Divide

212. 51 da. 18 hr. 15 min. 35 sec. by 13.
213. 34 T. 17 cwt. 83 lb. 13 oz. by 19.

214. 115 A. 130 P. 18 sq. yd. 37 sq. in. by 31.
215. Cong.5 0.4 f313 f37 m 43 by 48.

216. £718 17s. 5d. by 325.

217. 342 cd. 39 cu. ft. by 537.

218. 1135 lb. 9 oz. 15 pwt. 13 gr. by 872.

219. 132° 14′ 17′′ by 43.

220. If a farm containing 325 A. 115 P. be equally divided into 6 fields, what will be the area of each field?

221. 18 yd. of cloth were bought for £23 6d. Find the price per yard.

222. If a pedestrian walk 375 mi. in 18 da., what was the average distance traveled per day?

223. If 18 silver spoons weigh 2 lb. 7 oz. 10 pwt., what is the weight of each spoon?

224. A farmer delivered 12 cd. 1 cd. ft. 9 cu. ft. of firewood in 7 loads. What was the average quantity per load?

INDUCTIVE EXERCISE.

1. Is the divisor always an abstract number as in the preceding examples? If the divisor be concrete, with what term of division must the denomination of the concrete divisor agree? If the divisor be concrete, what kind of units will the quotient express? If the divisor express a different denomination but the same class of units as the dividend, how may both be made to express units of the same denomination? Ans. By reduction.

2. What is the quotient of 3 lb. ÷ 8 oz.? Of 48 in. ÷ 2 ft. ? Of 3 da. ÷ 12 hr.? Of 5 gal. ÷ 2 qt. ? Of 1 bu. ÷ 4 qt.? Of £3 ÷ 15s. ? Of 8 wk. ÷ 4 da. ?

231. Divide 98° 32′ by 8° 12′ 40′′.

232. Divide 2 lb. 2 oz. 5 pwt. 16 gr. by 3 oz. 5 pwt. 17 gr.

233. At 3s. 4d. per yard, how many yards of dress goods can be purchased for £2 6s. 8d.?

234. If a horse be given 5 qt. 1 pt. of oats three times a day, in how many days will he consume 7 bu. 2 pk. 7 qt. 1 pt. of oats?

235. If the average speed of a train be 18 mi. 180 rd. 4 yd. 2 ft. per hour, in how many hours can it make 352 mi. 236 rd. 2 ft.?

236. If the average capacity per barrel be 2 bu. 2 pk. 7 qt., how many barrels will be required to ship 230 bushels of potatoes?

237. How many bottles, each holding 1 pt. 3 gi., will be required to empty a cask containing 31 gal. 2 qt. 1 pt. 3 gi. of wine?

DENOMINATE FRACTIONS.

REDUCTION DESCENDING.

INDUCTIVE EXERCISE.

1. Is multiplication or division employed in reduction descending? By what methods can a fraction be multiplied by an integer? In reducing a denominate number, whether fractional or integral, to a lower denomination, what is selected as the multiplier? What will be the denomination of the resulting product?

2. Reduce gal. to qt.; pk. to qt.; § mi. to rd.; ft. to in.; lb., Avoir., to oz.; yr. to mo.

3. Reduce oz. to pwt. Reduce the fractional part of a pwt. in the result to gr. Hence, what is the equivalent of oz. in integral pennyweights and grains? Similarly reduce & yd. to integral feet and inches; minutes; bu. to integral pecks and quarts.

da. to integral hours and

[261. .4609375 of a cd. 262. .378125 of an acre. 263. .45 of a year.

256. .1375 of a bu. 1260. .15915625 of a T. [264. .00625 of a £.

1. Is multiplication or division employed in reduction ascending? By what general method can a fraction always be divided by an integer? In reducing a denominate number, whether integral or fractional, to a higher denomination, what is selected as the divisor? What will be the denomination of the resulting quotient? 2. Reduce of a gill to the fraction of a pint. Reduce the preceding result to the fraction of a quart? Reduce the last result to the fraction of a gallon. Hence, how would you reduce of a gill to an equivalent fraction of a gallon?

3. Reduce of an inch to an equivalent fraction of a yard; of a farthing to a fraction of a shilling; of a scruple to a fraction of an ounce.

EXAMPLES.

What common fraction of 289. A £ is 17s. 6d. ?

290. A pound is 4 oz. 18 pwt. 8 gr.?
291. A gallon is 2 qt. 1 pt.?
292. A shilling is 2d. 3 far.?
293. A yard is 2 ft. 6 in.?

294. An hour is 15 min. 12 sec.?
295. A mile is 8 rd. 4 yd.?
296. A ton is 31 lb. 4 oz.?

What decimal of 297. A bushel is 3 pk. 5 qt. 1 pt.? 298. A gallon is 1 qt. 1 pt. 2 gi.? 299. A £ is 1s. 3d.?

300. A ton is 1 cwt. 20 lb.?

301. A yard is 2 ft. 3 in. ?
302. An hour is 4 min. 30 sec.?
303. A day is 21 hr. 54 min.?
304. A £ is 13s. 9d.?

ADDITION OF DENOMINATE FRACTIONS.

INDUCTIVE EXERCISE.

1. What reduction is necessary before

of a gallon and of a gallon can be added? Before of a gallon and of a quart can be added? Hence, in what two respects must denominate fractions agree before they can be added?

2. What is the sum, expressed in integers, of a bushel and of a peck? Of of a gallon and of a day?

Find the sum of 305. bu., pk., and 1 qt. 306.mi., rd., and ft. 30%. $, £, and & fr. 308.

T., cwt., and § lb.

of a yard and 3 of a foot? Of of of a quart? Of of a week and

EXAMPLES.

309. cd., § cd. ft., and 4 cu. ft. 310. gu., £, and gs.

Find the sum of 311. .125 sq. yd. and 75 sq. in. 312. .9375 gal., .5 qt., and .25 pt. 313. .875 bu.,.125 pk., and .375 qt. 314. .535 A., .25 P., .0075 sq. yd. 315. .325 lb., .04 oz., .05 pwt.,.6 gr. 316. £.832, .0125s., .17d.

SUBTRACTION OF DENOMINATE FRACTIONS.

INDUCTIVE EXERCISE.

In what two respects must denominate fractions agree before one can be subtracted from the other? What is the difference, expressed in integers, between £ and £? Between } gal. and qt.? Between hr. and min. ? Between yd. and & ft.?

1. In multiplying § lb., Avoir., by 3, which is the concrete factor? The abstract factor? What is the product and its denomination? What is the product expressed in integers of the lower denominations?

2. Similarly express in integers the product of § ft. × 3. X 8. Of cd. X 4. Of .5 mi. × 9. Of .15 min. × 6.

Of § hr. X 7. Of } da. Of .25 hr. × 7.

Multiply

331.

332.

bu. by 31.

339. £.125 by 17. 340. .175 A. by 2.9.

In dividing da. by 2, is the divisor concrete or abstract? What is the quotient and its denomination? Expressed in integers of the lower denominations, what is the quotient of da.+3? Of 3 yd. ÷ 2? Of } gal. ÷ 4? Of § bu. ÷ 2 ?

345. rd. by 4.

346.

349. 3.09375 gal. by.15. 353. .3 T. by .625.

lb. Troy by 24. 350. 5.0635 yr. by 1.3. [354. .015625 mi. by 2.5.