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of a fraction have upon it? Why? What effect does multiplying the numerator of a fraction have upon the fraction? Why? In what other
could you produce the same effect, and why? What effect does dividing the numerator have upon a fraction? Why? In what other way could you produce the same effect, and why?
263. General Review, No. 2. 213. What are the prime factors of 420 ? 214. Divide 18 x 7 x 15 x 6 by 28 x 10 x 3 x 4. 215. Find the greatest common factor of 35, 84, and 56. 216. Find the least common multiple of 63, 18, 14, and 28. 217. Change 19 and 178 to their smallest terms.
218. Change 4651 and 84 to improper fractions, having 8 for their denominator ?
219. Change ope and 33. to mixed or integral numbers.
220. Change $, IT, and 3 to fractions having a common denominator.
221. Change it, and 97 to fractions having the least common denominator.
222. Add of 3, 3, and 8%. Add 254, 65, and 46.4.
4 227. Simplify the expressions and
38 228. What part of 43 is 3} ?
229. Two trains which are 75 miles apart are running towards each other, one 304 miles an hour, the other 403 miles an hour. How far apart will they be in half an hour ?
230. A man paid $ 189 for a load of hay weighing 1} tons. At the same rate what should he pay for of a ton ?
231. Having spent 4 of his money, Fred has $ 134. How much had he at first?
232. Make out a bill of sale for three barrels of sugar, weighing respectively 235 pounds, 241 pounds, and 254 pounds, at 1179 a pound.
264. Miscellaneous Oral Examples.
a. If % of a pound of candles cost 35 cents, what is the price of 1 pound ? of 18 of a pound ?
b. In f of an acre of land there are 120 square rods. How many square rods are there in / of an acre ?
c. When 14 bushels of oats will feed 10 horses for a certain time, how many horses will 24 bushels feed for the same time?
d. At $ each, how many cedar posts can be bought for $12? for $7}?
e. At $2} per day, how many days' work can be paid for with $ 20 ? with $37} ?
f. At $2 per day, how many days' work can be paid for with $77 ? with $9} ?
g. If it requires 12 yards of carpeting of a yard wide to carpet a hall, how much will be required of that which is 11 yards wide ?
h. What number is that, 4 of which exceeds } of it by 2 ?
i. If 4 of the distance from Springfield to Albany is 80 miles, what is of the distance ?
j. If $54 pays for the lodging and breakfast of 7 persons, for how many persons will $114 pay?
k. What is that number to which if of itself be added the sum will equal 64 ?
1. I sold my watch for $72, which was more than I gave for it. What did it cost me ?
m. Bought a horse and saddle for $ 75, giving , as much for the saddle as for the horse. What was the cost of each ?
n. A can build a wall in 3 days, and B can do the same work in 4 days. What part of the work can each do in one day? What part can both do in one day? In how many days can both do it working together?
0. C can do a piece of work in 5 days, and D in 8 days. What time will be required for both to do it ?
265. Miscellaneous Examples for the Slato.
233. What will 16} yards of cloth cost at 53% a yard? 234. What will 9} bushels of corn cost at 871a bushel ? 235. What will 2713 acres of land cost at $31% per acre ?
236. I paid 65% for 2 boxes of strawberries. What will be the cost of 45 boxes at the same rate ?
237. What is my bill for 7 pear-trees at 87} cents apiece for the trees, and $2 a dozen for setting?
238. What do I receive per pound by selling 15 pounds of coffee for $ 3.75 ?
239. If } of a man's property is in land, valued at $23245, what is the value of his whole property ?
240. Bought of a ship for $ 4075. What would the whole ship cost at the same rate ?
241. What is the cost of 3 pieces of calico, 37} yards in a piece, at 194 cents per yard ?
242. Sold my house and farm of 473 acres for $6150. Allowing $ 3500 for the house, what did I receive per acre for the land ?
243. How long will a quantity of flour last a family of 8 persons if it lasts 3 persons 144 months ?
244. If in 3214 years a man saved $ 1694, what was his average saving per year ?
245. What number is that which diminished by 11t will leave a remainder of 175 ?
246. What number is that to which if you add 97 the sum will be 1248 ?
247. What is that number to which if you add šof 26} the sum will be 147} ?
248. If you buy 7} yards of silk at $5 a yard, 14} yards of cashmere at $1.25 per yard, 45 yards of silk at 75 cents per yard, and of a yard of velvet at $4.50 per yard, giving in payment a $100 bill, what balance will be your due ?
249. What will 50 oranges cost at 62}$ a dozen ?
250. How long will 200 pounds of meat last 9 persons at the rate of of a pound a day for each person ?
251. A farmer has sold his eggs at an average of 237 cents per dozen, which is } higher than they averaged the previous year. What did they average then ?
252. He is paid for grain $ 1.80 per bag, which is t less than he was paid last year. What was he paid last year ? 253. Mr. Stevens, dying, left $ 75000 to his wife and two
To his wife he left $ 30000; to his oldest son just as large a part of the remainder as his wife's portion was of the entire property; and to his youngest son the rest. What was each son's share?
254. A man sold 54 yards of cloth at the rate of 3 yards. for 2 dollars. What did he receive for it?
255. Mr. Day bought a house and barn for $ 4050, giving f as much for the barn as for the house. What did he pay for each ?
256. If a body falls 161. feet in the first second of time, 3 times 1615 feet in the next second, and 5 times 1615 feet in the third second, how far will it fall in the three seconds ?
257. What length of time would a man require to travel around the earth if the distance is 25000 miles and he travels at the rate of 31} miles per day ?
258. If a man can build 2f rods of wall in a day, how much can he build in 64 days ?
259. What number is that of which exceeds of it by 114 ?
260. If I buy 1250 bushels of corn at 41 cents per bushel, and sell it at 52} cents per bushel, how much do I gain ?
261. What number divided by 4 equals 1254 ?
262. What are the contents of 3 floors measuring as follows: 134 square yards, 327& square yards, and 4934 square yards ?
263. The product of three numbers is 63}; two of them are 8} and 613. What is the third ?
264. I exchanged 42 tubs of butter, averaging 484 pounds, at 21} cents per pound, for 42 barrels of flour, at $ 93 per barrel, and received the halance in cash. What was the balance ?
265. Owing a man in Paris 1325 francs, I have shipped to him $375 worth of rice. If the franc is worth 194 cents, how much have I overpaid him in United States money? in francs ?
266. I have three boxes, each containing 12 pieces of cloth, each piece 48 yards in length, and weighing 37 pounds to the yard. What is the weight of the whole ?
267. What will 427 quires of paper weigh at $ pound per quire ?
268. Owning of a flour-mill, I sold of my share for $1750. What is the value of the whole mill at the same rate ?
269. When hay was $15 per ton, I gave of a ton for 14 tons of coal. What was the coal worth per ton ?
270. If a man walks 9} miles in 27 hours, how far will he walk in 48 hours ?
271. At the rate of 41 miles an hour, what time will be required to walk 122 miles ?
272. In 1860 I purchased cotton at 84 cents a pound, which I sold in 1862 at 907 cents. What did I gain on 1000 lbs. ?
273. If a man can earn $2.30 per day, how many days' work will he have to give for a suit of clothes, of which the coat costs $ 251, the trousers $8, and the vest $54 ?
274. If & off of a ship cost $ 42000, what is of it worth?
275. In a certain manufactory of the operatives are Germans, French, to Scotch, English, Swedes, and the remainder, 140, native Americans. What is the whole number, and the number of each nationality ?
276. If of my money is in gold, t of the remainder in silver, and the balance, $ 360, in bank-notes, how much money have I in all ?
277. A certain piece of work can be performed by A in 8 days, by B in 10 days, and by C in 16 days. In what time can all do it working together ?
278. In what time can A and B do it together ? 279. In what time can A and C do it together ? 280. In what time can B and C do it together ?