27. Reduce 2 qt. 1 pt. to the fraction of a gallon. 1 pt., or 5 pt., are § of 1 gal., or 8 pt. 28. Reduce 1 ft. 3 in. to the fraction of a yard. 29. Reduce 3 qt. 1 pt. to the fraction of a peck. 30. Reduce 4 pk. 3 qt. to the fraction of a bushel. 31. Reduce 2 qt. 1 pt. 3 gi. to the fraction of a gallon. 32. Reduce 2 pk. 4 qt. 1 pt. to the fraction of a bushel. 33. Reduce 4 yd. 2 ft. 6 in. to the fraction of a rod. ADDITION OF DENOMINATE NUMBERS. 232. 1. Find the sum of 3 gal. 3 qt. 1 pt.; 5 gal. 2 qt. 1 pt.; 6 gal. 2 qt. 1 pt.; 8 gal. 3 qt. gal. qt. pt. 3 3 1 5 2 1 6 2 1 8 3 24 3 1 EXPLANATION. The numbers are written so that units of the same denomination stand in the same column, and we begin at the lowest denomination to add. The sum of the pints is 3 pt., which are equal to 1 qt. 1 pt.; the 1 pt. is written under pints and the 1 qt. reserved to add to the quarts. The sum of the quarts is 11 qt., which are equal to 2 gal. 3 qt.; the qt. are written under the quarts and the 2 gal. reserved to add to the gallons. The sum of the gallons is 24 gal., which are written under the gallons. Find the sum of: 2. 3 gal. 3 qt. 1 pt.; 18 gal. 2 qt. 1 pt.; 12 gal. 3 qt. 3. 8 bu. 3 pk. 5 qt.; 16 bu. 2 pk. 7 qt.; 12 bu. 3 pk. 4 qt. 4. 7 da. 5 hr. 20 min.; 8 da. 14 hr. 10 min.; 6 da. 18 hr. 5. 24 lb. 6 oz. (Av.); 35 lb. 14 oz. ; 26 lb. 10 oz.; 83 lb. 6. 13 lb. 4 oz. 10 pwt. 8 gr.; 11 lb. 5 oz. 11 pwt. 16 gr.; 10 lb. 10 oz. 15 pwt. 21 gr. 7. 10 yd. 2 ft. 10 in.; 15 yd. 1 ft. 9 in.; 8 yd. 2 ft. 7 in. ; 18 yd. 1 ft. 11 in.; 16 yd. 2 ft. 8 in. 8. 15 gal. 3 qt. 1 pt. 3 gi.; 18 gal. 2 qt. 1 pt. 2 gi.; 28 gal. 2 qt.; 21 gal. 1 pt. 3 gi. 9. 12 A. 35 sq. rd.; 14 A. 110 sq. rd.; 15 A. 132 sq. rd.; 11 A. 96 sq. rd.; 25 A. 100 sq. rd. 10. 5 T. 6 cwt. 14 lb. 10 oz.; 7 T. 15 cwt. 36 lb. 15 oz.; 17 T. 8 cwt. 84 lb. 12 oz.; 10 T. 9 cwt. 94 lb. 11 oz. 11. 5 yd. 2 ft. 8 in.; 3 yd. 1 ft.; 4 yd. 8 in.; 4 yd. 1 ft. 11 in.; 4 yd. 2 ft. 9 in.; of a yard and of a foot. SUBTRACTION OF DENOMINATE NUMBERS. 233. 1. From 12 lb. 6 oz. 7 pwt. take 3 lb. 8 oz. 10 pwt. oz. pwt. lb. 12 6 7 3 8 10 8 9 17 EXPLANATION. - The numbers are written so that units of the same denomination stand in the same column, and we begin at the lowest denomination to subtract. Since 10 pwt. cannot be subtracted from 7 pwt., a unit of the next higher order is united with the 7 pwt., making 1 oz. 7 pwt., or 27 pwt. Then 27 pwt. 10 pwt. = 17 pwt., which we write under pwt. in the remainder. Since 1 oz. was united with the 7 pwt., only 5 oz. are left in the minuend. Inasmuch as 8 oz. cannot be subtracted from 5 oz., a unit of the next higher order is united with it, making 1 lb. 5 oz., or 17 oz. Then 17 oz. 8 oz. 9 oz., which we write under oz. in the remainder. Since 1 lb. was changed to ounces, there are but 11 lb. left in the minuend. Then 11 lb. - 3 lb. = 8 lb. Therefore, the remainder is 8 lb. 9 oz. 17 pwt. 2. From 8 bu. 4 pk. 3 qt. take 3 bu. 2 pk. 7 qt. 3. From 12 gal. 2 qt. 1 pt. 2 gi. take 5 gal. 3 qt. 1 pt. 3 gi. 4. From 10 da. 5 hr. 20 min. take 7 da. 7 hr. 10 min. 5. From 31 lb. 4 oz. 15 pwt. take 8 lb. 6 oz. 12 pwt. 6. From 15 yd. 2 ft. 7 in. take 4 yd. 2 ft. 10 in. 7. From 12 rd. 4 yd. 1 ft. take 8 rd. 4 yd. 2 ft. 8. From 13 lb. 8 oz. 5 dr. take 7 lb. 10 oz. 7 dr. 9. From 18 A. 18 sq. rd. take 7 A. 110 sq. rd. 10. From 40 sq. yd. 8 sq. ft. 51 sq. in. take 15 sq. yd. 6 sq. ft. 100 sq. in. 11. From 25 T. 8 cwt. 75 lb. 10 oz. take 10 T. 11 cwt. 35 lb. 15 oz. 12. How many years, months, and days intervened between Dec. 24, 1892, and May 26, 1842 ? yr. mo. da. 1892 12 24 1842 5 26 50 6 28 EXPLANATION. Since the later date expresses the greater period of time, it is written as the minuend, and the earlier date is, therefore, the subtrahend. In writing the dates the number of the month is given instead of its name. The subtraction is then performed as in denominate numbers, considering a month as 30 days, and a year as 12 months. 13. How long was it from Dec. 10, 1835, to May 15, 1887 ? 14. How long was it from June 13, 1864, to Jan. 1, 1890 ? 15. How long was it from Apr. 8, 1839, to July 7, 1891? 16. How long was it from Sept. 23, 1881, to Aug. 10, 1892 ? MULTIPLICATION OF DENOMINATE NUMBERS. 234. 1. Multiply 3 bu. 3 pk. 7 qt. by 7. bu. pk. qt. 3 7 7 3 27 3 1 EXPLANATION. -7 times 7 qt. are 49 qt., or 6 pk. 1 qt. The 1 qt. is written under qt. in the product, and the 6 pk. reserved to add to the pecks. 7 times 3 pk. are 21 pk. ; 21 pk. + 6 pk. reserved are 27 pk., or 6 bu. 3 pk. The 3 pk. are written under pk. in the product, and the 6 bu. reserved to add to the bushels. Seven times 3 bu. are 21 bu. ; 21 bu. + 6 bu. reserved are 27 bu. Therefore, the product is 27 bu. 3 pk. 1 qt. 2. Multiply 4 bu. 3 pk. 5 qt. by 7. 7. Multiply 2 T. 5 cwt. 48 lb. 15 oz. by 8. 9. Multiply 12 cu. yd. 15 cu. ft. 1115 cu. in. by 6. 12. Multiply 12 rd. 4 yd. 2 ft. 8 in. by 8. DIVISION OF DENOMINATE NUMBERS. 235. 1. Divide 14 gal. 3 qt. 1 pt. by 4. 4)14 qt. pt. gal. 3 3 2 EXPLANATION.- One fourth of 14 gal. is 3 gal. and 2 gal. remainder. The 3 gal. are written in the quotient, and the 2 gal. remainder are united with the 3 qt., making 11 qt. One fourth of 11 qt. is 2 qt. and 3 qt. remainder. The 2 qt. are written in the quotient, and the 3 qt. remainder united with the 1 pt., making 7 pt. One fourth of 7 pt. is 13 pt. Therefore, the quotient is 3 gal. 2 qt. 13 pt. 2. Divide 21 gal. 3 qt. 1 pt. 3 gi. by 6. 8. Divide 19 hr. 10 min. 36 sec. by 6. PRACTICAL MEASUREMENTS. 236. When a straight line meets another straight line forming two equal angles, each angle is called a Right Angle. When two lines form right angles, they are said to be perpendicular to each other. 237. Lines equidistant throughout their entire length are called Parallel Lines. 238. A figure having four straight sides and its opposite sides parallel is called a Parallelogram. 1. When the angles of a parallelogram are right angles, it is called a Rectangle. 2. The side upon which a figure is assumed to stand is called the Base. 3. The perpendicular distance between the base of a figure and the highest point opposite it is the Altitude. 4. The straight line joining the opposite angles of a parallelogram is called its Diagonal. Altitude Two Right Angles Parallel Lines Parallelogram Rectangle Diagonal 239. To compute the area of a rectangular surface. 1. What is a square inch? Draw a figure 6 in. long and 1 in. wide with all its angles equal. How many sq. in. does it contain? 2. If the figure were 2 in. wide, how many sq. in. would it contain? How many, if it were 3 in. wide? 4 in. wide? 5 in. wide? 6 in. wide? 3. What is a square foot? How many sq. ft. are there in a strip of ground 12 ft. long and 1 ft. wide, with all its angles equal? How many, if it is 2 ft. wide? 3 ft. wide? 4 ft. wide? 5 ft. wide? 6 ft. wide? 4. How many sq. yd. are there in a walk 15 yd. long and 5 yd. wide, having its angles all equal? |
