DENOMINATE NUMBERS 1. Write from memory the following tables : Liquid Measures, Dry Measures, Avoirdupois Weight, Time Measures, and Measures of Length or Distance. 2. 1 yr. = da. hr. mo. = = min. = sec. rd. = ft. lb. OZ. 3. 1 mi. yd. in. 4. 1 T. cwt. = 5. 1 bu. pk. qt. 6. 1 gal. qt. pt. The standard or principal units of measure are as follows: Liquid - gallon. Length or distance — yard. Dry — bushel. Avoirdupois — pound (16 oz.). Time — day All other measures are determined from the above unit measures. Thus, the ton is 2000 times 1 pound (16 oz.). The hour is of the day, the period of one revolution of the earth on its axis. A denominate number is a concrete number whose unit is a measure established by custom or law; as, 10 feet or 5 pounds, in which 1 foot and 1 pound are the units of measure. A simple denominate number is a number of one denomination; as, 12 rods, 2 ounces, 5 days, etc. A compound denominate number is composed of two or more concrete numbers that express one quantity; as, 6 yards, 2 feet, and 4 inches. Here yards, feet, and inches are used to express but one quantity, length. 1. Change 3 gal. 3 qt. 1 pt. to pints. gal. qt. pt. 3 3 1 Observe that 4 qt. is really the multi4 plicand and 3 the multiplier in finding the 12 first product; and that 2 pt. is really the multiplicand and 15 the multiplier in finding 15, number of quarts. the second product. In considering the num bers abstractly, however, either factor may 2 be regarded as the multiplicand and the 30 arrangement as indicated saves time. +1 31, number of pints. +3 2. Change .875 gallon to pints. .875 4 Since there are 4 qt. in a gallon, in .875 of a gallon there are .875 of 4 qt., or 3.5 qt. 3.500, number of qt. Since there are 2 pt. in 1 qt., in .5 of a quart 2 there is 1 pt. The answer is 3 qt. 1 pt. 1.00, number of pt. Change : 3. 15 lb. 8 oz. to ounces. 10. .75 yd. to inches. 4. 96 ft. 5 in. to inches. 11. 44 T. to pounds. 5. 5.5 bu. to quarts. 12.7 min. to seconds. 6. 3.5 pk. to pints. 13. 6.5 L. T. to pounds. 7. 18 cwt. 25 lb. to pounds. 14. 63.5 gal. to pints. 8. 23 hr. 16 min. to minutes. 15. bu. to quarts. 9. 8.3 mi. to yards. 16. 108 bu. to pecks. 17. Change 266 quarts to bushels. 8)266 There are 1 as many pecks as quarts, 4)33 no. of pk. + 2 qt. that is, 33 pk. + 2 qt. There are as 8 no. of bu. +1 pk. many bushels as pecks, that is, 8 bu. + 1 pk. Hence, 266 qt. 8 bu. 1 pk. 2 qt. = 8 bu. 1 pk. 2 qt. Change to higher denominations: 18. 342 inches. 23. 347 cwt. 28. 43920 in. 19. 6625 yards. 24. 6095 pounds. 29. 6875 sec. 20. 5281 feet. 25. 16857 rods. 30. 56.5 pk. 21. 2043 seconds. 26. 11097 qt. (Dry). 31. 684.5 rd. 22. 1033 ounces Av. 27. 952 pt. (Liquid). 32. 9643 min. 33. How many gallons of milk will a family consume in 75 days, if they use 2 qt. 1 pt. daily ? 34. How much is received for 11 bushels of chestnuts at 8 cents a quart ? 35. How much will 15 turkeys, averaging 14 lb. each, cost at 18 cents a pound ? 36. If 100 tons of coal are bought by the long ton, at $2.24 a ton, and sold by the short ton at the same price, how much is gained ? 37. At 20 cents'an hour, how much will a man earn in 26 days, working each day from 8 A.M. to 5 P.M., allowing 1 hour for lunch ? 38. If a flour mill grinds wheat at the rate of 1 pint in 5 seconds, in how many hours and minutes will it grind 21,600 bushels ? 39. A train goes 104 miles in 3 hours and 15 minutes. What is the rate per hour ? 40. At 6 cents a foot find the length in miles and rods of a telephone wire that costs $ 4672.80. 41. If a man's step averages 2 ft. 6 in., how far will he travel in taking 6600 steps ? Relations of denominate measures. 6 qt. 1. À pk. is what decimal part of a bushel ? pk. = 6 qt. 6 bu. = .1875 bu. 32 2. 3 ft. 2 in. is what fractional part of a rod ? 3 ft. 2 in. = 38 in. 1 rod = 198 in. 3 ft. 2 in. or gird. Find the fractional part: 3. 24 hr. is of 1 day. 6. 13 pt. is of 3 qt. 4. 71 ft. is of 1 rod. 7. 21 in. is of 10 ft. 5. 31 qt. is of 1 gallon. 8. 11 qt. is of 2 gal. 38 198" Find the fractional part: 9. 15 hundredweight is of 1 ton. 10. 3.5 quarts is of 1 bushel. 11. 280 rods is of 1 mile. 12. 37 pounds 8 ounces is of 1 hundredweight. 13. 440 yards is of 1 mile. Find the decimal part: 14. 16 hours 48 minutes is of 1 day. 15. 1 foot 8 inches is of 1 rod. 16. 183 pounds 12 ounces is of 1 ton. 17. 15 minutes 50 seconds is of 1 hour. 18. A machinist works 10 hr. per day in summer and 84 hr. per day in winter. If his wages in summer are $3.35 per day, at the same rate find his wages per day in winter. pt. ADDITION AND SUBTRACTION 1. Find the sum of 2 gal. 3 qt. 1 pt., 4 gal. 1 qt. 1 pt., 7 gal. 1 pt., 5 gal. 3 qt. gal. qt. 2 3 1 The sum of the pints = 3 pt. = 1 qt. and 1 pt. 4 1 1 The sum of the quarts +1 qt. carried = 8 qt. = 7 0. 1 2 gal. O qt. 5 3 0 The sum of the gallons + 2 gal. carried = 20 gal. 20 0 1 Add: 3. 5 T. 11 cwt., 4 T. 15 cwt. 60 lb., 11 T. 80 lb., 19 T. 3 cwt. 64 lb. 4. 9 yr. 120 da. 8 hr., 12 yr. 104 da. 17 hr., 14 da. 5. 3 wk. 6 da. 15 hr., 4 wk. 3 da. 9 hr., 7 wk. 5 da. 14 hr. |