Multiplication of mixed numbers and integers. Multiply Multiply 271. $731 by 95. 275. $421 by 9. ||279. $173 by 251. 283. $921 by 19%. 272. $36 by 481. 276. $381 by 5. 280. $45 by 827. 284. $35 by 46. 273. $560 by 344. 277. $48 by 38.281. $6270 by 254 285. $94 by 87. 274. $75 by 360. 278. $136 by 3143|| 282. $198 by 6.286. $894 by 393. 287. What is the total cost of 285 yards of calico at 6 cents per yard, 175 yards of muslin at 8 cents per yard, 867 yards of alpaca at 28 cents per yard, 34ğ yards of cashmere at 72 cents per yard, 95 yards of percale at 114 cents per yard, and 75 yards of gingham at 15 cents per yard? 288. A farm wagon, carrying 64 barrels of corn at a load, delivered all the corn grown in a certain field in 58 loads. What was the total yield of that field? 289. The average yield per acre of a field of wheat was 18 bushels. What was the total yield, if the field contained 35 acres? Multiplication of one mixed number by another. 303. What is the cost of 793 bushels of wheat at $1.20 per bushel ? 304. I bought 375 yards of calico at 5 cents per yard. 9 yards being damaged, were sold at 2 cents per yard, and the remainder at 6 cents per yard. What was my net profit? pounds of pork at cents per bushel, cents per yard, 25 alpaca at 37 cents 305. A farmer sold to a country merchant 460 8 cents per pound, and 50 bushels of corn at 87 receiving in part payment 30 yards of calico at 7 yards of sheeting at 25 cents per yard, 18 yards of per yard, and 75 pounds of sugar at 83 cents per pound. What is the balance due the farmer? DIVISION OF FRACTIONS INDUCTIVE EXERCISE. 1. How many fractional units in $1? What is the name of each fractional unit? What is the quotient of dividing the fractional units in $1 by 2? What is the name of each fractional unit of the quotient, and why? What fraction will therefore express the quotient? Similarly divide of an ounce by 3; § of a gallon by 4; of a mile by 2; 1 of an acre by 5; 1 of a year by 7; of an hour by 5; of an estate by 6. 2. If you give John of an orange, and you wish to give James one-fourth as much, in what two ways can you effect your purpose? Ans. By giving to James one-fourth as many pieces of the same size as John's; or by giving to James the same number of pieces as to John and making James's pieces one-fourth as large as John's. What term of expresses the size of the pieces? What must be done to that term to make it express a size one-fourth as large? Similarly find what part of an orange is one-third as large as of an orange; is one-half as large as of an orange; is one-fourth as large as as of an orange. 3. Divide $ by 5; $ 11; $ by 8; $ by 4; $ of an orange; is one-fifth as large by 7; $ by 4; $ by 3; $ by 5; $f by 5; $‡ by by 7; $r by 4. [u] The quotient is inversely as many times greater or less than the dividend as the divisor is times greater or less than 1. 338. of an estate was left to be equally divided among 15 legatees. What part of the estate did each receive? 339. Divide the sum of ounces. of an ounce and of an ounce by 12 340. What is the cost of 7 pounds of beef, if 4 pounds cost $? Division of integers by fractions. INDUCTIVE EXERCISE. 1. What is the quotient of $1 + $? Of $3 $3 ? Of $4÷$}? Of $6 Hence, what is the quotient of $2 + $}? $3? Of $7 ÷ ${? 2. Divide 3 ounces by of an ounce; 8 feet by of a foot; 15 miles by of a mile; 9 yards by of a yard; $7 by $3. [v] The quotient of 1 divided by a fraction equals such fraction with its terms inverted. [w] The quotient of any integer divided by a fraction is as many times the fraction inverted as such integer is times 1. Divide EXAMPLES. Divide Divide Divide 356. $1827 by $3. 341. $18 by. 346. $15 by 1.351. $63 by 13. 342. $18 by $1.347. $69 by 27. 352. $3 by $13.357. $480 by 19. 343. $5 by $1.348. $11 by $1. 353. $11 by . 358. $225 by $78. 344. $25 by $. 349. $144 by 13. 354. $516 by $3.359. $1215 by 18. 345. $9 by 4. 350. $135 by $18.355. $9 by 27. 360. $4 by $1f. 361. A customer was charged $19 for tea purchased at $7 per pound. How many pounds did he purchase? 362. I expended $15 in buying cheese at $ per pound. How many pounds of cheese did I buy? 363. I have $56 to invest in dress goods. How many yards can I buy at $ per yard? Division of one fraction by another. INDUCTIVE EXERCISE. 1. What is the quotient of $1 + $? Hence, what is the quotient of of $1, or $} + $? Of } of $1, or $} + $? Of } of $1, or $1÷ $? Of of $1, or $1 + $4? 2. What is the quotient, and why, of $3 $? Of $} + $} ? Of $1⁄2 + $} ? Of $ + $? Of $} + $1? Of $1 + $}? Of $} + $}? [x] The quotient of a fraction divided by a fraction is such a part of the divisor inverted as the dividend is of 1. 379. If tea is worth $3 per pound, what part of a pound can be bought for $? 380. At $ per pound, how many pounds of cut loaf sugar can be bought for $18? 381. I bought of a pound of butter for $3. What was the price per pound? Division of integers by mixed numbers. [y] A mixed number may be divided by an integer by separately dividing the integral and fractional parts of the dividend by the divisor, or by applying [z] following. 384. $832500 397. The sales of a average sales per day? grocer were $432 in 6 days. What were the 398. A retail shoe dealer bought 24 pairs of shoes for $72. What was the average price per pair? 399. If a vessel average 15 miles per hour, in how many hours can she sail 18313 miles? Division of integers by mixed numbers. [x] To multiply both dividend and divisor by the same number does not change the value of the quotient. Hence, the division of an integer by a mixed number may be simplified by multiplying both terms by the denominator of the terminal common fraction, producing integral terms. Division of one mixed number by another. [zz] The division of one mixed number by another may be simplified by multiplying both terms by the least common multiple of the denominators of their terminal common fractions, producing integral terms. EXAMPLES. Divide 415. $53 by $183. 420. $75834 by 5377.425. $1289 by $5184. 421. $8235 by $184. 426. $48294 by $3711. 422. $5172 by $75. 427. $8216,7 by $51. 423. $82417 by $925. 428. $38267 by $931. 424. $41897 by $375.429. $513 by $84§. 431.4 of a pint. 434. 25 436. of an oz. 439. 48 $18-$16 15 437. of an inch. 440. of a rod. 35 435. 45ofamile. 438. $25+$6441, of $3. 19 7 445. ($51+$31) × 32 447. 8 $3+ (53 of $21) of of $ ($3+$5)÷3 ($35 - $24) × |