost of a dollar, what will Ans. of a dollar. 50 Ans. of a dollar. ▲ yard cost? 24. If 8 bushels of apples cost 5 dollars, what will 1 bushel cost? 25. If of 10 pounds of butter cost 14 dollars, what will 1 pound cost? Ans. of a dollar. 26. A man distributed 18 of a dollar equally among 6 beggars; what part of a dollar did he give to each ? 27. If of 9 cords of wood cost 123 dollars, what will 1 oord cost? |