8. How many are 9 and 1 ? 89 and 1 ? 99 and 1 ? 109 and 1 ? 199 and 1 ? 209 and 1 ? 299 and 1 ? 9. How many are 6 and 4? 6 and 5 ? 16 and 4 ? 16 and 5 ? 26 and 5 ? 36 and 5 ? 56 and 5 ? 10. How many are 8 and 7? 18 and 7? 118 and 7? 128 and 7? 28 and 7? 38 and 77 638 and 7? 11. What is 3+9 equal to ? 4+9? 23+9 ? 24 +9? 54 +9?55 +9? 56 +9? 52 +9? 12. What is 2 +5+7 equal to ? 12+5+7? 22+ 5+7 ? 42 +5+7? 72 +5+7? 92+5+7 ? 13. How many are 63 and 5 ? 79 and 2? 103 and 8? 47 and 6? 99 and 3 ? 102 and 7 ? 113 and 5 ? 14. How many are 10 and 10? 20 and 10? 50 and 10? 90 and 10? 100 and 10 ? 200 and 10 ? 15. 6 and 9 make how many ? 34 and 6 ? 43 and 9? 52 and 8 ? 58 and 2 ? 50 and 3 ? 79 and 6 ? 88 and 4 ? 103 and 3? 111 and 9 ? 124 and 4? 16. How many are 7 and 7 and 8? 21 and 9 and 6 ? 34 and 8 and 7 ? 41 and 10 and 9? 72 and 4 and 5 ? 99 and 10 and 1 ? 199 and 2 and 9 ? 17. One tree bears 34 apples, another 6, and a third 10; how many apples do all three bear? MODEL. If one tree bears 34 apples, another 6, and a third 10, all three together will bear the sum of 34, 6, and 10 apples, or 50 apples. Answer, 50 apples. 18. A farmer set out 42 apple, 8 pear, and 9 plum trees; how many trees did he set out altogether ? 19. If I travel 75 miles by boat, 7 by railroad, and 10 by stage, how many miles do I go in all ? 20. 103 English books, 20 French books, and 6 German books, make how many books in all ? APPLETONS' MATHEMATICAL SERIES. A MENTAL ARITHMETIC. BY G. P. QUACKENBOS, LL. D., AUTHOR OP "AN ENGLISH GRAMMAR;" "FIRST LESSONS IN COMPOSITION; ADVANCED " "A NATURAL PHILOSO- " ILLUSTRATED SCHOOL HISTORY OF THE UNITED STATES, ETC. ול NEW YORK: KC 1273 ARD UNIVERSITY LIBRARY A 2*130 [ADVERTISEMENT. .] APPLETONS MATHEMATICAL SERIES. BY G. P. QUACKENBOS, LL. D., 4. Primary Arithmetic. Beautifully illustrated; carries the beginner through the first four Rules and the simple Tables, combining mental exercises with examples for the slate. 16mo. 108 pages. 22 cents. An Elementary Arithmetic. Reviews the subjects of the Primary in a style adapted to somewhat maturer minds. Also embraces Fractions, Federal Money, Reduction, and the Com pound Rules. 12mo. 144 pages. 40 cents. A Practical Arithmetic. Prepared with direct reference to the wants of Common Schools, giving special prominence to the branches of Mercantile Arithmetic. 12mo. 336 pages. 80 cents A Mental Arithmetic. Designed to impart readiness in mental calculations, and extending them to the various operations needed in business life. Introduces short methods, and new and beautiful processes. 16mo. 168 pages. 35 cents. A Higher Arithmetic. 12mo. 420 pages. $1.10. Entered, according to Act of Congress, in the year 1868, by D. APPLETON & CO., In the Clerk's Office of the District Court of the United States for the Southern District of New York. PREFACE. The study of Mental Arithmetic has two principal objects in view, to discipline the mind and impart quickness and accuracy in mental calculations. To secure these objects in the highest degree and in the pleasantest way to both teacher and learner is the aim of this little volume. It is intended for pupils who have gone through a Primary Arithmetic, and know how to read and write numbers up to thousands inclusive; and may be used either by itself to succeed the Primary or Elementary, or as an auxiliary to the Elementary or Practical, on alternate days. Among the more important features of the present work are the following:-1. The gradual and inductive mode of unfolding the subject, with the aid of rigid but clear analyses expressed as briefly as possible. 2. The introduction of necessary definitions, too often excluded from Mental Arithmetics. 3. The great variety and practical bearing of the Examples ; the careful avoidance of obscurity in wording them, and the exclusion of all questions involving impossibilities or absurdities. 4. The presentation of the Metric System, hitherto confined mainly to text-books on written Arithmetic. 5. The teaching of short methods and processes actually used in the counting-room. 6. The extension of mental calculations to more of the operations of every-day business life than has hitherto been attempted; such as equation of payments, stock jobbing, U. S. securities, taxes, duties, &c. The value of this last feature, it is believed, can hardly fail to be appreciated in this practical age. The interest and profit with which classes will use this work will depend entirely on the thoroughness with which the successive steps are taken. Review again and again if necessary, and let nothing pass till it is mastered. Short lessons should be given, to be prepared beforehand. The books should be closed at recitation, the |