MULTIPLICATION OF FRACTIONS. CASE I. 77. To multiply a fraction by an integer. 1. What is 2. What is 3. What is ORAL EXERCISES. ++? What, then, is 3 × 4? +3+3+}? What, then, is 4 X ? 4. How may we multiply a fraction by an integer? 5. What is + + expressed in its lowest terms? Ans., §. What, then, is 3 X? How may we obtain this result from? 6. In what other way, then, besides multiplying the numerator, may we multiply a fraction by an integer ? 78. Principle. Multiplying the numerator or dividing the denominator of a fraction by any number, multiplies the value of the fraction by that number. Multiplying the numerator, we have × 23 114, Ans. NOTE.-Multiplying an integer by a fraction is the same as multiplying a fraction by an integer. Thus, 7 × Cancel all common factors. = × 7. Multiply the numerators together for the numerator of the product, and the denominators for the denominator. = The word "of" between two fractions is equivalent to the sign of multiplication. Thus, of X. Such expressions are called Compound Fractions. WRITTEN EXERCISES. 2. Multiply by 5. PROCESS.× 54 = Ans. 3. Find the value of×× 11 × 13. Reduce mixed numbers to improper fractions. Cancel all common factors. 37. Multiply of 4 of 4 by § of 41 of 13. What is the cost of 38. 8 tons of coal at $53 a ton? 42. 75 pounds of sugar at 63 cents a pound? 43. 20 cows at an average price of $311⁄2 a head? 44. 24 horses at an average price of $175g a head? 45. 213 yards of cloth at $8 a yard? 46. 32 dozen of eggs at 28 cents a dozen? 47. 18 stoves at $34% apiece? 48. 16 tons of coal at $51⁄2 a ton? 49. There are 24 cubic feet in a perch of stone; how many cubic feet in 53 perches? 50. A sold of 150ğ cords of wood at $103 a cord; what did he receive for it? 51. B owns of a farm containing 1123 acres; what is the value of B's share when land is selling at $911 an acre? 52. A miller bought 2365 bushels of grain at 90 cents a bushel of it he sold at $1.10 a bushel, of it at 95 cents a bushel, and the remainder at cost; how much did he gain? 81. Principle.-Dividing the numerator or multiplying the denominator of a fraction by any number divides the value of the fraction by that number. |