189. What is the difference between 19° 30′ east, and 37° 6' west? SUGGESTION. Add the longitudes of the two places to find the difference. 190. What is the difference between 120° 14′ E., and 36° 46′ W.? 191. What is the difference in time between 44° 8' E., and 7° 10′ 4′′ W.? 192. A grocer bought a hogshead of molasses containing 80 gallons. He sold 54 gals. 3 qts. 1 pt.: how much remained? 193. A firkin of butter contained 133 pounds: how much remained after selling 35 lbs. 7 oz.? 194. From three quarter-sections of land, there were sold 258 A. 34 p.: how much remained? MULTIPLICATION OF COMPOUND NUMBERS. WRITTEN PROBLEMS. 135. What will 6 boxes of grain contain, if each hold 11 bu. 3 pks. 5 qts.? PROCESS. bu. pks. qts. 11 3 5 6 71 1 6 ANALYSIS. (1.) For convenience, write the multiplier under the lowest denomination of the multiplicand. = (2.) 6 times 5 quarts=30 quarts 3 pecks, 6 quarts; write the quarts in the proper place, and add the pecks to the product of the pecks. (3.) 6 times 3 pecks = 18 pecks, which with 3 pecks added = 21 pecks, or, 5 bushels, 1 peck; write the peck in the proper place, and add the bushels to the product of bushels. = (4.) 6 times 11 bushels 66 bushels, which with 5 bushels added 71 bushels, which write in the proper place. ANS. REVIEW. How can pounds avoirdupois be reduced to pounds troy? (127.) By changing the pounds avoirdupois to grains, then the grains to pounds troy. How many steps? Which is reduction ascending? Which reduction descending? 195. Multiply £5 7 s. 8 d. 2 far. by 3. By 7. 196. Multiply 2 rds. 4 yds. 2 ft. 6 in. by 6. By 18. 197. Multiply 5 hrs. 42 min. 37 sec. by 13. By 42. 198. How many cranberries in 16 boxes, each containing 2 bu. 2 pks. 6 qts.? 199. If 2 lbs. 5 oz. grapes are put in a box, what will be the weight of a crate containing 24 boxes? 36 boxes? 200. What will be the weight of 2 dozen spoons, each weighing 1 oz., 5 pwt., 12 grs.? What will they cost, at 7 cents per pwt.? DIVISION OF COMPOUND NUMBERS. WRITTEN PROBLEMS. 136. Divide 12 lbs. 3 pwt. 11 gr. by 8. = the quotient, and reduce the 4 lbs to ounces. 4 lbs 48 oz. (3.) 1 eighth of 48 oz. is 6 oz. Write the 6 oz. in the quotient. (4.) Eight is not contained in 3 pwt. Write a cipher in the quotient, and reduce the pennyweights to grains. 3 pwts. = 72 grs., which, added to 11 grs. 83 grs. = (5.) 1 eighth of 83 grains is 10% grains, which write in the quotient. 201. Divide 35 lbs. 8 oz. 4 pwts. by 8. By 5. 202. A teamster drew 450 bu. 16 lbs. wheat at 15 loads, how much did he average per load? 203. A half-dozen spoons weighed 10 oz. 3 pwt., what was the weight of each? 204. 472 gal. 3 qts. ÷ 7 = what? REVIEW. Give the number of pounds in a barrel of flour. (128.) Beef. Pork. Fish. Salt. Give the number of pounds in a bushel of oats. Corn. Rye. Wheat. Beans. Peas. Barley. 209. How many spoons weighing 8 pwts. can be made from 11 oz. of silver? SUGGESTION. - Reduce both divisor and dividend to the lowest denomination mentioned in either, then divide as in simple numbers. 210. A man feeds his horse five quarts of oats a day, how long will 13 bu. 3 pks. last him? 211. How many bottles, each containing 1 qt. 1 pt., can be filled from 36 gallons of vinegar? 212. How many packages, each containing 3 oz., can be filled from 136 pounds of pepper? DENOMINATE FRACTIONS. 137. Reduction Descending. WRITTEN PROBLEMS. (a.) Reduce of a mile to inches. (b.) Reduce of a mile to integral numbers of lower denominations. may be found by the process used in division of denominate num bers. REVIEW.- What is time? (129.) winter months? Which the spring? Give the number of days in each. How is the year divided? Which are the Which the summer? Which the autumn? Write the table. (b.) ANAL. STEPS. 1 (§) in. ANS. 182 rds. 4 yds. 2 ft. 14 in. - (1.) Change the fraction of a mile to rods. (1.) Since in 1 mile there are 320 rods, in of a mile there are of 320 rods; or, 182 (2.) Since in 1 rod there are of yards; or, 44 yards. rods. yards, in of a rod there are (3.) Since in 1 yard there are 3 feet, in of a yard there are of 3 feet; or, 24 feet. (4.) Since in 1 foot there are 12 in., in of a foot there are of 12 in.; or, 1 inches. Reduce .5714 of a mile to integers of lower denominations. NOTE. It will be observed that the analysis of the reduction of denominate fractions is the same as that of denominate numbers. When the multiplier is a common fraction or a decimal, the word "of" is used instead of "times." 213. Change of a mile to integers of lower denominations. In the same way, change .3 of a mile. 1 214. Reduce of a rod to integers of lower denominations. In the same way, reduce .17 of a rod. 215. How many inches in .5 of a yard? In 2.7 of a foot? In 2% of a rod? 216. What is the sum of 5 mile and & rod? 217. What is the sum of .785 ton and 3.65 cwt. 218. Find the amount of lb. +23 oz. + pwt.; of .375 mi. +3.625 rd. - .275 yds. 219. What is the cost of 33 lbs. of gold, at $16 per oz.? 220. Bought 37.85 lbs. of gold-dust, at $0.80 per pwt.: what did it cost? What will lb. cost? 138. Reduction Ascending. (a.) Reduce 3 inches to the fraction of a rod. (b.) In the same way, reduce 3 inches to the decimal of a rod. (a.) PROCESS. (1.) 3 in.÷12 in. = 1 (ft.) = (b.) PROCESS. (1.) 3 in. 12 in. .25 (ft.) = (yd.) (2.) .25 ft.÷3 ft. .083+ (yd.) yd. (rd.) (3.) .083 yd. yd. = .0150+(rd.) (2.) ft. 3 ft. = 66 (1.) Reduce inches to the fraction of a foot. (2.) Reduce fraction of a foot to fraction of a yard. (3.) Reduce fraction of a yard to fraction of a rod. ANALYSIS (Process a). (1.) Since in 12 inches there is 1 foot, in 3 inches there are as many feet as 12 inches are contained times in 3 inches; or, of a foot. What is REVIE - What is a circle? (130.) Where is the center of a circle? meant by the circumference of a circle? By an arc? By a quadrant? By a diameter? Write the table. What is the use of angular measure? |
