19. The wheel of a bicycle is 9.13 feet around. many times will it turn in going a mile, or 5280 feet? How 20. A man owning .4725 of a vessel, sold .3 of his share. What part had he left? 21. The distance around a circle is about 3.1416 times the distance across it. If the distance across a certain circular race-course is 1710 feet, what is the distance around it? 22. Two men start from the same place at the same time and travel in opposite directions. One goes 4.31 miles an hour, the other 3.92 miles an hour. How far apart will they be in 17 hours? 24. A grocer bought 15 barrels of sugar, each containing 219 pounds, for $125, and sold it at 5 cents a pound. What was his gain? 25. If .67 of a ton of hay is worth $7.50, what are 6.75 tons worth? 26. If the price of gas is $1.75 per thousand cubic feet, find the amount of a man's bill when 11,350 cubic feet have been consumed. 27. At $57.60 per acre, what are three fields worth containing, respectively, 14.6 acres, 20.25 acres, and 27.625 acres? 28. A real estate agent having 2735 acres of land to sell, sold, at different times, 183.26 acres, 412.625 acres, 640 acres, 150.875 acres, 240.5 acres, and 61.971 acres. How much remained unsold? 29. A merchant bought 150 barrels of apples for $1.87 a barrel. He sold seven tenths of them at $1.95 a barrel, and the remainder at $1.80 a barrel. Did he gain or lose, and how much? 30. How many rods of fence will surround a rectangular field 29.0345 rods long and 22.3265 rods wide? 31. A flour dealer bought 326 barrels of flour at $5.25 per barrel. He sold 58 barrels at a loss of $.37 per barrel, How must he sell the rest per barrel to gain $12 on the investment? 34. A has 137 cords of wood in one pile, 15.66 cords in a second, 18 cords in a third, and 21 cords in a fourth. How many cords has he in all, and what is the wood worth at $4.25 per cord? 35. Twenty-three miles of a railroad, 47.95 miles long, cost $11,578.40 per mile; 12 miles cost $13,357.82 per mile, and the remainder cost $19,125.26 per mile. What was the average cost per mile of the entire road? 36. A contractor built a house for $3575. The material cost him $2150.65, and he employed 15 men for 6 weeks of 6 days each, at $2.10 per day. Did he gain or lose money, and how much? 12-0.6, 16-0.8 17 37. What is the value of (12-0.6+ 117) + 183 ? 4 2 38. Mr. D. H. Noble bought of Henry Daron & Co., 9 pairs of calf boots at $4.25 a pair, 7 pairs of kip boots at $3.15 a pair, 12 pairs of ladies' kid shoes at $2.65 a pair, and 8 pairs of ladies' cloth shoes at $2.25 a pair. Make out and receipt the bill. 39. Mrs. B. D. Ross bought of Cook & Co., Philadelphia, 14 yards of silk at $1.37 a yard, 45 yards of sheeting at 7 cents a yard, 9 handkerchiefs at 25 cents apiece, 3 pairs of kid gloves at $1.12 a pair, and 5 neckties at 50 cents each. Make out and receipt this bill as clerk for Cook & Co. DENOMINATE NUMBERS. 198. A concrete number in which the unit of measure is established by law or custom is called a Denominate Number. Thus, 7 dollars, 2 feet, 4 inches, 5 hours, 8 quarts, 6 pounds, are denominate numbers. 199. A denominate number which is composed of units of one denomination only is called a Simple Denominate Number. Thus, 5 ounces, 7 yards, 3 miles, 6 hours, 10 pounds, 12 quarts, are simple denominate numbers. 200. A denominate number which is composed of units of two or more denominations that are related to each other, is called a Compound Denominate Number. Thus, 3 yards, 2 feet, 4 inches, is a compound denominate number. So also is 1 year, 5 months, 3 days. 201. A unit of measure, from which other units of the same kind may be derived, is called a Standard Unit. Thus, the yard is the standard unit of length, because the other units are derived from it. 202. The ratio by which numbers increase and decrease is called a Scale. Scales are either uniform or varying. Thus, in United States currency the scale is uniform, being decimal; in Linear measure it is varying, for 12 inches equal one foot, 3 feet one yard, etc. REDUCTION. LINEAR MEASURES. 203. That which has length only is called a Line. Thus, the distance between two objects or places is a line. 204. Measures that are used in measuring length only are called Linear Measures. NOTE. The tables of Denominate Numbers will be found on page 416 and the subsequent pages. 1. How many inches are there in 5 ft. ? 5. How many rods are there in 2 mi. ? 10 mi.? In 30 mi.? In 100 mi. ? In 7 ft.? In 7 yd.? In 4 rd. ? In 4 rd.? In 3 mi.? In 6. How many inches are there in 2 ft. 6 in. ? 4 in.? In 5 ft.? In 5 ft. 2 in. ? In 3 ft. 7. How many feet are there in 2 yd. 2 ft.? In 3 yd. 2 ft.? In 10 yd.? In 10 rd.? 8. How many yards are there in 2 rd. 3 yd.? In 4 rd. 2 yd.? In 10 rd. 2 yd.? In 1 mi.?. 9. How many rods are there in 1 mi. 80 rd.? In 2 mi. 60 rd.? In 5 mi. 80 rd.? 10. How many inches are there in ft.? Inft.? In ft.? In & ft.? In ft. ? 205. The process of changing a denominate number from one denomination to another without altering its value is called Reduction. 206. The process of changing a denominate number to an equivalent number of a lower denomination is called Reduction to Lower Denominations. 3 15 2 17 12 204 8 212 WRITTEN EXERCISES. 1. Reduce 5 yd. 2 ft. 8 in. to inches. EXPLANATION. - Since there are 3 feet in 1 yard, in 5 yards there are 5 × 3 feet 15 feet, and 15 feet + 2 feet: = 17 feet. Since there are 12 inches in 1 foot, in 17 feet there are 17 x 12 inches = 204 inches + 8 inches 212 inches. Hence 5 yd. 2 ft. 8 in. 212 inches. = RULE. 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 feet: 6. 30 rd. 6 ft. 7. 2 mi. 15 rd. 8 ft. 13. 25 rd. 12 ft. 4 in. of a rod to units of lower denominations. |