59. Add together .83 of a mile + 4 of a yard + .25 of a foot. 60. What will be the cost of painting the walls of a room at 1s. 7d. per square yard, the length being 19 ft. 10 in., the breadth 16 ft. 13 in., and the height 10 ft. 3 in.? Solve by decimals. 61. Find the sum of 4, 1, and 1, and divide it by 3 5 63. Which is the greater, and by how much, .0475 of a guinea or .325 of half a crown? 64. Reduce the decimals .125, 3, and 45 to a vulgar fraction, and then find their sum. 65. If 48 men can do a piece of work in thirty days, working ten hours per day, how many additional men will be wanted to complete it in twenty days, working eight hours per day? 66. Reduce 411 crowns to the fraction of 12 guineas. 67. Divide .0001 by 50. 68. Find the value of 69. Simplify (4/1/2 + 1 also as a decimal. 01875 of a ton. 7) ÷ (41 − 1 − ). Express 70. If A can reap of a field in 23 days, and B can reap of it in 4 days, in what time can A and B reap the whole field together? 74. If my share of a picture was, and I received £12, 3s. 4 d., what was the picture worth? 75. Simplify the expression 21 of 15 of 3 + 13 76. What fraction must be added to the sum of 31, 41, 5, and to make the result a whole number? 77. If a clock gain 6 of a second in 20 minutes, in what time will it gain 20 minutes? 78. By how much is of of 1 greater than of of 15? 28 79. What fraction of 5s. 113d. is 11 of 7s. 9d.? 80. Divide .000460408 by .0247. Prove your work by vulgar fractions. 81. If A and B, working together, can finish a piece of work in 3 days, B and C in 3 days, and A and C in 4 days; in what time could they do it, all working together? (See solution, page 49.) 82. Divide of by of 7%, and multiply the quotient by 1 of 3. 83. If of a coal mine cost £780, 1s. 3d., what will cost? 32 84. Multiply 1.021 by .0037, and divide 16 by .0004; and give the reason for placing the decimal point in each 86. Divide 2 by .64 and .004 by .0001. 3.16 1.2 2.5.025 87. Simplify of of 5.17 .375 4 88. Find the average of 17, 251, 96, 10, 0, 42, and 56. 89. If 7 men earn £10 in 9 days, how much will 17 men earn in 20 days? 90. If a piece of work be done in 50 days of 8 hours each by 23 men, in what time will 161 men do a piece of work 3 times as great? 91. A, B, and C can do a portion of work in 8 days; A is able to do it in 20 days, and C in 24 days. In what time can B do it? 92. If 1.5 lb. of tea cost .06375 of 100s., what would .0875 ton cost? 93. If you owed amount of your debt? of £5, 2s., what would be the 94. A young man received £5000, which was just of of his father's estate? whom her father left of 7 What did the daughter receive to of the estate? take, and divide the answer by 96. A train going at the rate of 16 miles an hour, travels a certain distance in 4 hours; how long would a train, going at the rate of 205 miles an hour, be in running the same distance? 97. If the owner of of a ship sold (of) of his 1 share for £4000, what was the value of of of the 339 whole ship at the same rate? 1 98. Find the value of å of of £1, 18s. + of 0.0375 of 15s. + of 0.429 of 8s. 3d., and express the result as a decimal of £5. of 1d., and reduce the difference to the fraction of 100. How many oranges at £.084375 per dozen, ought to be given in exchange for 378 eggs at .0625 shillings each? 101. Arrange in order of magnitude the fractions 06, .06, .069, .069, .069, and express their average decimally. METHOD OF SOLVING QUESTION 56. X in 1 hour can do & of the work. Z can finish the remainder, that is in 10'; .. in 1 hour he can do of the work. X, Y, and Z in 1 hour can do + + of the work = ; .. all working together can do the piece of work in METHOD OF SOLVING QUESTION 81. A and B in 1 day can do of the piece of work. of the piece of work. A and B in 1 day and A and C in 1 day can do (} + 1) of it, or A in 2 days and B and C in 1 day can do (3 + 1) of it. and.. A + B + C together can do the piece of work in 24 days. .. twice A and twice B and twice C do 3 of work in 1 day. .. 2 (A + B + C) = of work. D A measure of any number is such a number as will divide the given number without a remainder. Thus 2 into 8 goes 4. A Common Measure of two or more numbers is such a number as will divide each of the given numbers without a remainder. Thus, 2 will divide 4, 6, 8, and 10, and is therefore a Common Measure. The Greatest Common Measure of two or more numbers is the greatest number that will divide each of the given numbers without a remainder. Thus, 8 is the highest number that will divide 16 and 24, and is therefore the Greatest Common Measure of 16 and 24. LEAST COMMON MULTIPLE. A multiple of any number is a number which will contain the other so many times without a remainder. Thus, 24 is a multiple of 2. A Common Multiple of two or more numbers is such a number as will contain each of the given numbers so many times without a remainder. Thus, 24 is a Common Multiple of 2, 3, 6, 8, and 12. The Least Common Multiple of two or more numbers is the least number that will contain each of the others without a remainder. Thus, 24 is the L. C. M. of 2, 3, 6, 8, and 12. |