MULTIPLICATION. WRITTEN EXERCISES. 443. 1. Multiply 28 rd. 2 yd. 2 ft. by 7. OPERATION. 28 rd. 2 yd. 2 ft. 199 1 (1) 2 =1 6 in. 2 0 6 199 ANALYSIS.-Write the multiplier under the lowest denomination of the multiplicand, and multiply. 7 times 2 ft. are 14 ft., equal to 4 yd. 2 ft. Write the 2 ft. under the feet, and reserve the 4 yd. to add to the product of yards. 7 times 2 yd. are 14 yd., and 4 yd. added make 18 yd., equal to 3 rd. 14 yd. Write the 13 yd. under the yards, and reserve the 3 rd. to add to the product of rods. 7 times 28 rd. are 196 rd., and 3 rd. added make 199 rd., which write under the same denomination. The yd. is equal to 1 ft. 6 in., which added to the product, gives 199 rd. 2 yd. 6 in. for the entire product. 1. The multiplier must be an abstract number. (103.) 2. When the multiplier is large and is a composite number, the work may be shortened by multiplying successively by its factors. (109.) 2. In 9 bbl. of walnuts, each containing 2 bu. 3 pk. 6 qt., how many bushels ? 3. If a man cut 3 Cd. 36 cu. ft. of wood in 1 da., how many cords can he cut in 12 days? 4. Multiply 8 gal. 3 qt. 1 pt. 3.25 gi. by 96. 5. If 1 A. produce 42 bu. 1 pk. 5 qt. 1 pt. of corn, how many bushels will 64 A. produce? 6. Multiply O. 8 f39 £36 m 34 by 24. 7. What will 84 yd. of cloth cost, at £1 8s. 91d. a yd.? 8. If $80 will buy 3 A. 24 P. 20 sq. yd. 4 sq. ft. of land, how much will $4800 buy? 9. How many bushels of grain in 47 bags, each con taining 2 bu. 2 pk. 6 qt.? 9 OPERATION. 47 (9 x 5) + 2 2 bu. 2 pk. 6 qt. ANALYSIS.-Multiplying the contents of 1 bag by 9, and the resulting product by 5, gives the contents of 45 bags, which is the composite number next less 6 qt. in 9 bags. than the given prime num 5 66 ber, 47. Next find the contents of 2 bags, which, added to the contents of 45 bags, gives the contents of 45+2, or 47 bags. 10. If a load of coal by the long ton weigh 1 T. 6 cwt. 2 qr. 26 lb. 10 oz., what will be the weight of 67 loads? 11. Multiply 4 yd. 1 ft. 4.7 in. by 125. 12. Multiply 7 T. 15 cwt. 10.5 lb. by 1.7. 13. At $1.371⁄2 a gallon, what will be the cost of 5 casks of wine, each containing 28 gal. 2 qt. 1 pt.? 14. A farmer sold 4 loads of oats, averaging 41 bu. 3 pk. each, at $.75 a bushel. What did he receive for the whole? DIVISION. 444. 1. Divide 56 lb. 9 oz. 12 pwt. by 6. OPERATION. lb. OZ. pwt. 6)56 9 12 9 5 12 ANALYSIS.-Write the divisor at the left of the dividend. The object is to find 1 sixth of a compound number. of 56 lb. is 9 lb. and a remainder of 2 lb. Write the 9 lb. in the quotient, and reduce the 2 lb. to ounces, which, added to 9 oz., make 33 oz. of 33 cz. is 5 oz. and a remainder of 3 oz. Write the 5 oz. in the quotient, and reduce the 3 oz. to pwt., which added to 12 pwt., make 72 pwt. of 72 pwt. is 12 pwt., which write in the quotient. 2. Divide 358 A. 57 P. 6 sq. yd. 2 sq. ft. by 7. 4. Divide 282 bu. 3 pk. 1 qt. 1 pt. by 9; by 10; by 12. When the divisor is large, and is a composite number, the work may be shortened by dividing successively by its factors. 5. Divide 254 yd. 4 ft. 3 in. by 21; by 42. 6. Divide 196 Cd. 4 cd. ft. 12 cu. ft. by 72. 7. How many iron rails, each 16 ft. long, are required to lay a railroad track 26 mi. long? 8. Divide 24 sq. mi. 140 P., by 221. 9. Divide 202 yd. 1 ft. 6 in. by 3. 10. Divide 336 bu. 3 pk. 4 qt. by 4 bu. 3 pk. 2 qt. Reduce both dividend and divisor to the same denomination, and divide as in simple numbers. 11. How many boxes, each holding 1 bu. 1 pk. 7 qt., can be filled from 356 bu. 3 pk. 5 qt. of cranberries? 12. Divide 311 gal. 1 qt. 1 pt. by 53. OPERATION. 53)311 gal. 1 qt. 1 pt. (5 gal. 3 qt. 1 pt. 13. The aggregate weight of 41 hhd. of sugar is 19 T. 6 cwt. 22 lb. What is the average weight? 14. If a town 4 mi. square be equally divided into 62 farms, how much land will each farm contain? LONGITUDE AND TIME. 445. The Longitude of a place is its distance east or west from a given meridian, measured on the equator. The meridian from which longitude is reckoned is called the first meridian, and is marked 0°. All places east of this, within 180°, are in east longitude, and all places west, within 180°, are in west longitude. The English and Americans usually reckon longitude from the meridian of Greenwich, England; the French, from Paris. 446. Since the earth revolves on its axis once in 24 hours, the sun appears to pass from east to west around the earth, or through 360° of longitude once in 24 hours of time. Hence in 1 hour the sun appears to pass through of 360°, or 15°; in 1 minute, through of 15°, or 15'; and in 1 second, through of 15', or 15′′. 1. Since the sun appears to move from east to west, when it is 12 o'clock at one place, it will be past 12 o'clock at all places east, and before 12 at all places west. Hence, knowing the difference of time between two places, and the exact time at one of them, the exact time at the other is found by adding their difference to the given time, if it is east, and by subtracting, if it is west. 2. If one place is in east and the other in west longitude, the difference of longitude is found by adding them, and if the sum is greater than 180°, by subtracting it from 360°. 447. 1. The earth revolves on its axis once in every 24 hr. What part of a revolution does it make in 12 hr.? 2. How many degrees of the earth's surface pass under the sun's rays in 24 hr.? In 12 hr.? In 4 hr.? In 1 hr.? 3. How many degrees of longitude cause a difference of 1 hr. in time? 2 hr.? 3 hr.? 4. When it is 6 o'clock at Chicago, what is the hour 15° east of Chicago? 15° west of Chicago? 5. When it is noon in New York, what is the hour 15° east of New York? 30° west of N. Y.? 6. When it is 3 o'clock at Washington, what is the time 15° 15' east of Washington? 30° 30' west? 7. What difference of longitude causes a difference of 1 hr. in time? Of 1 minute? Of 1 second? 8. If the difference in the time of Boston and of St. Louis is 1 hr. 15 min., what is the difference in their longitude? 9. A man left New Orleans and traveled until his watch was 1 hr. 2 min, too fast. How far had he traveled, and in what direction? 10. Two persons, at different points, observe an eclipse of the moon; one seeing it at 9 P. M., and the other at midnight. What is the difference in their longitude? 11. A tourist leaves home at 12 м. on Monday, and on Saturday finds his watch 1 hr. 15 min. slow. In what direction has he been traveling? How far? 12. A and B start from opposite points and travel towards each other. When they meet, A's watch is 40 min. slow and B's 1 hr. fast. How far apart are the two points of starting, and in what direction did each travel? |