63. At $ per yard, how much silk can be bought for $15.75? 64. If .625 of a barrel of flour is worth $4, what is of a barrel worth? 65. The sum of two fractions is 125, and the 1769 What is the larger CHAPTER VIII DENOMINATE NUMBERS 108. A concrete number in which the unit of measure has a fixed value is called a denominate number. 4 feet, 30 minutes, 2 pounds, 4 yards, etc., are denominate numbers. COMPARISON OF OPERATIONS WITH SIMPLE AND DENOMINATE NUMBERS 109. SIMPLE NUMBER 324 or DENOMINATE NUMBER 3 hundreds, 2 tens, 4 units. 3 bushels, 2 pecks, 4 In simple numbers, the place value of the figures by the Arabic system of notation enables us to write at once the number of units, so that we do not have to make the computations shown above. In denominate numbers, we are often obliged to make the full operations as shown. These operations are: 4 pecks in each bushel, 5 times 4 pecks in 5 bushels or 20 pecks; 20 pecks and the 3 pecks are 23 pecks. 8 quarts in each peck, 23 times 8 quarts in 23 pecks, or 184 quarts; 184 quarts and the 6 quarts are 190 quarts. 5 bu. 3 pk. 6 qt. 190 quarts. Reduce to higher denominations: = In adding simple numbers, we carry 1 for each ten, as it takes 10 of the units of each column to make 1 of the next higher column. The scale is uniform. In adding denominate numbers, the scale varies H for different measures. In denominate numbers the scale may be written between the columns and used as a guide to carrying. The operations are the same, except that we carry 1 for each 8 quarts in adding quarts, and 1 for each 4 pecks in adding pecks, while in simple numbers we carry 10 each Ans. 2 gal. 3 qt. 1 pt. In subtracting the denominate numbers in the exercise shown, we first reduce one of the quarts to pints, making 2 pints; in subtracting the simple numbers, we first reduce one of the units to tenths, making 10 tenths. Trace the remainder of the operations with the simple numbers, and then apply the same plan with the denominate numbers, using the scale written between the columns to guide your reductions. The operations in the denominate number exercise are 5 times 6 quarts = 30 quarts, which are 3 pecks and 6 quarts. 5 times 2 pecks = 10 pecks, and 3 pecks are 13 pecks, which are 3 bushels and 1 peck. 5 times 4 bushels = 20 bushels, and the 3 bushels carried are 23 bushels. Compare these operations with those of your regular practice in multiplication of simple numbers. 2 tens 6 units 8 tenths 2)5 (10) 3 (10) 6 DIVISION 2 bushels 3 pecks 7 quarts 3 (8) 6 2)5 (4) The operations in the exercise in simple numbers are 5 tens are 2 times 2 tens, and 1 ten or 10 units remaining. 10 units and 3 units are 13 units; 13 units are 2 times 6 units and 1 unit or 10 tenths remaining. 10 tenths and 6 tenths are 16 tenths; 16 tenths are 2 times 8 tenths. Ans. 26.8. The operations in the exercise in denominate numbers are: 5 bu. are 2 times 2 bu. and 1 bu. or 4 pk. remaining. 4 pk. and 3 pk. are 7 pk.; 7 pk. are 2 times 3 pk. and 1 pk. or 8 qt. remaining; 8 qt. and 6 qt. are 14 qt. 14 qt. are 2 times 7 qt. 2 bu. 3 pk. 7 qt. Ans. 110. The operations of reduction, addition, subtraction, multiplication, and division of denominate numbers are like the corresponding operations with simple numbers, except that in denominate num |