CHAPTER VII DENOMINATE NUMBERS 98. Denominate Number. A concrete number that expresses measure is called a denominate number. For example, $7 and 2 feet 3 inches are denominate numbers, but not 5 chairs or 8 rivers. 99. Compound Number. A denominate number involving two or more different units is called a compound number. For example, 2 feet 3 inches, or 3 hours 20 minutes. We do not usually speak of $2.50 as a compound number because it is written as an integer and a decimal fraction. If we should write 24 feet or 2.25 feet instead of 2 feet 3 inches, we should not be using compound numbers. Some work in compound numbers is done in the primary grades, and many of the common measures are therefore already known. 100. Measures of Length. The table of common measures of length is as follows: 320 rods, or 5280 feet = 1 mile (mi.) A hand (4 in.) is used in measuring the height of horses; a fathom (6 ft.) and cable length (120 fathoms) in measuring depths of water; a knot (nautical mile, 1.152 common or statute miles, or 6080.27 ft.) in measuring distances at sea. Carpenters and mechanics usually write 2' 6" for 2 ft. 6 in. 101. Reduction. The process of changing the unit of a number without changing the value is called reduction. Thus 2 ft. 6 in. = 30 in. : = 2.5 ft. 102. Reduction Descending. Reduction from a higher to a lower denomination is called reduction descending. For example, required to reduce 2 ft. 3 in. to ft. in. 2 3 For convenience the actual multiplications and additions are carried out as shown at the right. In practical life we seldom have reductions involving more than two different units (denominations), and in this arithmetic other cases will not in general be considered. Therefore, in reduction descending, multiply the number of the highest denomination given, by the number showing how many units of the next lower denomination are equal to one of the higher. To the product add the given number of this lower denomination. Proceed thus with each successive result until the required denomination is reached. 19. A knot being 1.152 miles, how many miles does a ship sail in going 480 knots ? 103. Reduction Ascending. Reduction from a lower to a higher denomination is called reduction ascending. For example, required to reduce 104 in. to higher units. For practical purposes the work may be arranged as shown at the left, but the explanation is better understood from the following: 12)104 (in.) Since 1 in.1⁄2 ft., 104 in. =104 × ft. = 8 ft. = 8 ft.8 in. Since 1 ft. yd., 8 ft. 8x yd. =2} yd. =2 yd. 2 ft. Therefore the answer is 2 yd. 2 ft. 8 in. Therefore, in reduction ascending, Divide the given number of units by the number of units required to make one of the next higher denomination. Divide this quotient and each successive quotient in like manner until the required denomination is reached. The last quotient with the several remainders arranged in order is the answer sought. Reduce to yards, or to yards and one lower unit : 104. Square. A flat surface that has four equal sides and four equal angles is called a For example, if this figure represents a surface 4 yd. long and 2 yd. wide, the area is 2 x 4 x 1 square yard, or 8 square yards. 106. Square Measure. The common table of square measure is as follows: 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) 30 square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq. mi.) 62 sq. yd. 6. 124 sq. rd. 8. 15 A. 11. 25 sq. mi. 9. 35 A. 12. 150 sq. mi. 3. 60 sq. ft. 13. Reduce 75 sq. ft. 36 sq. in. to square inches. 14. Reduce 2 sq. yd. 58 sq. in. to square inches. 15. Reduce 52 sq. yd. 8 sq. ft. to square feet. 16. Reduce 67,592 sq. in. to higher units. 17. Reduce 47,916 sq. ft. to higher units. 18. Reduce 22,471 sq. yd. to higher units. |