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334. If of a lot of land is worth $7853, what is § of it worth?

335. If of a farm is worth $9000, what is

of it worth?

of a foot at 12

336. A staff 3 feet long cast a shadow o'clock; what is the length of a shadow cast by a steeple 125 feet high, at the same time?

337. If a staff 3 feet long casts a shadow of 2 of a foot at 12 o'clock, what is the height of a steeple that casts a shadow 313 feet, at the same time?

338. Sold a watch for $433, which was of its cost; what was its cost?

339. If a man earns $13 a day, in how many days will he earn $100?

340. Divide 98 by 1113, and multiply the quotient by 3 of 82. 341. What is the smallest sum of money with which I can buy horses at $50 each, cows at $30 each, or sheep at $8 each, using the same sum in each case?

342. If of a meter of cloth cost of a dollar, what will § of a meter cost?

343. A man sold a wood-lot for $2250, which was of what it cost him; how much did he lose by the bargain?

344. A man lost of his money, and then earned $117, when he found he had § of his original sum; how much had he at first?

345. If a man can perform a journey in 84 days, what part of it can he perform in 34 days?

346. A merchant owned of a cargo of tea. The value of the whole cargo was $6500. If he sells of his share for $2750, how much does he make, or lose?

347. A man gave, by will, 3, 4, and of his estate to various objects, and the residue, which was $ 200, he ordered to be expended in the purchase and care of his burial-place. What was the value of the whole estate?

of his

348. A painter worked 27 days, and after paying earnings for board and other expenses, had $414 left. What did he receive a day?

349. How many bushels of oats at $ § a bushel must be given for of a barrel of flour at $10 a barrel?

350. If $16 will buy 2 cords of wood, how many cords will $743 buy?

351. If you can buy 301 pounds of sugar at 10 cents a pound for 91 dozen of eggs, what are eggs a dozen?

352. If a man's expenses are $1784₫ a year, and he saves of his income, what is his annual income?

353. A man engaging in trade lost of his investment and then gained $ 8343, when he had as much as he put in and as much more. How much did he put in?

354. If a man loses of an investment, then gains $5423, and has $1287, how much was his investment, and how much was his loss?

355. A farmer sold 25 barrels of apples for $ 371⁄2, which was as much as he afterward received for all the rest at $12 a barrel. How many barrels did he sell in all?

356. If 25 tons of coal cost $ 2163, how much will 9 tons cost?

357. If of a pound of tea cost $, what will 75 pounds cost?

358. If $67 will buy 94 barrels of flour, how many barrels can be bought for $55?

359. If 6 meters of cloth cost $ 16, what will 93 meters cost? 360. If $23 will buy 3 of a meter of cloth, how many meters can be bought for $1474?

361. If 10 bushels of corn cost $83, how many bushels can be bought for $2?

362. How many pounds of coffee can be bought for $27, if 6 pounds cost $211?

363. If I pay $5 for 3 of a ton of coal, how much can I buy for $213?

364. If 7 horses eat 22 tons of hay in a certain time, how many horses will eat 813 tons in the same time?

365. If 4 meters of cloth cost $104, how many meters can be bought for $ 33} ?

366. If of a cheese that weighs 40 pounds is sold for $23, how much ought of the same cheese to be sold for?

367. If of a cord of wood cost $24, how many cords can be bought for $25} ?

368. If I paid $ 487 for a lot of apples, at the rate of $ for of a barrel, how many barrels did I buy?

369. A gentleman left his son an estate, of which he spent in 7 months, and of the remainder in 3 months more, when he had only $5000 remaining; what was the value of the estate?

370. A can build a certain wall in 12 days, and B in 15 days. How long will it take A and B together to build the wall?

of it in 1 of it in 1 day;

of it in 1 day.

Solution. If A can build it in 12 days, he can build day; and if B can build it in 15 days, he can build therefore, A and B together can build, or If they can build of it in 1 day, it will take as many days to do the whole as is contained times in 88, or 9 in 60, that is, 64 days.

371. Two men and a boy engage to reap a field of rye; one of the men can reap it in 10 days, the other in 12, and the boy in 15 days. In how many days can the three together reap it? 372 How long will it take the two men together? 373. How long will it take the first man and the boy? 374. How long will it take the second man and the boy?

375. Three men, A, B, and C, can do a piece of work in 10 days. If A and B together can do it in 14 days, how many days will it take C to do it alone? If A and C together can do

it in 16 days, how long will it take B to do it alone? how long will it take A alone?

376. A merchant bought a number of bales of hops, each bale containing 247 lb., at the rate of $3 for 10 lb., and sold them at the rate of $5 for 12 lb., and gained $693; how many bales did he buy?

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109. If anything is divided into two equal parts, what is each part called? 110. If a unit is divided into three equal parts, what is each part called? If into four? 111. What are such expressions as,, ,, etc., called? Why use the term Common Fraction? 112. What is a Fraction? 113. How is a Common Fraction expressed? 114. What is the number below the line called? Why? 115. The number above the line? Why? 116. The numerator and denominator together are called what? 117. What are whole numbers called? 118. A fraction is only an expression of what? What is the value of a fraction? How do changes in the numerator or denominator affect the value of a fraction? How does multiplying or dividing both terms by the same number affect a fraction? 119. What is a Proper Fraction? 120. An Improper Fraction? 121. A Simple Fraction? 122. A Mixed Number? 124. What is Reduction of Fractions? 125. What is meant by lowest terms of a fraction? 127. Rule for reducing a fraction to its lowest terms? 130. How can an integer be written as a fraction? 131. Rule for reducing a mixed number to an improper fraction? Reason? 133. Rule for reducing an improper fraction to an integer or mixed number? 135. What is meant by Common Denominator? Least Common Denominator? 137. How are fractions reduced to fractions having their least common denominator? 140. Give the Rule for adding fractions. 143. For subtracting fractions. 145. Illustrate with a line, or otherwise, that of 2 equal things is equal to % of either one of them. 146. Give the Rule for multiplying a fraction by a fraction. Explain the Rule. How does it apply to integral and mixed quantities? When a fraction is multiplied by its denominator, what is the product? 147. Dividing by 5 is the same as multiplying by what? 148. Give the Rule for dividing a fraction by a fraction. Explain the Rule. How does it apply to integral and mixed quantities?

DECIMALS.

152. The following table is a continuation to the right of the table in Art. 21.

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NOTE. This table can be extended to any number of periods to the right, as shown in the Appendix.

153. A Decimal Fraction, or a Decimal, is a fraction whose denominator is 10, 100, 1000, or 1 with one or more ciphers annexed. As its denominator is known, the numerator alone may be written with the decimal point, and read, according to the Rules in Arts. 24 and 26.

154. The value of the decimals in the table, expressed in words, is five hundred forty-eight million seven hundred sixty-three thousand two hundred forty-five billionths.

Exercises in the Numeration of Decimals.

155. Read the following numbers :

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