258. Miscellaneous Examples.

208. I have 3.75 yards of binding for a square bed spread 2.25 yards on each side. How much more bin ling do I need?

209. A cubic foot of water weighs 62.5 pounds; granite is 2.72 times as heavy as water. What is the weight of a cubic foot of granite? of 3.2 cubic feet?

210. How many meters of silk, 1.0936 yards to a meter, should I buy to make a dress requiring 18 yards?

211. How many yards are there in a piece of dress goods measuring 15 meters, 39.375 inches to a meter?

212. How many inches are there in 4.8 meters? In 6.66 meters?

213. What would be received for the use of $480 for a certain time, at $0.076 on each dollar?

214. An architect received $ 314.50 for planning a house. If this sum was 0.075 of the cost of the house, what was the cost?

215. Edinburgh is 393.6 miles from London. With close connections a traveler can go from London to Edinburgh and return in 18 hours, and make stops equal to 24 minutes. What is the average speed of the cars per hour while in motion? (Answer to the nearest hundredth.)

216. If 3.5 pounds of grain loses 1.5 ounces of its weight in thoroughly drying, what part of the original weight of the grain was liquid? (Answer to the nearest thousandth.)

217. If, by exposure to dampness, a certain article weighing 3.5 pounds absorbs 1.5 ounces of water, what part of the full weight is the weight of the water which is absorbed?

218. What would be received on $120 of an account that is worth 62 cents on a dollar?

219. A man owning 0.33 of a store bought half of the remainder. What part of the store did he then own? If his share was then worth $1700, what was the value of the whole store?

220. A man owning 0.15 of a ship sold of his share for $800. What part of the ship did he sell, and what was the whole ship worth at the same rate?

221. Mr. James loaned $1268 for 3 years, receiving for its use for the first year 0.07 of its value, for the second year 0.06 of its value, and for the third year 0.05 of its value. How much in all did he receive for its use?

222. How many days, at $1.75 a day, must David work to earn enough to buy a coat worth $ 8, a vest worth $1.12, and a hat worth $ 3.87?

223. How many miles an hour must a person travel to go 153 miles in 3 days, traveling 8.5 hours a day?

224. If a road rises 4.3 feet in every 50 feet, how much does it rise in a mile?

225. A wagon wheel is 3.5 feet across and 3.1416 times as far around; what is the distance around the wheel? How many times does it turn in going a mile?

226. A man sold a house for $ 7250, which was 0.04 more than he paid for it. How much did he pay for it?

SUGGESTION. $ 7250 = 1.04 of what he paid.

227. When mining stock sells for 0.23 more than its original value, and its value was $100 a share, what must pay for 1 share? for 200 shares?

I

228. By giving a bank his written promise to pay the sum of $300 in 2 months, Mr. A. obtained 0.986 of $300 for present use. What sum did he obtain?

229. A bushel even measure equals 2150.42 cubic inches. If this is 0.783 of a heaped bushel, how many cubic inches are there in a heaped bushel?

230. 50 shares of railroad stock, which cost $114 a share, were sold at a loss of $432. At what price per share was the stock sold?

231. If an ore loses 0.4 of its weight in roasting and 0.4 of the remainder in smelting, how much ore will be required to make 1 ton of metal?

232. What is the cost of 475 melons at $12 per hundred?

NOTE. - 475 equals 4,75 (475) hundreds. Since 1 hundred melons cost $12, 4.75 hundreds will cost 4.75 times $12.

Find the cost of:

233. 6 casks of lime, each 240 pounds, at $1.75 per C.* 234. 1260 posts at $20 per C.

235. 2842 pounds bituminous coal at 43¢ per C.

236. 220 bunches of onions at $8.50 per C.

237. 397 heads of lettuce at $5.20 per C.

238. What will be the cost of printing 6760 ems at 30% per thousand ems ?

239. Make out a lumberman's bill for the following items:

1230 ft. White Wood at $18 per M.*

240. My water meters registered 33,660 gallons for my house and 32,164 gallons for my store. Find the amount of the bill for water at 35 per thousand gallons.

241. My gas meter registered April 1st 207,300 feet; the bill for January 1st showed 202,800 feet. What is the bill for gas for the 3 months at $1.80 per thousand feet, if 0.163 of the bill is deducted for prompt payment?

What are Decimal Fractions? How are their written expressions distinguished from those of integral numbers? What indicates the denomination of the decimal? How do you read a decimal expression? How do you write decimals? What is the effect of annexing ciphers to a decimal expression?

How do you change decimals to common fractions? Common fractions to decimals? How do you add and subtract decimals? Perform an example in multiplication by a decimal, explain and give the rule. Perform an example in division by a decimal, explain and give the rule. How do you express the multiplication of a decimal by 10; 100; 1000; 0.1; 0.01; 0.001? How do you express the division of a decimal by 10; 100; 1000; 0.1; 0.01; 0.001?

* C is used for "hundred" and M for "thousand.”

DRILL TABLE No. 6. (See Supplement, Art. 1.) 259. For supplementary practice in decimals.

~42-255. Read the numbers expressed in E and in G. 256-269. Write in figures the numbers expressed in F. 270-283. Change E to equivalent common fractions in lowest terms.

284-297. In the same way change G.

298–311. Change H to equivalent decimals (4 places).

SECTION XI.

COMPOUND DENOMINATE NUMBERS.

260. Illustrative Example. How many pints are there in 2 quarts 1 pint? Ans. 5 pints.

The number, 5 pints, is made up of units of one denomination only. Such a number is a simple number, and because the kind of unit is named, it is a denominate number; hence, it may be called a simple denominate number.

261. The number, 2 quarts 1 pint, is made up of units of two different denominations. A number made up of units of two or more different denominations is a compound denominate number.

262. Denominate numbers are also called concrete numbers, and numbers considered apart from any object are called abstract numbers.

Name a simple denominate number; a compound denominate number; a concrete number; an abstract number.

NOTE. The tables of measures in common use required to solve the examples in this section will be found in the Supplement, Arts. 20–46.

MEASURES OF EXTENSION.

Examples for Oral and Written Work.

263 a. Repeat or write from memory the tables of Long Measure; of Square Measure; of Cubic Measure.

b. What is the standard unit of length?

c. What divisions are there in the yard besides those given in the table?