DENOMINATE NUMBERS LESSON 91 A Denominate Number is a concrete number whose unit is a fixed measure of quantity. Thus, 5 pounds is a denominate number, because the pound is a unit used to measure quantity of weight. Likewise, 4 feet is a denominate number, the foot being used to measure quantity of length. A quantity expressed in a single unit is called a Simple Quantity, or a Simple Denominate Number. Thus, 5 pounds, 14 gallons, 9 feet, etc., are examples of simple denominate numbers. A quantity expressed in several different units is called a Compound Quantity, or a Compound Denominate Number. Thus, 4 rd. 3 yd. 2ft. 7 in. is an example of a compound quantity, or compound denominate number. Long Measure is used in measuring lines or estimating distances. 1. How many inches are there in 61 ft. ? 14 yd. ? 5 ft. ? .25 ft. ? .33} ft. ? 75% of 1 yd. ? 2. How many feet are there in 2 rd. ? 4) yd. ? 3. What part of a yard is 1 ft. ? 11 ft ? 2 ft. ? 9 in. ? 4. If a yard of ribbon costs 27¢, how much will 2 ft. cost at the same rate ? 5. What part of a mile is 1 rd. ? 20 rd. ? 80 rd. ? LESSON 92 OPERATION 51 26 yd. 1. Change 4 rd. 4 yd. 2 ft. 8 in. to inches. rd. yd. ft. in. In 4 rd. there are 4 times 5] yd., or 22 yd. Add 4 4 2 8 ing the 4 yd., we get 26 yd. In 26 yd. there are 26 times 3 ft., or 78 ft. Adding the 2 ft., we get 80 ft. In 80 ft. there are 80 times 12 in., or 960 in. Adding 3 the 8 in., we get 968 in., the answer. 80 ft. 2. Change 2 mi. 40 rd. 3 yd. to feet. 12 3. Change 12 rd. 3 yd. 1 ft. 7 in. to inches. 968 in. Ans. 4. Change 1856 in. to rods, yards, etc. Dividing 1856 by 12 to change to feet, we get 154 ft. and 8 in. over. 12 | 1856 in. 3 154 ft. 8 in. Dividing 154 by 3 to change to yards, we get 51 yd. and 1 ft. over. Dividing 51 51 yd. 1 ft. 51 by 54 to change to rods, we get 9 rd. 14 yd. 9 rd. and 11 yd. over. Ans. 9 rd. 11 yd. 1 ft. 8 in. 5. How many rods, yards, etc., in 4260 ft.? 6. Change to higher denominations 4365 yd., 7264 ft. 7. Change 9 mi. 84 rd. 24 yd. to feet. OPERATION LESSON 93 OPERATION mi. in. 1. Add 4 mi. 29 rd. 3 yd. 1 ft. 7 in.; 6 mi. 78 rd. 5 yd. 2 ft. 11 in.; 7 mi. 36 rd. 4 yd. 1 ft. 8 in. Adding the column of inches, we get 26 in., which equal 2 ft. 2 in. Writing the 2 in. under the column of inches, and rd. yd. ft. 4 29 3 1 7 carrying the 2 ft. to the column of feet, 6 78 5 2 11 and adding we get 6 ft., which equal 2 yd. 7 36 4 1 8 Carrying the 2 yd. to the column of yards and adding, we get 14 yd., which equal 17 145 3 0 2 Ans. 2 rd. 3 yd. Writing the 3 yd. under yards, and carrying the 2 rd. to the column of rods and adding, we get 145 rd. Adding the column of miles, we get 17 mi. 2. Add 12 rd. 4 yd. 2 ft. 8 in.; 16 rd. 2 yd. 1 ft. 10 in.; 19 rd. 5 yd. 11 in.; 9 rd. 3 yd. 2 ft. 9 in. 3. Add 8 mi. 42 rd. 3 yd. 2 ft. 9 in.; 7 mi. 14 rd. 13 ft. 8 in.; 16 mi. 14 rd. 7 in.; 32 rd. 2 yd. 9 in. 4. From 21 mi. 125 rd. 5 yd. 1 ft. 9 in. take 10 mi. 136 rd. 2 yd. 2 ft. 7 in. OPERATION mi. rd. 7 in. from 9 in. = 2 in., which we write under the column of inches. Since 2 ft. yd. ft. in. cannot be taken from 1 ft., we take 1 yd. 21 125 5 1 9 (1 yd. = 3 ft.) and add it to the 1 ft., thus 10 136 2 2 7 making 4 ft. 2 ft. from 4 ft. = 2 ft., which 10 309 2 2 2 Ans. we write under the column of feet. 2 yd. from 4 yd. 2 yd., which we write under the column of yards. Since 136 rd. cannot be taken from 125 rd., we take 1 mi. (1 mi. 320 rd.) and add it to the 125 rd., thus making 445 rd. 136 rd. from 445 rd. = 309 rd., which we write under the column of rods. 10 mi. from 20 mi. : 10 mi. 4. Subtract 32 mi. 310 rd. 3 yd. 2 ft. 9 in. from 84 mi. 5 yd. 5. Subtract 39 mi. 12 ft. 6 in. from 126 mi. 1 rd. 1 yd. 1 ft. 6. Multiply 3 mi. 59 rd. 3 yd. 5 ft. 8 in. by 7. 7 times 8 in. 56 in. = 4 ft. 8 in. We write the 8 in. under the inches, and add rd. yd. ft. in. the 4 ft. to the product of feet. 7 times 5 ft., 3 59 3 5 8 plus 4 ft. (7 x 5 ft.) + 4 ft. = 39 ft. 7 We write a cipher under feet, and add the 22 99 1 0 8 Ans. OPERATION mi. 13 yd. 13 yd. to the product of yards. 7 times 3 yd., plus 13 yd. (7 3 yd.) + 13 yd. = 34 yd. 6 rd. 1 yd. We write the 1 yd. under yards, and add the 6 rd. to the product of rods. 7 times 59 rd., plus 6 rd. (7 X 59 rd.) + 6 rd. = 419 rd. = 1 mi. 99 rd. We write the 99 rd. under rods, and add the 1 mi. to the product of miles. 7 times 3 mi., plus 1 mi. (7 3 mi.)+1 mi. = 22 mi., which we write under miles. Multiply: 7. 8. 9. rd. yd. yd. 18 16 10 3 25 36 7 18 120 2 9 7 8 6 mi. rd. ft. in. mi. mi. rd. ft. 10. Multiply 60 mi. 240 rd. 9 ft. by 9. OPERATION mi. LESSON 95 1. Divide 129 mi. 50 rd. 7 ft. by 8. * of 129 mi. = 16 mi., and 1 mi. remaining. We write the 16 mi. in the quotient rd. ft. under miles, and change the 1 mi. to its 8)129 50 7 equivalent, 320 rd., which we add to the 16 46 5 Ans. 50 rd., thus making 370 rd. } of 370 rd. 46 rd., and 2 rd. remaining. We write the 46 rd. under rods, and change the 2 rd. to its equivalent, 33 ft., which added to 7 ft. make 40 ft. of 40 ft. 5 ft., which we write in the quotient under feet. Divide: 2. 3. 4. ft. 9) 69 4 6 11)3030 11 12)54 14 9 6. 7. rd. yd. ft. rd. yd. ft. in. 7)49 160 94 6)95 0 1 8 8)191 4 2 10 8. Change 2 yd. 2 ft. 3 in. to inches. 9. Multiply 3 mi. 90 rd. 2 yd. 4 ft. 7 in. by 6. rd. yd. yd. ft. in. rd. ft. in. 5. mi. 10. Find 1 of 21 rd. 3 yd. 4 ft. 8 in. 13. How many steps, each 2 ft. 8 in. long, will a man take in walking 5 miles ? 14. How much will 361 ft. of wire fencing cost at $ 1.20 per rod ? 15. If 18 seconds intervene between the flash and report of a gun, what is its distance, the velocity of sound being 1090 ft. per second ? Answer in miles, rods, and feet. 16. If a horse can trot 280 rd. in 3 minutes, how far, at the same rate, would he travel in 10 minutes ? LESSON 96 feet are 1. For what is Surveyors' Linear Measure used ? many there in 50 li. ? Gunter's chain, named after its inventor, Edmund Gunter, is 792 in. long, or 66 ft., or 4 rd. Surveyors generally use a chain or tape 100 ft. long. 6. For what is Surface or Square Measure used ? 7. Recite the table of surface or square measure. 8. How many square feet are there in 4 sq. yd. ? 9. 36 sq. ft. equal how many square yards ? 10. 12 sq. in. equal what part of a square foot ? 11. 36 sq. in. equal what part of a square foot ? |