How many yards in a mile? How many feet? Remember these numbers. (Perform without analysis.) 1. How many inches in 5 feet? 7 feet? 8 feet? 15 feet? 16 feet? 183 feet? 7.8 feet? 5.16 feet? 2. How many feet in 5 yards? 12 yards? 163 yards? 181 yards? 24 yards? 33 yards? 42.6 yards? 3. How many yards in 4 rods? 10 rods? 32 rods? 331 rods? 37 rods? 9.52 rods? 4. How many rods in 6 miles? 9 miles? 16 miles? 24} miles? 5. How many inches in 4 feet, 5 inches? 16 feet, 6 inches? 31 feet, 8 inches? 6. How many inches in 5 yd. 1 ft. 6 in.? 8 yd. 2 ft. 8 in.? 19 yd. 2 ft. 3 in.? 4 rd. 2 yd. 3 in.? 22 rd. 2 ft. 11 in.? 7. How many feet in 36 inches? 60 inches? 84 inches? 100 inches? 115 inches? 8. How many yards in 12 feet? 18 feet? 22 feet? 26 feet? 82 feet? 9. How many rods in 11 yards? 33 yards? 44 yards? 38 yards? 49 yards? 353 yards? 10. How many miles in 640 rods? 960 rods? 1,280 rods? 1,350 rods? 2,080 rods? 11. How many feet and inches in 65 inches? 88 inches? 131 inches? 164 inches? 236 inches? 12. How many yards, feet, and inches in 62 inches? 93 inches? 167 inches? 328 inches? 434 inches? 13. How many rods, yards, and feet in 37 feet? 62 feet? 69 feet? 86 feet? 14. How many miles, rods, and yards in 1,797 yards? 3,569 yards? 19,540 yards? 207. Define reduction. Define each kind. What is the form employed in Problem 1, above? In Problem 7? What is the general rule for reduction ascending? for reduction descending? (See Art. 17.) Illustrative Example. 1. Reduce 2 mi. 46 rd. 3 yd. 2 ft. 8 in. ANALYSIS. Since in 1 mile there are 320 rods, in any number of miles there are 320 times as many rods; hence, in 2 miles there are 320 times 2 rods, which are 640 rods. 640 rods +46 rods. 686 rods. Since in 1 rod there are 5 yards, in any number of rods there are 5 times as many yards; hence, in 686 rods there are 5 times 686 yards, etc. 2. Reduce 3 yd. 2 ft. 10 in. to inches. 3. Reduce 21 rd. 4 yd. 1 ft. to feet. Reduce to feet: 4 5 rd. 3 yd. 2 ft. 5. 8 rd. 4 yd. 1 ft. 6. 13 rd. 5 yd. 1 ft. 7. 38 rd. 2 yd. 8. 2 mi. 124 rd. 4 yd. 9. 5 mi. 312 rd. 2 ft. 10. 6 mi. 196 rd. 3 yd. 1 ft. Reduce to inches: 11. 3 yd. 2 ft. 12. 4 yd. 1 ft. 8 in. 13. 5 yd. 2 ft. 10 in. 14. 4 yd. 2 ft. 5 in. 15. 2 rd. 4 yd. 7 in. 16. 1 mile. 17. 1⁄2 mile. 208 Reduce to units of lower denominations: 1. of a mile. NOTE. .375 X 3 = 1.125 feet. .125 X 12 = 1.5 inches. 209. Reduce to units of higher denominations: 1. 80526 inches. ANALYSIS. Since there are 12 inches in 1 foot, in 80526 inches there are as many feet as there are 12's in 80526. There are 6710 12's in 80526, with a remainder of 6; hence, in 80526 inches there are 6710 feet and 6 inches. Since there are 3 feet in one yard, in 6710 feet there are as many yards as there are 3's in 6710. There are 2236 3's in 6710, with a remainder of 2; hence, in 6710 feet there are 2236 yards and 2 feet. Since in 1 rod there are 5 yards, in 2236 yards there are as many rods as there are times 5 yards in 2236 yards, or as there are times 11 half-yards in 4472 halfyards. There are 406 times 11 in 4472, with a remainder of 6; hence, in 4472 half-yards there are 406 rods, with a remainder of 6 half-yards, or 3 yards. Since there are 320 rods in a mile, etc. 210. 1. Reduce § of a foot to the fraction of a rod. ANALYSIS. 1 foot is of a yard. of a foot is of of a yard, which is of a yard. Since there are rod, and 1 yard is of a rod. yards in a rod, 1⁄2 of a yard is of a of a yard is off of a rod, which is 12 of a rod. Short form. ×× • 2. 6 inches are what part of a rod? 3. of a yard are what part of a mile? 4. 6 feet are what part of a rod? of a mile? 5. of an inch is what part of a yard? of 2 yards? of 21 yards? 6. 2 feet 3 inches are what part of a yard? of a rod? 7. 1 foot 9 inches are what part of a yard? of a rod? 8. 4 yards 2 feet are what part of a rod? of a mile? 9. of a foot are what part of a rod? 10. 2 feet are what part of a rod? 33 feet? 4 feet? 11. of a rod are what part of a mile? 21 rods? 31 rods? 12. Reduce to the fraction of a rod .12 of a foot; .015 of a foot? .08 of a yard; .7 of an inch. 13. Reduce .25 of a foot to the fraction of a mile; .375 of a yard; .875 of a rod. 14. Reduce of a foot to the fraction of 2 miles; of 3} miles. 211. 1. Change 3 yd. 2 ft. 3 in. to the decimal of a rod. ANALYSIS. 3 in. are of a foot. 2.25 ft. = = = .25. as many yds. = .75 yd. 375 yd. as many rd. = .68+ rd. 2. Change 4 yd. 2 ft. 6 in. to the decimal of a rod. (Reject all terms below fourth place.) 3. Change 3 rd. 5 yd. 1 ft. 8 in. to the decimal of a mile. 4. Change to the decimal of a mile: 4 rods; 6 rods; 20 rods; 10 rods, 3 yards; 50 rods, 5 yards, 2 feet; 80 rods, 2 yards, 2 feet, 9 inches. 212. SURFACE MEASURE. 1. A surface is that which has length and breadth only. 2. A surface is measured by finding how many surface units it contains? 3. The surface unit is usually a square whose side is a linear unit. 4. A square has the following properties: (a) It is a plane. (b) It is bounded by four equal straight lines. (c) Its angles are all right angles. 5. How many square inches in a square foot? square feet in a square yard? square yards in a square rod? 6. Draw a square rod on the scale of 1 inch to the yard. 7. Complete and learn the following table. 1. Reduce 2 sq. rd. 7 sq. yd. 5 sq. ft. 86 sq. in. to square inches. 2. Reduce 3 A. 84 sq. rd. 10 sq. yd. 2 sq. ft. to a simple number. 3. Reduce 3 sections, 480 A. 125 sq. rd. to square yards. 4. Reduce 12,652 square inches to a compound number. 5. Reduce 224,725 square rods to square rods, acres, and square miles. NOTE. The only troublesome divisor in square measure is 30. Ob serve the method in the following problem. |