2. From 1ğ bu. subtract .8 of a bushel. EXPLANATION.-First find the value of each denominate fraction in integers of lower denominations (198); then subtract as in integers. bu. pk. 2 3 3 1ğ bu. = 1 .8 bu. = Find the difference between 9. 8 cwt. and 48 lb. 10. lb. and 5 lb. 4 oz. 8 pwt. 11. .659 wk. and 2 wk. 3 da. 5. From a tub of butter containing 1 cwt. 28 lb., was taken 56 lb. 8 oz.; how much remained? 6. From a pile of wood containing 42 Cd. 5 cd. ft., take 16 Cd. 6 cd. ft. 12 cu. ft., and how much remains ? 12. .9 da. and wk. .0625 bu. and 3 pk. 14. 54 bbl. and 4 hhd. Find the result 7. Of 7 T. 5 cwt. 18 lb. 6 oz. 2 T. 9 cwt. 12 lb. 10 oz. 8. Of 29 sq. yd. 6 sq. ft. 84 sq. in. sq. in. 16 sq. yd. 2 sq. ft. 96 15. If from a hhd. of molasses 14 gal. 1 qt. 1 pt. be drawn at one time, 10 gal. 3 qt. at another, and 29 gal. 1 pt. at another, how much will remain ? 16. From a pile of wood containing 1254 Cd., was sold at one time 26 Cd. 7 cd. ft.; at another, 30 Cd. 4g cd. ft.; at another, 37 Cd. How much remained? 203. To find the interval of tiine between two dates. WRITTEN EXERCISES. 1. How many yr., mo., da., and hr., from 3 o'clock P. M. of May 16, 1874, to 9 o'clock A. M. of Sept. 25, 1885 ? EXPLANATION.-Since the later date expresses the greater period of time, write it as the minuend, and the earlier date as the subtrahend, writing first the year, next the number of the month, next the number of the day, and next the number of the hour, reckoning from 12 o'clock at night. yr. mo. 9 5 4 1885 1874 11 da. hr. 25 9 16 8 15 18 1. In finding the difference of time between two dates, 12 mo. are usually considered a year, and 30 days a month. 2. When the time is less than a year, to be exact the true number of days in each month and parts of a month are added. 3. The day on which a note, draft, or contract is dated, and that on which they mature, are not both included. The former is generally omitted. Find the time 2. From June 12, 1879, to Sept. 21, 1883. 3. From Jan. 4, 1872, to Oct. 3, 1881. 4. From April 10, 9 o'clock A.M., 1873, to 2 o'clock P.M., July 15, 1883. 5. How many days did a note run, that was dated May 20, 1882, and paid Sept. 14, 1882? SOLUTION.-In May there were 11 da. remaining, 30 in June, 31 in July, 31 in Aug., and 14 in Sept., or 117 da. in all. 6. How long has a note to run that is dated Jan. 16, 1883, and made payable July 10, 1883? 7. A note dated May 28, 1885, was paid Feb. 10, 1886. What length of time did it run? 8. The construction of the Brooklyn Suspension Bridge was commenced Jan. 3, 1870, and opened for travel May 24, 1883. How long was it in building? 204. To multiply a denominate number by an abstract number. WRITTEN EXERCISES. 1. Multiply 12 T. 15 cwt. 27 lb. 9 oz. by 8. EXPLANATION. Write the multiplier under the lowest denomination, and multiply as in simple numbers. Thus, 8 times 9 oz. are 72 oz., 12 T. 15 cwt. 27 lb. 9 oz. 8 102 T. 2 cwt. 20 lb. 8 oz. equal to 4 lb. 8 oz. Write the 8 oz. under the ounces, and reserve the 8 times 27 lb. are 216 lb., and 4 lb. added make 220 lb., equal to 2 cwt. 20 lb. Write the 20 lb. under the pounds, and reserve the 2 cwt. to add to the product of cwt. Proceed in the same manner until all the denominations are multiplied. When the multiplier is large, and a composite number, multiply successively by its factors (57). What is the result 2. Of 6 hhd. 20 gal. 3 qt. × 5? by 8? by 15 ? 3. Of 2 rd. 4 yd. 2 ft. 6 in. × 6? by 18? 4. Of 9 cu. yd. 15 cu. ft. 520 cu. in. ×? by 14? 5. Of 5 hr. 42 min. 50 sec. × 12? by 36 ? 6. Of 26 cd. 3 cd. ft. 12 cu. ft. x 18? 24? 7. What is the weight of 1 doz. spoons, each weighing 1 oz. 12 pwt. 16 gr. ? 8. What is the weight of 48 loads of hay, each weighing 1 T. 3 cwt. 50 lb.? Find the product in integers of lower denominations of 9. .36 cwt. × 12. 12. .875 hhd. x 9. 15. 3.96 in. x 36. 16. 10. .12 hr. x 18. 11. lb. × 24. 17. 18. At $1.37 a gallon, what will be the cost of 5 casks of wine, each containing 28 gal. 2 qt. 1 pt. ? 19. A farmer sold 4 loads of oats, averaging 41 bu. 3 pk. each, at $.75 a bushel. What did he receive for the whole? of .225 mi. × 8. 13. 14. 6 A. × 6. .216 gr. x 15. mo. x 21. 205. To divide a denominate number into equal parts. WRITTEN 1. Divide 56 lb. 9 oz. 12 pwt. by 6. EXPLANATION.-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 oz. 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. When the divisor is large, and is a composite number, the work may be shortened by dividing successively by its factors. EXERCISES. lb. oz. pwt. 6) 56 9 12 9 5 12 Find the result of 2. 376 gal. 3 qt. 1 pt. 9. 15. ÷ 3. 328 yd. 1 ft. 3 in. ÷ 6. 6. 4. 9 hhd. 28 gal. 2 qt.÷12.7. 196 Cd. 4 cd. ft. 12 cu. ft.÷36. 192 bu. 3 pk. 1 qt. 1 pt. ÷ 9. 45 T. 15 cwt. 25 lb. 7. 8. Divide 282 bu. 3 pk. 1 qt. 1 pt. by 9; by 10; by 12. 9. Divide 254 yd. 4 ft. 34 in. by 21; by 42. 10. A teamster drew 19 Cd. 2 cd. ft. 11 cu. ft. of wood in 15 loads. How much did he average per load? 11. Bought 6 spoons, which weighed 11 oz. 3 pwt. What was the weight of each spoon ? 12. How many iron rails, each 18 ft. long, will be required to lay 3 miles of railroad track? 13. The total weight of 18 hhd. of sugar is 7 T. 15 cwt. 66 lb. 4 oz. What is their average weight? 14. A man traveled by railroad 1000 miles in one day. What was the average rate per hour? 15. If a town 4 mi. square is divided into 62 farms of equal size, how much land will each farm contain? MEASUREMENTS. 206. Measurements involve a practical application of measures to the industrial and mechanic arts, and the common business of life. DEFINITIONS. 207. Dimensions are length, breadth, and thickness. 208. A line has only one dimension, length. A straight line is the shortest distance between two points. FIG. 1. 209. An Angle is the difference in the direction of two straight lines proceeding from a common point, called the vertex of the angle. A C Thus, in Fig. 1, ACD and DCB are angles, and C is their vertex. Thus, in Fig. 2, the lines AB and CD are perpendicular to each other, and form the two right angles ACD and DCB. 210. When two straight lines meet, so as to form equal adjacent angles, they are said to be perpendicular to each other, and the angles are called right angles. FIG. 2. A 213. A rectangle is a plane figure bounded by four straight lines, having four right angles. A square is a rectangle whose sides are equal. D B Rectangle. 211. A surface has two dimensions, length and breadth. 212. A plane figure is a portion of a plane surface bounded by straight or curved lines. B Square. |