1. Multiply 33 yds. 2 ft. 11 in. by 17. 7. Multiply 150 rds. 2 yds. 1 ft. by 235. 9. Divide 200 mi. 56 rds. 3 yds. 2 ft. by 121. 10. Multiply 11 mi. 200 rds. by 14. 11. Multiply 52 mi. 1021 yds. by 47. 12. Divide 43 mi. 280 rds. by 24. FRACTIONS OF SIMPLE AND COMPOUND QUANTITIES. 152. Express of a mile in rods, feet, and inches. Express 0.6275 of a mile in rods, feet, and inches. Find the value of § of 3 rds. 14 ft. 7 in. Here we multiply by the numerator of the fraction, and divide the product by the denomi rds. ft. in. 3 14 7 5 NOTE. When the multiplier is a mixed number, multiply by the integer and the fraction separately, and add the resulting products. 10. Take of 4 mi. from 7 of 3 mi. 18 rds. 3 yds. 2 ft. 11. Add 0.525 mi., 0.125 rd., 0.5 yd., 0.16 ft. TO EXPRESS ONE QUANTITY AS THE FRACTION OF ANOTHER. 153. Express 145 rds. 2 yds. 1 ft. 6 in. as the fraction Express 120 rds. 3 yds. 1 ft. 6.72 in. as the decimal of a 6.72 in. ÷ 12 = 0.56 ft., and this joined with mile. 12 6.72 in. the 1 ft. gives 1.56 ft. 1.56 ft. ÷ 3 and this joined with 3 yds. gives 3.52 yds. 3.52 yds. 5.5 gives 0.64 rds., and this joined with 120 rds. gives 120.64 rds. 120.64 rds. ÷ 320 gives 0.377 mi. 0.377 of a mile. Ans. NOTE. When the quotient is in any case a non-terminating decimal, find the quotient to five decimal places, and the required answer will be sufficiently accurate for all practical purposes. 154. Express 1 yd. 2 ft. 3 in. as the fraction of 5 yds. 1 ft. 3 in. NOTE. If the answer to the last problem is to be expressed as a decimal fraction, first find the answer as a common fraction, and reduce this common fraction to a decimal fraction. Ex. 104. Express : 1. 125 rds. 4 yds. 2 ft. 6 in. as the fraction of a mile. 2. 1 yd. 2 ft. 3 in. as the fraction of 5 yds. 3. 51 rds. 1 yd. 3.6 in. as the decimal of a mile. 4. rd. + yd. as the fraction of a mile. 5. 3 mi. 53 rds. 4 yds. 1.2 ft. as the decimal of 5 mi. 89 rds. 3 yds. 2 ft. 6. 2 mi. 138 rds. 1 yd. as the fraction of 3 mi. 265 rds. 3 yds. 7. 233 rds. 9 ft. 10.8 in. as the decimal of a mile. 8. 3 mi. 242 rds. 23 yds. as the decimal of 7 mi. 160 rds. 9. 2 ft. 7 in. as the decimal of 100 yds. 10. 11 rds. 4 yds. 4 in. as the fraction of a mile. 11. rd. + yd. + ft. as the fraction of a rod. 12. 195 yds. 1 ft. 8 in. as the fraction of of a mile. 13. 1 mi. 232 rds. 4 yds. 1 ft. 6 in. as the fraction of 8 mi. 204 rds. 0 yd. 1 ft. 6 in. 14. 127 rds. 3 ft. 3.6 in. as the decimal of a mile. 15. 261 rds. 4 yds. 1 ft. 6 in. as the fraction of a mile. 16. of the difference between 3 yds. 2 ft. 11 in. and 10 yds. 7 in. as the fraction of 16 yds. 17. 7 rds. 1 ft. 3.17 in. as the decimal of 76 rds. 2 yds. 5 in. 18. 248 rds. 4 yds. 2 ft. 8 in, as the fraction of 2 mi. MEASURES OF SURFACE. 155. A surface has two dimensions, length and breadth. 156. If a surface is flat and has four square corners, it is called a rectangle. 157. If a rectangle has its four sides equal, it is called a square. 158. The unit of surface is a square each side of which is a linear unit. 159. The area of a surface is the number of square units it contains. 160. Suppose the rectangle in the margin is 3 in. long and 2 in. wide. If lines are drawn as represented in the figure, the surface will be divided into square inches. There will be 2 horizontal rows of 3 square inches each; that is, in all, 2 x 3 square inches. Hence, Express the length and breadth of a rectangle in the same linear unit; the product of these two numbers will express its area in square units of the same name as the linear unit of the sides. Conversely, the number of square units in a rectangle divided by the number of linear units in one side will give the number of linear units in its adjacent side, |
