20 NOTE. Compare the 34th with the following:- What is the value of 24 qr. 7 lb. - 19 qr. 21 lb. By writing the work of the 34th example in the following form, and placing opposite it the work of the example in this note, the resemblance of the two is very clearly exhibited. Answer. 1 is one fourth of 4, because times 1 are 4.* 21. What part of 8 yards is 1 yard? First Form of Answer. 1 yard of 8 yards, because 8 times 1 yard = 8 yards. = Second Form of Answer. 1 yard is the same part of 8 yards that I is of 8, which is . Hence, 1 yard = of 8 yards. 25. Of 4 cwt. is 3 cwt.? Of 10 da. is 7 da.? 24. Of 4 lb. is 3 lb. ? 27. Of 8 yr. is 5 yr.? 28. What part of is ? Answer. is the same part of that 3 is of 4, which is . Hence, 49. Of 113 is 1 lb. ? 51. What part of & is 1? 50. Of 8 da. is 1 w. ? Solution. 1, and is the same part of that 6 is of 5, which is = of, or 1 times . f. Hence, 1 Solution. 1; 2 = 21; and 2 of 11 times 63. What part of 1 m. 3 fur. is 2 m. 5 fur.? Solution. 1 m. 3 fur. = 11 fur.; and 2 m. 5 fur. =21 fur.; 21 fur. = of 11 fur., or 1 times 11 fur. What part 64. Of 1 d. 3 qr. is 11 d. 1 qr.? 65. Of 13 is 11? 66. Of 8 w. 3 da. is 2 w. 4 da.? 67. Of 8 is 24? 68. Of 5 da. 7 h. is 3 da. 11 h.? 69. Of 5 is 311? T 70. Of 11 h. 27 m. is 21 h. 38 m.? 71. Of 15 pk. is 3 pk. 7 qt.? 72. What part of 1 lb. is 3 oz. 5 dwt. 17% gr.? Suggestion. Reduce 1 lb. and also 3 oz. 5 dwt. 173 gr. to the lowest denomination mentioned, i. e., to fifths of a grain. 73. Of 1 gal. is 3 qt. 1 pt. 3 gi.? 74. Of £1 is 17 s. 11 d. 2 qr.? 75. Of 1 w. is 5 da. 11 h. 35 m. 29 sec.? 76. Of 1 T. is 13 cwt. 2 qr. 19 lb. 13 oz. 11 dr.? 77. Of 4 yd. 2 ft. 7 in. is 1 yd. 1 ft. 11 in.? 78. Of 17 A. 3 R. 16 sq. rd. is 2 A. 1 R. 28 sq. rd.? 130. Other Methods of expressing the Value of a Fraction. (a.) 1. Explain the fraction . Answer. number. = 3 times, as of a number 3 times of the (b.) Explain each of the above by the following method. = 2, or of 1, of 3, as of a number= of 3 times the num ber. For if each of 3 equal things should be divided into 4 equal parts, and 1 of the parts of each taken, the result would equal † of 1. NOTE. This may be illustrated to the eye, by taking 3 equal lines, and dividing them into 4 equal parts, arranged thus one of the parts will then contain of 3 lines, which, as will be seen, is equal to of a line. 11. To what simple fraction is of 3 equal? (c.) To what simple fraction is each of the following equal? 131. To find a Fractional Part of a Number. 1. What is of 5459? First Solution. of 54597 times of 5459; of 5459, found by dividing by 8, is 6823, and 7 times 68234776ğ. Second Solution. of 5459 = of 7 times 5459; 7 times 5459 = 38213, and of 38213 By First Solution. 8) 5459 6828 = 4776. WRITTEN WORK. By Second Solution. 5459 7 The following forms of writing the work exhibit very clearly the reason for every step which is taken. The letters a, b, &c., are used as explained in the note on the 88th page. NOTE. a= 5459 7 X a = = b =38213 of b = of a = 4776 It will be seen that by both methods of solution, we multiply by the numerator, 7, and divide by the denominator, 8. The only difference between them is, that by the first we divide before we multiply, while by the second we multiply before we divide. involves somewhat smaller numbers than the second. What is the value of each of the following? 8. What is the value of .0014 of 16.427 ? The first method 6. of 46935. 7. 127 of 87516. First Solution. .0014 of 16.427 14 times .0001 of 16.427; .0001 of 16.427, found by removing the point four places towards the left, is 0016427, and 14 times this is .0229978 = Ans. The work may be written in full after either of the following models Second Solution. .0014 of 16.427 .0001 of 14 times 16.427; 14 times 16.427 229.978, and .0001 of 229.978, found by removing the point four places towards the left, is .0229978 = Ans. The work may be written in full after either of the following models |