An Integer divided by a Fraction.

ORAL EXERCISES.

295. How many fourths of a dollar in $1? In $3? 296. How many times is in 1? In 2? In 3?

297. In 4 how many times ? ? ? ? ??

298. At $ a pound, how many pounds of tea can be bought for $6?

Solution.

As many pounds as times in 6. In 6 there are 24, and are contained in 24 8 times. Ans. 8 pounds.

299. In how many days can a horse consume 4 bushels of oats, if he consume of a bushel a day?

300. Divide any given integer by the fractions in Exercises 27 to 33.

301. At $11 a yard, how many yards of cloth can be bought for $10?

302. In how many weeks will a boy earn $ 8, if he is paid $23 a week?

7 times 65 times, or 91 times. This process is the same as multiplying the dividend by the divisor inverted.

314. How many yards of cloth at $7 a yard can be bought for $56?

315. If a family consumes 23 pounds of sugar a week, in what time will it consume 44 pounds?

316. There is a board 17 feet long, which I wish to saw into pieces 23 feet long. What will be the number of pieces ?

A Fraction divided by a Fraction.

ORAL EXERCISES.

317. How many times of a yard in ‡ of a yard?

318. At of a dollar a pound, how many pounds of coffee can be bought for & of a dollar?

319. How many times in ? in ? in ?

320. How many pounds of raisins at can be bought for 3 of a dollar?

of a dollar a pound

in. In & there are 12, Ans. 4.

Solution. As many pounds as times and are contained in 12, 4 times.

321. How many times in ? in? in?

322. If it takes of a yard of cloth for a vest, how many vests can be made from 24 yards?

This is the same as multiplying the dividend by the divisor

inverted.

327. What is the quotient of

divided by ?

328. What is the quotient of

divided by fo?

133. Rule for Division of Fractions.

Change the fractions, if necessary, to fractions having a common denominator, and divide the numerator of the dividend by the numerator of the divisor. Or,

Invert the divisor, and proceed as in multiplication of fractions.

NOTE 1. —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.

NOTE 2. A fraction having a fraction in one or both of its terms, as in 211 is called a Complex Fraction, and may be considered an expression

3 # 1

of division.

339. How much is tea a pound when 1 of a pound cost of a dollar?

340. How much is hay a ton when § of a ton cost $ 114? 341. If a man walks 33 miles in an hour, in what time will he walk 15 miles?

15=112ering the fraction as an

expression of division, we reduce its terms to improper fractions, and, dividing, have 5, or 11.

Or, multiplying both terms of the complex fraction by 12, the least common multiple of the denominators of the fractional parts, we have, as before,, or 11.

350. If a man can do 3 of a piece of work in 233 days, in what time can he do the whole?

351. At the rate of 316 miles an hour, in what time will a train of cars move 125 miles?

To find the Fraction one Number is of another.

352. One is what part of 2? Of 3? Of 4 ? Of 5?

353. What part of 5 dollars is 1 dollar? 2 dollars? 3 dollars? 4 dollars?

354. What part of 7 miles is 3 miles? 4 miles? 5 miles? 6 miles ?

355. What part of 5 is ?

Solution. 1 is of 5, and of 1 is of of 5, or of 5.

356. What part of 4 dollars is § of a dollar?

357. What part of 13 is 13 ? What part of 1⁄2 is 2, or ? 358. What part of 8 dollars is 2 dollars?

134. The Fraction one number is of another is found by dividing the number denoting the part by the number denoting the whole.

367. What fraction of 84 is 91 ?

368. What fraction of 33 is 2?

369. A tree, whose height was 85 feet, was broken off in a gale, 55 feet from the top. What part of the tree was left standing?

370. A sportsman started up a flock of 144 birds, and shot of them. What number escaped?

371. If 25 yards of carpeting cost $37.50, what should 35 yards cost at the same rate?

372. John has 156 cents, and Peter 106 cents. How does Peter's money compare with John's?

373. If a man can do a piece of work in 73 days, what part of it can he do in 5 days?

374. What will be the cost of of a cord of wood, when 12 cords cost $68 ?

To find the Whole when a Fractional Part is given.

375. 4 is of what number? 6 isof what number? 8 is of what number? 3 is of what number?

376. I spent $6, which was of all my money; how much had I?

377. I lost of my sheep, but had 8 left; how large a flock had I at first?

378. 18 years is 3 of my age; how old am I?

Solution.

Since 18 years is 3 fourths of my age, 1 fourth of my age is of 18 years, or 6 years; 4 fourths of my age is 4 times 6 years, or 24 years. Ans. 24 years.