25. Reduce .885 of a yd. to feet and inches. 30. .375 rd. 32. .725 mi. 31. .645 rd. 33. .975 mi. ? In 72 in.? In 48 ft.? In 22 yd.? In 66 ft.? 26. .75 yd. 28. .625 yd. 27. .95 yd. 29. .875 yd. 207. 1. How many feet are there in 48 in. 2. How many yards are there in 30 ft.? 3. How many rods are there in 11 yd.? 4. How many rods are there in 33 ft. ? 5. How many miles are there in 640 rd. ? 6. What part of a rod are 81 ft. ? 4 ft.? 11 ft. ? 208. The process of changing a denominate number to an equivalent number of a higher denomination is called Reduction to Higher Denominations. In 960 rd.? are 12 inches in 1 ft., in 641558 inches there are as many feet as 12 in. are contained times in 641558 in., or 53463 ft. and 2 in. Since there are 3 ft. in 1 yd., in 53463 ft. there are as many yards as 3 ft. are contained times in 53463 ft., or 17821 yd. 5 Ans. 10 mi. 40 rd. 1 yd. 2 in. Since there are 5 yd. in 1 rd., in 17821 yd. there are as many rods as yd. are contained times in 17821 yd., or what is the same thing, as many times as 11 half-yards are contained times in 35642 half-yards, or 3240 rd. and 2 half-yards, or 1 yd. remaining. Since there are 320 rd. in 1 mi., in 3240 rd. there are as many miles as 320 rd. are contained times in 3240 rd., or 10 mi. and 40 rd. -. 641558 in. = 10 mi. 40 rd. 1 yd. 2 in. RULE. · Divide the given quantity by the number indicating how many units of the given denomination make one of the next higher denomination. 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, if any, annexed, will be the required answer. Reduce to higher denominations: 17. Reduce of a ft. to the fraction of a mile. 30. Reduce 3 yd. 2 ft. 6 in. to the decimal of a rod. .6969+ rd. 3.8333+ yd. 53.8333+ yd. We arrange the numbers as Therefore there are 2.5 ft. 3.8333+ yd. Therefore there are 3.8333+ yd. ÷ 5 = .6969 rd. Reduce to the decimal of a rod: 31. 3 yd. 2 ft. 8 in. 32. 4 yd. 1 ft. 6 in. Express as rods and decimals of a rod : 34. 4 rd. 3 yd. 1 ft. 5 in. 33. 2 yd. 2 ft. 5 in. 35. 8 rd. 1 yd. 2 ft. 9 in. SURFACE MEASURES. 209. Anything that has only length and breadth is called a Surface. Thus, this page, the floor, or the outside of anything is a surface. 210. The difference in the direction of two lines that meet is called an Angle. 211. A figure that has four equal sides and four equal angles is called a Square. A square inch is a square each of whose sides is one inch long; a square foot is a square each of whose sides is one foot long. The angles of a square are called right angles. 212. A figure that has four straight sides and four right angles is called a Rectangle. It will be seen that a square is a rectangle whose four sides are equal each to each. ANGLE. SQUARE. RECTANGLE. 213. The number of square units in the surface of anything is called its Area. Thus, if a rectangle is 4 inches long and 3 inches wide, the area will be 12 square inches. For it may be divided into 4 rows, each containing 3 square inches or units, and the entire area will be 12 square inches. The method of computing the area of figures that are not rectangular is given in MENSURA TION. 214. PRINCIPLE. The area of a rectangle is equal to the product of the numbers that express its length and breadth. The length and breadth must be expressed in units of the same denomination. 1. How many square inches are there in the surface of a rectangle that is 6 in. long and 4 in. wide? In one 8 in. long and 5 in. wide? In one 7 in. long and 6 in. wide? feet are there in the surface of a In one 8 ft. by 7 ft.? In one 10 ft. 2. How many square rectangle 9 ft. by 5 ft.? by 8 ft.? 3. How many square inches are there in a square whose sides are 5 in. ? 6 in. ? 8 in.? 12 in., or 1 ft.? How many square inches, then, are there in a square foot? 4. How many square feet are there in a square whose sides are 2 ft.? 3 ft., or 1 yd.? How many square feet are there, then, in a square yard? 5. How many square yards are there in a square whose sides are 3 yd.? 4 yd.? 5 yd.? 5 yd., or a rod? How many square yards are there in a square rod? 6. How many square rods are there in a rectangle 8 rd. by 6 rd.? 10 rd. by 12 rd. ? 10 rd. by 16 rd.? A rectangle that contains 160 square rods is called an Acre. 7. How many rods are there in a mile? How many square rods are there in a square whose sides are each a mile, or how many square rods are there in a sq. mi. ? 8. Since there are 160 sq. rd. in an acre, how many acres are there in a square mile? 9. Write out a table of square measures. 28. Reduce SOLUTION. 29. Reduce of a sq. yd. to the fraction of a sq. rd. of a sq. ft. to the fraction of a sq. rd. 30. Reduce & of a sq. in. to the fraction of a sq. yd. 31. Reduce .65 of a sq. yd. to the fraction of an A. 32. Reduce 5 sq. ft. 100 sq. in. to the decimal of a sq. yd. STAND. AR.- 12 |