223. Multiply 398 by 75. 224. Multiply 125 by 80. 221. Multiply 40 by 27. 8 222. Multiply 813 by 63. 225. What will 72 barrels of St. Louis flour cost at $8§ à barrel? An Integer multiplied by a Fraction. ORAL EXERCISES. 226. If a bushel of corn costs 64 cents, what will of a bushel cost? of a bushel? 227. If a pound of tea costs 60 cents, what will of a pound cost? of a pound? 228. What is of 4? of 4 is 4, and 4 of 4 must be 5 times 4, or 20, equal 229. What is of 8? # of 3? of 5? § of 10? 230. What is the cost of of a cord of wood at $6 a cord? What is $6 multiplied by ? 129. Principle. Multiplying a number by a fraction is taking such a part of the number as is denoted by the fraction. 245. What cost 25 acres of land at $ 50 an acre? A Fraction multiplied by a Fraction. ORAL EXERCISES. 246. What part of a dollar is of of a dollar? } of of a dollar? 247. What part of a dollar is of of a dollar? of of a dollar? 248. What is of ? of? 249. What is of ? of? 250. How much is of ? of? ↓ of } ? of ? of 1 of 1 = 16 1 of 2 = 1% 2 of 2 = 16 Solution.of is, and of is 3 times, equal to This, also, appears by the illustration. 251. 3 × 3 = ? 3 × = ? 252. 253. 254. Give the product of each pair of fractions in Exercises 150 to 153. 130. A Compound Fraction is a fraction of a fraction, as of, and may be considered an expression of multiplication. A Simple Fraction is a fraction not connected with another, and having both its terms integers. of i; of is, and off is 5 times, equal to 18, or 35. NOTE.- By cancellation we may shorten the process, as shown in the second form of the work. 256. Multiply 18 by 11; 15 by 2. 131. Rule for Multiplication of Fractions. Write the product of the numerators over the product of the denominators. NOTE. The rule is general, since a mixed number may be changed to an improper fraction, and an integer may be expressed in a fractional form. 257. Multiply 3 by 27. 258. Multiply 8 by 88. 259. Multiply 367 by 7. 260. Multiply by 3 of fr 263. What is the value of 2 of § of 3} ? 264. What is the value of 2× × ×? 265. What cost 113 cords of wood at $75 a cord? 268. What is the product of of 8% multiplied by of 94? 269. What will 5% tons of hay cost at $21 a ton? 270. If a man walks 4 miles in an hour, how can he walk in of 3 hours? many miles changed; and that multiplying the denominator by 2 halves the size of the fractional units, while the number remains unchanged. Either process divides the fraction by 2. by 11. 272. What is fo divided by 3? 1 by 5? 273. Divide by 7; 14 by 9; 3 by 7; 274. Divide the fractions in Exercises 99 to 3; by 5; by 6; by 8; and simplify the result. 275. If 8 men can mow of a field in a day, what part of it can one man mow? 276. How is divided by 5? 277. Divide by 6; 13 by 7; 278. If 7 pounds of coffee cost pound cost? 103 by 2; by by 8? # by 9? by 10; 1 by 6. $21, how much will 1 Solution.-$2 $; if 7 pounds cost $, 1 pound must cost of $21, or $ 279. How much is 2 divided by 7? 11 divided by 17? 104 divided by 25? 280. If 9 bushels of wheat cost $193, what is the cost of 1 bushel ? 132. Principle. A fraction is divided either by dividing its numerator or by multiplying its denominator. 291. When $28 is paid for 2 tons of hay, what part of a ton will $1 purchase? 292. When $1077 is shared equally by 7 men, how many dollars will each man receive? 293. The product of two numbers is 30%, and one of the numbers is 9. What is the other number? 294. When 12 cords of wood cost $76, what is the cost a cord? |