customs are followed, and the needs of the future citizen are always kept in mind. But in this book is found no trace of the unfortunate tendency of some of our recent writers to consider an example concrete when it treats of topics or contains technicalities that no pupil understands and few teachers are expected to know. This volume covers all of the topics ordinarily studied in the seventh and eighth school years. Under each topic there are found an unusually large number of well-graded examples, and at frequent intervals collections of problems without numbers have been inserted as exercises in terse mathematical statement. The topics properly close with sets of exercises that relate to the vocational interests of our people, to the end that pupils may leave school with the real applications of arithmetic to common life clearly in their minds. A few recreations are given in the Appendix, that the lighter side of arithmetic may be seen along with its more serious aspect, and a large amount of drill work has been added for the use of pupils who may be in need of more work than is commonly required. Any corrections or suggestions relating to the work will be thankfully received. The authors hope that teachers who recognize the strong features of the topical arrangement, who wish for an abundance of well-graded problems requiring thought in their solution, who are sympathetic with the movement to replace the obsolete by the genuine applications of arithmetic to the American life of to-day, who are opposed to certain of the extreme attempts of the present time that are sure to result disastrously to scholarship, that such teachers will find in this work a sane, modern, and helpful treatment of the subject. GEORGE WENTWORTH COMPLETE ARITHMETIC PART II CHAPTER I PERCENTAGE 1. Per Cent. Another name for hundredths is per cent. Thus 0.01 or ro is the same as 1 per cent. That part of arithmetic which treats of per cent is called percentage. 2. Symbol for Per Cent. The symbol for per cent is written thus: %. १९ We may read 0.06 either "6 hundredths or 6 per cent." In the same way, we may think of 6% either as "6 per cent" or "6 hundredths," although it is read "6 per cent." The expression 800% means 88 and equals the whole number 8; 225% equals the mixed number 2.25, or 21; 1% means of ráð, or zoo, and is read either " per cent" or, quite commonly, "1⁄2 of 1%." 3. Relation to Fractions. Since 6% means, which equals 0.06, or, we see that we may express per cent as a decimal fraction or as a common fraction. 4. Per Cents as Common Fractions. Since 62% 188, therefore = = 621 100 = To express per cent as a common fraction, write the number indicating the per cent for the numerator and 100 for the denominator, and reduce this fraction to lowest terms. Reduce to a common fraction, integer, or mixed number: 41. How much is 42. How much is 43. How much is of 75? 4% of 75? of 1728? 50% of 1728? 44. How much is 3 of 8440? 75% of 8440? 45. How much is 14 × 864? 125% of 864? 46. Instead of multiplying 64 by 121%, what fractional part of 64 may we take? Do this. 47. Instead of multiplying 720 by 371%, what fractional part of 720 may we take? Do this. 48. Take 87% of 80 in the shortest way. 49. Take 33% of 66 in the shortest way. Find the following: 50. 16% of 66. 51. 163% of 738. 52. 121% of 736. 53. 1121% of 176. 56. 1331% of 729. 54. 1371% of 256. 57. 1331% of 801. 55. 1621% of 312. 58. 166% of 708. |