RULE. Divide the given number 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. EXPLANATION.-Since there are 12 in. in 1 ft., 12 of the number of inches equals the number of feet. 1 of 6 equals .5; therefore there are 2.5 ft. Since there are 3 ft. in 1 yd., of the number of feet equals the number of yards. of 2.5 is .8333+; therefore there are 3.8333+ yd., etc. 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 is bounded by four equal straight sides and has 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. 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? 2. How many square feet are there in the surface of a rectangle 9 ft. by 5 ft.? In one 8 ft. by 7 ft.? In one 10 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. Reduce to units of lower denominations: 20. sq. rd. 22. sq. rd. 24.172 sq. yd. 26. sq. rd. 21..625 A. 23..545 sq. rd. 28. Reduce SOLUTION. 25. .875 sq. ft. 27..495 A. of a sq. yd. to the fraction of a sq. rd. 29. Reduce 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 MEASURES OF VOLUME. 215. Anything which has length, breadth, and thickness is called a Solid. 216. A solid having six equal square sides or faces is called a Cube. A cube whose sides or faces are each a square inch is called a Cubic Inch. One whose sides are each a square foot is called a Cubic Foot. One whose sides are each a square yard is called a Cubic Yard. 217. The number of solid units any body contains is its Solid Contents or Volume. Thus, if a solid is 4 ft. long, 3 ft. wide, and 3 ft. thick, its solid contents or volume is 36 cubic feet. For it may be divided into 3 blocks, each containing 12 cubic feet. The number of cubic feet in each block is equal to the product of the numbers expressing the length and breadth of the solid, and the number of blocks is equal to the number of units of thickness. Therefore, 218. PRINCIPLE. The volume of any rectangular solid is equal to the product of the numbers expressing its length, breadth, and thickness. The length, breadth, and thickness must be expressed in units of the same denomination. 1. How many cubic inches are there in a rectangular solid 3 in. long, 2 in. wide, and 2 in. thick? 2. How many cubic inches are there in a rectangular solid 1 ft. long, 1 ft. wide, and 1 ft. thick, or a cube whose edge is 1 ft.? |