This method of solving a problem is known as the analytical method. It is called also the unit method, because the value of the unit of the quantity under consideration is first sought and from this the value of any number of units is then obtained. Note that the answer is obtained by multiplying $2437 by, the reciprocal of . In this problem there are given the product of two factors and one of the factors. The other factor is sought. The problem is therefore one of division. EXERCISE 30 1. Find the price of 78 acres of land if 25 acres are worth $1,375. 2. When 18 pounds of sugar sell for $1, find the cost of 45 pounds. 3. When 7 bushels of wheat sell for $5.95, how much can a person get for 255 bushels ? 4. If 5 bushels of barley sell for $2, how much will 343 bushels sell for? 5. If 6 barrels of flour are sold for $45, at this rate how much will 84 barrels sell for? 6. Seven barrels of pork sell for $80.50. Find the cost of 50 barrels of pork. 7. Nine barrels of salt cost $11.70. 19 barrels of salt. Find the cost of 8. Eleven bushels of oats are sold for $4.51. Find the value of 168 bushels. 9. Six barrels of lard bring $115. How much will 46 barrels bring? 10. When 7 yards of sheeting cost 50, find how much must be paid for 98 yards. 11. Six yards of cambric sell for 754. How much must be given for 34 yards of cambric? 12. Four yards of flannel cost $1.15. How much will 29 yards of flannel cost? 13. Eight yards of gingham cost 60%. How much will 103 yards cost? 14. Nine yards of cotton fabric cost 75%. How much will 69 yards cost? 15. Six yards of cotton cheviot cost $1. will 81 yards cost? How much 16. Five eighths of a man's money is $75. How much money has he? 17. Three fourths of the length of a pole is 81 feet. Find the length of the pole. 18. The sum of the eighth and the twelth of a number is 15. What is the number? 19. A dealer sold of his coal and had 170 tons left. How many tons had he at first? 20. The sum of the fourth part and the sixth part of a number is 25. What is the number? COMPLEX FRACTIONS A complex fraction is a fraction at least one of whose terms contains a fraction or fractions. Thus, 21 3 1 + 1 - 1 are complex fractions. Such expressions merely indicate that the quantity in the numerator is to be divided by the quantity in the denominator. The numerator and denominator should each be simplified and then the numerator should be divided by the denominator by the usual methods for the division of fractions. 2}+15=+= } × † =}=1{ Example 2. Simplify 36-21. 1-11 Fractions whose denominators are 10, 100, 1000, or some other power of 10, are usually written as decimals. Before taking the following work on decimals, review thoroughly the explanation and exercises in decimals on pages 7 and 8. ADDITION OF DECIMALS Find the sum of 3.4, 2.38, 5.005, 6.2374, 11.1. 3.4 2.38 5.005 6.2374 11.1 28.1224 Write the numbers in a column so that the decimal point of each number is directly below the decimal point of the next number above. This brings all figures of the same denomination into the same vertical column. Then add as in the case of integers, being careful to keep each figure in the vertical column to which it belongs. Write the decimal point of the sum in the same vertical line with the decimal points of the numbers added. EXERCISE 32 Add: 1. 2.2, .025, 37.3, 5.284, 6.294, 538.1, 77.77. 2. 3.5, 7.12, .339, 47.35, 39.28, .123, 54.275. 3. 9.28, 11.18, .999, 39.28, 7.451, 94.354, 98.76. 4. 12.49, 1.492, 38.75, 53.41, 98.69, 845.5, 892.9. 5. .009, 5.976, 40.99, 6.385, 9.278, 8.239, 64.271. 6. .098, 9.853, 19.47, 17.392, 28.394, 8.01, 77.47. 7. .285, 11.95, 29.99, 94.931, 1.732, 64.6, 78.75. 8. 11.4, 17.5, 99.37, 15.273, 9.394, 71.3, 92.95. 9. 1.21, 12.1, .121, 8.295, 7.777, 68.7, 78.28. 10. 15.9, 9.158, 91.58, 9.158, 2.293, 84.5, .139. 11. 98.5, 11.667, 66.66, 8.394, 9.928, 76.8, 9.359. 12. 77.8, 88.88, 99.99, 6.325, 7.384, 94.9, 1.798. 13. 1.412, 1.732, 3.142, 62.85, 19.76, 856.2. 14. 631.5, 729.8, 65.47, 18.19, 343.7, 685.9. SUBTRACTION OF DECIMALS Find the difference between 4001 and 1.7003. 4001.0000 1.7003 3999.2997 Arrange the numbers so that the decimal points stand in the same vertical column. Ciphers may be inserted at the right of either number to give it as many decimal places as the other number. Perform the subtraction as if the numbers were integers. Place the decimal point in the remainder in the same vertical column as the decimal points of the minuend and subtrahend. EXERCISE 33 Find the remainder and verify your answer in each case: 27. From seven hundred four thousandths take two hundred five ten-thousandths. 28. From five hundred ten thousandths take five hundred ten-thousandths. |