There are 12 months in a year. The names and the number of days in each are as follows: 1. January (Jan.) 31 days. 3. March (Mar.) 31 da. 4. April (Apr.) 30 da. 5. May (May) 31 da. 6. June (June) 30 da. 7. July (July) 31 da. 8. August (Aug.) 31 da. 9. September (Sept.) 30 da. 10. October (Oct.) 31 da. 11. November (Nov.) 30 da. 12. December (Dec.) 31 da. The 29th day of February is the day added to make the leap year. The following rhyme will serve to fix in memory the days in each month: Thirty days hath September, All the rest have thirty-one, Save February, which alone Hath twenty-eight, and one day more We add to it one year in four. EXERCISES. 1. How many sec. are there in 5 min. ? In 6 min.? In 10 min.? In 35 da.? 2. How many min. are there in 2 hr.? In 3 hr.? 3. How many hr. are there in 2 da.? In 4 da.? In da. ? 4. How many da. are there in 3 wk.? In 6 wk.? 5. How many wk. are there in 14 da. ? 6. How many hr. are there in 240 min.? 7. How many min. are there in 120 sec.? 8. How many da. are there in 4 wk. 3 da.? In 180 min. ? In 300 sec.? In 5 wk.? 9. Which of the following named years are leap years? 1880? 1892? 1900? 2000? 1864? 1870 ? 10. How many da. are there in June? In Dec.? In Mar.? In Aug.? In Jan.? In Sept.? In Feb.? STATIONERS' TABLE. 223. The following table is used in the paper trade: 1. How many things are there in 3 doz.? In 6 doz.? 2. How many are 3 score? 3 score and 10? 3. How many doz. are there in 3 gr.? In 1 G. gr.? 4. How many sheets are there in 2 qr.? In 5 qr.? 3. How many qr. are there in 3 R.? In 6 R.? In 61 R.? 6. How many qr. are there in 48 sheets? In 96 sheets? REDUCTION OF DENOMINATE NUMBERS. 225. The process of changing a denominate number from one denomination to another without altering its value is called Reduction. 226. The process of changing a denominate number to an equivalent number of a lower denomination is called Reduction to Lower Denominations, or Reduction Descending. 227. The process of changing a denominate number to an equivalent number of a higher denomination is called Reduction to Higher Denominations, or Reduction Ascending. REDUCTION TO LOWER DENOMINATIONS. 228. 1. How many inches are there in 7 yd. 1 ft. 4 in. ? 7 EXPLANATION. - Since there are 3 ft. in 1 yd., in 7 yd. there are 7 times 3 ft., or 21 ft., and 21 ft.+ 1 ft. = = 22 ft. Since there are 12 in. in 1 ft., in 22 ft. there are 22 times 12 in., or 264 in., and 264 in. + 4 in. 268 in. Therefore 7 yd. 1 ft. 4 3 21 1 22 12 The business method of reducing denominate numbers to 264 lower denominations is more convenient than that given in the 4 explanation. It is illustrated by the process in the margin. 268 229. Hence the business method is as follows: To reduce denominate numbers to lower denominations, multiply the number of the highest denomination given by the number indicating how many units of the next lower denomination are equal to one of the higher, and to the product add the number given of this lower denomination. Proceed in like manner with this and each successive result thus obtained, until the number is reduced to the required denomination. Reduce to lower denominations: 2. 4 yd. 2 ft. 8 in. 3. 12 yd. 1 ft. 7 in. 4. 15 yd. 2 ft. 10 in. 5. 27 yd. 2 ft. 11 in. 6. 6 gal. 3 qt. 1 pt. 7. 13 gal. 2 qt. 1 pt. 8. 15 gal. 1 qt. 1 pt. 2 gi. 9. 18 gal. 3 qt. 1 pt. 3 gi. 10. 4 hr. 15 min. 15 sec. 11. 10 hr. 12 min. 18 sec. 12. 18 hr. 20 min. 35 sec. 13. 4 cwt. 20 lb. 8 oz. 14. 8 cwt. 75 lb. 12 oz. 15. 2 T. 5 cwt. 80 lb. 12 oz. 16. 4 T. 7 cwt. 35 lb. 9 oz. 17. 4 lb. 6 oz. 18 pwt. 10 gr. 18. 8 lb. 4 oz. 10 pwt. 8 gr. 19. 5 lb. 5 oz. 15 pwt. 9 gr. 20. 3 bu. 3 pk. 5 qt. 1 pt. 21. 5 bu. 2 pk. 7 qt. 1 pt. 22. 6 bu. 1 pk. 4 qt. 1 pt. 30. 31. 32. 23. 4 rd. 3 yd. 2 ft. 6 in. 24. 5 rd. 2 yd. 1 ft. 8 in. 25. 8 rd. 1 yd. 2 ft. 10 in. 26. 3 sq. yd. 4 sq. ft. 18 sq. in. 27. 5sq.yd. 8 sq. ft. 100 sq.in. 28. 2 A. 110 sq. rd. 5 sq. yd. 29. 8 A. 25 sq. rd. 4 sq. yd. 2 cu. yd. 10 cu. ft. 85 cu. in. 4 cu.yd. 6cu. ft. 714 cu. in. 3 lb. 2 oz. 7 dr. 1 sc. 33. 4 lb. 8 oz. 5 dr. 2 sc. 34. 3 R. 10 qr. 18 sheets. 35. 4 R. 8 qr. 10 sheets. 36. 3 lb. 6 oz. 10 pwt. 37. 5 lb. 10 oz. 3 sc. 38. 6 da. 10 hr. 25 min. 39. 8 bu. 3 pk. 7 qt. 1 pt. 40. 8 rd. 4 yd. 2 ft. 6 in. 41. 30 bu. 3 pk. 6 qt. 42. 5 A. 140 sq. rd. 3 sq. yd. 43. 7 mi. 100 rd. 13 ft. 6 in. 44. Reduce .75 yd. to feet and inches. .75 3 2.25 12 3:00 .75 yd. = 2 ft. 3 in. EXPLANATION. -Since in 1 yd. there are 3 ft., in .75 yd. there are .75 of 3 ft. or 2.25 ft. Since in 1 ft. there are 12 in., in .25 ft. there are .25 of 12 in., or 3 in. Therefore, .75 yd. = 2 ft. 3 in. REDUCTION TO HIGHER DENOMINATIONS. 230. 1. Reduce 235 pints to bushels, pecks, etc. Since there are 2 pt. in 1 qt., in 235 pt. there are as many quarts as 2 pt. are contained times in 235 qt., or 117 qt. 1 pt. Since there are 8 qt. in 1 pk., 235 pt. =3 bu. 2 pk. 5 qt. 1 pt. there are as many pecks in 117 qt. as 8 qt. are contained times in 117 qt., or 14 pk. 5 qt. Since there are 4 pk. in 1 bu., in 14 pk. there are as many bushels as 4 pk. are contained times in 14 pk., or 3 bu. 2 pk. Therefore, 235 pt. are equal to 3 bu. 2 pk. 5 qt. 1 pt. 231. Hence it is evident that: To reduce a denominate number to units of higher denominations, the given number is divided by the number indicating how many units of the given denomination make one of the next higher denomination. We proceed in like manner with this, and each successive quotient, till the whole is reduced to the required denomination. The last quotient, with the remainders (when there are any) annexed, will be the required answer. 2. Reduce 3265 inches to rods, yards, etc. |
