4.42 03 280. Change 41% to a decimal. 281. Change .75 to a common fraction. QUESTIONS.-What is reduction ascending? (165.) What is reduc tion descending? (164.) What is the comparison of numbers? (166.) What axiom is used in the comparison of numbers? (16., c.) What are the rules for the addition and subtraction of fractional denominate numbers? (168., a., b.) LESSON XXVIII. REDUCTION OF DENOMINATE DECIMALS. 181. Reduction Descending in denominate decimals is the same as in integral denominate numbers. 182. Reduction Ascending in denominate decimals is the same as in integral denominate numbers. Change .34672£. to integral numbers of lower denominations. (a.) ANALYSIS.-1. Change pounds to shillings. Since in one pound there are 20 shillings, in .34672£. there are 20 times as many shillings as pounds, which are 6s. and .93440 of a shilling. 2. Change .9344 of a shilling to pence. Since in one shilling there are 12 pence, in .9344s. there are 12 times as many pence as shillings, which are 11d. and .2128 of a penny. 3. Change .2128 of a penny to farthings. Since there are 4 farthings in one penny, in .2128d. there are *NOTE.-When only tenths and hundredths are changed to common fractions, the example will not prove exactly correct, but nearly enough so for all practical purposes. 4 times as many farthings as pence, which are 0 far. with a remainder of .85* of a farthing, equal to 17 far. Therefore .34672£.=6s. 11d. 17+far. (b.) ANALYSIS OF PROOF.-1. Change 17 far. to a decimal. Since in twenty 20ths there is one far., in seventeen 20ths there are one-twentieth as many farthings as 20ths, which are .85 far. 2. Change farthings to pence. Since in 4 far. there is one penny, in .85 far. there are one. fourth as many pence as farthings, which are .2125d., which with 11d. added equals 11.2125d. 3. Change pence to shillings. Since in 12d. there is one shilling, in 11.2125d. there are onetwelfth as many shillings as pence, which are .9343+s., which with 6s. added equals 6.9343+s. 4. Change shillings to pounds. Since in 20 shillings there is one pound, in 6.9343s. there are one twentieth as many pounds, &c. Reduce .34£. .9s. .13d. .83 far. to integers of lower denominations. Therefore .34£. .9s. .13d. .83 far.=7s. 8d. 2198 far. *NOTE-The remainder of the fraction may be rejected, because of its trifling value. ANALYTICAL STEPS.-1. Reduce pounds to shillings, and add the shillings. 2. Reduce shillings to pence, and add the pence. 3. Reduce pence to farthings, and add the farthings. 4. Reduce .995 to a common fraction. QUESTIONS.-What is said of the decimal scale? (169.) What is said of units' place? (170.) Which are integral numbers, and which are decimals? (171., a.) Repeat the numeration table from right to left. (171., a.) From left to right. (171., a.) How is a mixed number formed? (172.) How are numbers usually divided for convenience in reading? (173.) Write a rule for the addition of decimals. LESSON XXIX. EXAMPLES FOR PRACTICE. 293. Reduce $.28125 to integers of lower denominations. 294. Reduce .3746 lbs. to integers of lower denominations. 295. Reduce .437 cwt. to integers of lower denominations. 296. Reduce .37 lb. apothecaries' weight, to lower denominations. 297. Reduce .34 lb. Troy weight, to lower denominations. 298. Reduce .374 A. to integers of lower denominations. 299. What is the value of .27 A. .62 R. in lower denomination? 300. How many cubic inches in .371 cd. of wood? 301. How many gills in .16 hhd. .43 gal.? QUESTIONS.-Write a rule for the subtraction of decimals? (175.) Analyze an example in the multiplication of decimals. (176.) When any denomination is multiplied by units, what is the denomination of the product? (177., a.) If multiplied by a tenth? (177., b.) If multiplied by hundredths? (177., c.) By thousandths? (177., d.) LESSON XXX. 302. How many ounces in 4.34 cwt.? 303. How many drams in 3.264 tons? 304. How many sq. in. in 4.3 A. 1.12 sq. rds. ? 305. Reduce 3 rds. to the decimal of a mile. 306. Reduce 6 fur. 8 rds. 9 ft. to miles. 307. Reduce 9 A. 4 R. 2 sq. rds. to square miles. 308. Reduce 3 cwt. 9 qrs. 18 lbs. to hundred weight. 309. Reduce 9 cwt. 1 oz. to cwt. 310. Reduce 14 mi. 23 yds. 3 in. to miles. 311. Reduce 13 m. 143 fur. 9 yds. 8 in. to miles. QUESTIONS.-What is the general law for the multiplication of decimals? (177., e.) Repeat the rule for multiplication of decimals. (177., f.) Analyze an example in the division of decimals. (178.) When any denomination is divided by units, what will be the denomination of the quotient? (179., a.) If divided by tenths? (179., b.) If divided by hundredths? (179., c.) By thousandths? (179., d.) What is the general law for division of decimals? (179., c.) Repeat the rule. (179., f.) LESSON XXXI. MISCELLANEOUS EXAMPLES. 312. What will 13 lbs. of hay cost, at $20 per ton? 313. What will 173 lbs. of hay cost, at $17 per ton? 314. What will 13 eggs cost, at 17 cts. per doz.? 315. What will 4 doz. eggs cost, at 19 cts. per doz.? 316. What is the value of 15 cwt. 3 qrs. 14 lbs. of coffee, at $9.50 per cwt.? 317. What cost 17 T. 18 cwt. 1 qr. 7 lbs. of pork, at $2.50 per cwt.? 318. What cost 15 yds. of cloth, at $3.75 per yard? |