13. A, B, and C start together and travel round a circular island, in the same direction. It takes A 21 days, B 25, C 27 days to walk round the island. They travel until they all meet at the point of starting. In how many days will they be together at the point of starting? 14. If the step of a man be 21a and that of a horse be 23a, find the smallest number of feet which is an exact number of man-paces and of horse-paces. 15. Find the largest number that is contained without remainder in 25, 67, 114, and 191. EXERCISE XXXVI. MISCELLANEOUS EXAMPLES IN FRACTIONS. 2436 1. Simplify 788, 48785, 781316, 1887. 2. Which is greater, and by how much, or ? - 5. Simplify 1+35 — 27 +423 – 375. 8. Simplify the expressions: 712×8; 431 × 65; 65÷84; 551; of; 8 of 7 of 7 of 3 of 3; 17 of t; 1 × × × × 4. 9. By what must ? to obtain be multiplied to obtain ? to obtain ? to obtain ? to obtain ? 10. By what must be divided to obtain ? to obtain ? to obtain ? to obtain ? to obtain ? 8 to obtain 719? 11. What number exceeds 52 by 47? 12. From what must 63 be subtracted to leave of 31? 13. What fraction falls short of by? 14. What fraction is that to which must be added to give ? 15. Convert into decimals: ; 1; 1; 1; 1, §, §, 1 ; 16, 3 16 F, F, 1, 1, 11, 18, 15; 1,6; † ; §; å; 70. 16. Convert into common fractions: .16; .016; .125; .13; .725; .625; .00625; .8125;*.03125; .08; .54; .016; .5437; .027; .277; .68494; 1.345. 18. Multiply 6.954 by 5.303, and express the result as a whole number and common fraction. 19. Simplify 1 of 24+67÷24 and reduce the result to a decimal. 20. From what number can 417 be taken 9 times and leave no remainder? 21. Of what fraction is 17 the 7th part? 22. Add 4, 0.35, §,, 0.112, 45.28. 23. Convert into decimals 1; 1; *; H; H; K3; 33. 24. What part of 13 is 12341? 25. Divide .0015 by .012, and express the result as a common fraction in lowest terms. 26. Convert into decimals:: 32800; 47; 4. 27. If the product of two factors is g, and one factor is 14, find the other factor. 28. If the dividend is and the quotient 61, find the divisor. 29. The dividend is 1247, quotient 3, remainder 15; find the divisor. 30. Find the G. C. M. and the L. C. M. of 833, 1127, 1421, 343. 31. Arrange in order of magnitude, 13, 14, 13, 38. 32. Find the L. C. M. of 1, f, 102. 39 33. Find the G. C. M. of 5, 32, 4, and 61. 34. Convert into common fractions in lowest terms: 7.2011; 6.954; 5.303; 21.396. 40. Simplify 14 of 24 + 67 ÷ 28+ (51 +24+53). 41. Simplify .9 of § of 4 of 154. 42. What part of is ? o 43. What part of .390625 is .05? 44. .09 is what fraction of .2045? 45. Convert into decimals 42; 14; 27. 2.2.64 46. The G. C. M. of three numbers is 15, and their L. C. M. is 450. What are the numbers? CHAPTER XII. MEASURES IN COMMON USE. 285. The unit of measure for lengths is a yard; and from this are derived the units of surface and volume. 286. The standard yard of Great Britain, as defined by act of Parliament, is the distance between the centres of two cylindrical holes in a certain bar of gun-metal, when the metal has a temperature of 62 degrees Fahrenheit. The standard yard of the United States conforms as nearly as possible to that of Great Britain. 320 rods, 1760 yards, or 5280 feet = 1 mile (mi.). 288. A quantity expressed with reference to a single unit is called a simple quantity; but a quantity expressed with reference to different units is called a compound quantity. Thus, 20 miles is a simple quantity; but 20 mi. 70 rds. 5 ft. is a compound quantity. NOTE. A number expressed with reference to a particular unit is sometimes called a denominate, or concrete, number; and, in distinction, a number expressed without reference to a unit is called an abstract number. But it is to be observed that all numbers are abstract. (1) Change 20 mi. to rods. 320 rds. 20 6400 rds. Since a mile contains 320 rds., 20 miles contain twenty times 320 rds. (2) Change 20 mi. 70 rds. 5 ft. to feet. 20 mi. 70 rds. 5 ft. = 6400 rds. 320 6400 70 6470 rds. 161 3235 38820 6470 106755 5 = 70 rds. are added. Again, 6470 times 16 ft. 106,755 ft., to which the 5 ft. are added. Observe that multiplicand and multiplier are interchanged in the operation. 106760 ft. (3) Change 6400 rds. to miles. 320) 6400 Since there are 320 rds. in 1 mi., in 6400 20 mi. rds. there are (6400 ÷ 320) mi. = 20 mi. |