IRLF ^ss ir rAr~ ^y$ OOK OF Arithmetic. f n ru. REESE LIBRARY UNIVERSITY OF CALIFORNIA. THE PESTALOZZIAN SERIES. -YEAR TEH-BOOK OF PRIMARY ARITHMETIC. For Pupils in the Second Grade, Second Year, of Public Schools. Based upon Pestalozzi's System of Teaching Elementary Number. BY JAMES H. HOOSE, A. M., Ph.D., F.S. Sc., Principal of the State Normal and Training School at Cortland, N. Y., Author of " Studies in Articulation," "On the Province of Methods of Teaching," etc. SYEACUSE, N". Y. : C. W. BARDEEN, PUBLISHER, 1890. Copyright, 1890, by JAMES H. HOOSE. DEDICATED To those teachers, who desire to say with Pesta- lozzi, " My aim was to carry the simplifying of all means of teaching so far that every common man can easily bring hiniself to teach his children, and to make the school gradually superfluous for the first elements." MISCELLANEOUS REMARKS. 1. See the First-Year Text-Book for the ele- mentary principles which control the form of this system of number. Miss Mary L. Roberts has had the immediate charge of the classes that have pursued this work, since the introduction of the system, Nov. 21, 1881. The system has been elaborated under my supervision. This Second- Year Text- Book contains the amount of work that has been actually accomplished during a series of years, by our second grade pupils (second year in school). The school year consists of two terms of twenty weeks each. Pupils not acquainted with the First- Year Text-Book have entered the second grade and have completed this book with the grade. 2. The principal portion of class-work is with abstract numbers; the teacher gives, once a week, several examples in concrete numbers (see the text) ; the pupils also construct practical examples upon the forms given in the daily lessons. The pupils use objects for a brief time only, in order to enable them to obtain a proper notion of num- ber; after that notion is acquired, objects are discarded. VI MISCELLANEOUS REMARKS. 3. This book is for mental work; yet pupils write any lesson upon their slates for review or for special exercises. The book contains but little dictation work. 4. The processes of addition, multiplication, and subtraction, are taught with thoroughness. Examples in addition and subtraction include numbers that contain six figures. 5. In formal subtraction, no figure of the sub- trahend is taken from a number that exceeds 10 e. g., the child is never asked to take 8 from 17, or 9 from 18, but follows the forms laid down in the text (which see). 6. Division is not introduced into the work of the second grade. Addition, multiplication, and subtraction appear. 7. The pupils are not taught formal numeration of numbers ; they are not taught the terms "units," "tens," "hundreds," etc.; they simply read and write the numbers at sight. 8. The new matter and forms introduced into this year's work are formal subtraction and addi- tion of numbers placed in vertical columns. 9. The Eoman letters are continued in this grade; each letter is written carefully by itself alone e. g., six is written VI. 10. No tables are introduced to try to teach pupils the processes of addition, multiplication, and subtraction. MISCELLANEOUS REMARKS. VU 11. The teacher gives to the pupils no form for adding numbers together e. g., the children are not instructed to add by 10s, or by 20s, or by 4s, etc. ; the child invents his own form of procedure. 12. The pupils are not taught (or allowed) to use the terms " to carry," or " borrow/' in addi- tion and subtraction. 13. Teachers will find ample explanatory notes distributed throughout the text. 14. A few forms in letters (pure algebra) are introduced. No explanations of them are made to the class, when these examples are reached; the pupils give the answer, then read the example and answer, precisely as they do with figures. 15. The pupils recite daily the lessons from the book ; they become accustomed by this course to handle subject matter when it is set to them in the form of the printed page. The value of the black- board has its limitations in the recitation, when compared with the value of the text form. 16. The Pestalozzian system of number proceeds on the theory and practice of introducing to the pupil a minimum variety of objects, and of giving to him a maximum amount of practice upon a few forms. The forms are those which constitute mathematics ; they are as general as mathematics are general; learned once, useful always. The system recognizes the difference between processes in arithmetic, and the reasoning required Vlll MISCELLANEOUS REMARKS. in so-called practical examples. The mastery of a process (addition, multiplication or subtraction) is a language, is an expertness, is a facility in pro- cedure ; it is acquired by practice, repetition ; it is habit, which is power acting in a particular form. Practical examples introduce relations which are discovered by the logical aptitudes of mind. The child masters easily a form of operation, a process ; this mastery gives the pupil ambition : this ambition to test in a greater degree his powers, constitutes his interest in his work ; his interest stimulates his courage, The pupil is trained in this manner in his moral character. The very uni- formities in the system are sources of strength to the child, the same as the uniformities of action in learning the keyboard of the piano are the elements of mastery in learning to play the instrument. State Normal and Training School, ) Cortland, N. Y., May, 1890. ) J. H. HOOSE. SECOND-YEAR TEXT-BOOK. LESSON I. 1. 3 X 1 + 5 X 1 + 4 xi- +-6X1: 2. 7 X 1 + 3 X 1 + 5 X 1 + 4 Xl 3. 6 X 1 + 5 X 1 + 7 X 1 + 4 X 1 4. 7 x 1 + 8 x 1 + 6 x 1 + 5 X 1 5. 9 X 1 + 7 X 1 + 4 X 1 + 3 Xl 6. 8 X 1 + 5 X 1 + 3 X 1 + 6 Xl 7. 7 X 1 + 7 x 1 + 7 X 1 + 3 Xl 8. 8 X 1 + 3 X 1 + 5 X 1 + 4 X 1 9. 6 X 1 + 7 X 1 + 3 X 1 + 5 Xl 10. 9 X 1 + 3 X 1 + 8 X 1 + 6 Xl 11. 7 X 1 + 7 X 1 + 3 X 1 + 7 Xl 12. 9 X 1 + 5 X 1 + 6 X 1 + 8 X 1 13. 4: x 1 + 7 x 1 + 3 x 1 + 9 x i 14. 8 X 1 + 7 X 1 + 3X 1 + 2 X 1 15. 5 X 1 + 5 X 1 + 8 X 1 + 4 Xl 16. 7 X 1 + 5 X 1 + 6 X 1 + 3 X 1 17. 3 X 1 + 7 X 1 + 5 X 1 + 4 Xl 18. 8 X 1 + 5 X 1 + 5 X 1 + 5 X 1 19. 9 X 1 + 9 X 1 + 3 X 1 + 3 Xl (9) 10 SECOND-YEAR ARITHMETIC. 20. 8X1 + 7X1 + 5X1+4X1 = 21. 3X2+3X2+2X2=8X2=16X1. 22. 5 X 2 + 3 X 2 + 2 X 2 = 23. 2 X 2 + 3 X 2 + 4 X 2 24. 2 X 2 + 3 X 2 + 2 X 2 25. 1 X 2 + 1 X 2 + 1 X 2 26. 2 X 2 + 1 X 2 + 3 X 2 27. 1 X 2 + 2 X 2 + 1 X 2 28. 1 X 2 + 3 X 2 + 1 X 2 : 29. 1 X 3 + 1 X 3 + 1 X 3 : ; 30. 2 X 3 + 1 X 3 + 2 X 3 31. 3 X 3 + 2 X 3 + 3 X 3 32. 3 X 3 + 1 X 3 + 3 X 3 33. 2 X 3 + 5 X 3 + 2 X 3 34. 1 X 3 + 2 X 3 + 1 X 3 35. 2 X 3 + 6 X 3 + 2 X 3 - 36. 1 X 3 + 1 X 3 + 4 X 3 37. 2 X 3 + 3 X 3 + 3 X 3 = 38. 3 X 3 + 5 X 3 + 1 X 3 39. i: 1-- 45 XI 40. IV = 46 XT 41. VI = 47 XT 42. 111 = 48 XX 43. IX = 49 XI 44. XI = 50 X3 LESSON II. 1. 8X1+7X1+3X1+4X1=22X1. SECOND-YEAB TEXT-BOOK. 11 2. 5 X 1 + 7 X 1 + 6 X IH L 3 X 1 = 3. 9 x 1 + 4 X 1 + 8 x 1 - f-2 x 1 4. 7 X 1 + 6 X 1 + 5 X IH h4 X -J 5. 6 X 1 + 3 X 1 + 8 X l-\ -7 X 1 6. 2 X 1 + 9 XI + 5 X IH -8 x 1 = 7. 7 X 1 + 4 XI + 3 X 1- h6 X 1 8. 9 X 1 + 2 X 1 + 8 X 1- 1-7 X 1 9. 7 X 1 + 9 X 1 + 6 X 1- M X 1 = 10. 9 X 1 + 4 xi + 9 X 1- h4 X -4 _ 11. 7 X 1 + 5 xi + 5 X 1- h-7 X 1 = 12. 9 X 1 + 6 XI + 7 X 1- h-6 X 1 = 13. 4 X 1 + 8 X 1 + 4 + 1 - f-9 X -J 14. 7 X 1 + 6 X 1 + 9 X 1- f-3 X 1 = 15. 9 X 1 + 9 X 1 + 3 X 1- h5 X 1 16. 8 X 1 + 8 X 1 + 3 X 1- h6 X 1 = 17. 9 X 1 + 9 xi + 9 X 1- h 2 X 1 = 18. 3 X 1 + 9 xi + 5 X 1- [-9 X 1 = 19. 4 X 1 + 8 xi + 9 X 1- t-3 X 1 = 20. 5 X 1 + 5 X 1 + 8 X 1- 1-8 X 1"= 21. 2 X 2+2 X 2+2 X 2=6 X 2=12x1. 22. 3X2 + 2X2 + 3X2 = 23. 2X2 + 2X2 + 1X2 = 24. 4X2 + 3X2 + 2X2 = 25. 3X2 + 3X2 + 4X2 = 26. 2x2+lx2-(-lx2 = 27. 4x2 + 2x2 + 1X2 = 28. 2X2 + 3X2 3X2 = 12 SECOND-YEAR ARITHMETIC. 29. 5X2 + 2X2- f- 1 x 2 = 30. 3 X 2 + 4X2- 4-2 X 2 = 31. 1X2 + 2X2- + 3X2 = 32. 2X2 + 3X2- -4-4X 2 = 33. 6X2 + 1X2- + 1 X 2 = 34. 7X2 + 1X2 + 2X2 = 35. 2X2 + 5X2- 4-4x2 = 36. 3X2 + 1X2 + 1 X 2 = 37. 2X2 + 4X2 + 3 X2 = 38. 1X2 + 3X2 + 1 X 2 = 39. 1X2 + 2X2 + 1 X 2 = 40. 3X2 + 1X2 + 2X 2 = 41. 2X3 + 3X3 + 3 X 3 = 42/3 X 3 + 2X3 + 5 X3 = 43. 1 X 3 + 1 X3 + 1 X 3 = 44. 2X3 + 2X3 + 3 X 3 = 45. 3X3 + 3X3 + 1 X 3 = 46. 2X3 + 3X3 + 3 X 3 = 47. 1X3 + 1X3 + 3 X 3 = 48. 2 X 3 + 3X3 + 1 X3 = 49. 3X3 + IX 3 + 1 X 3 = 50. 1X3 + 2X3 + 1 X3 = 10 X 3 = 7X3 9X3 = 5X3 8X3 = 4X3 6X3 = 2X3 2X3 = 3X3 SECOND-YEAR TEXT-BOOK. 13 LESSON III. 1. 3X1+6X1+4X1+6X1=19X1. 2. 7X1 + 3X1 + 5X1 + 4X1 = 3. 9 X 1 + 6 Xl + 7 X 1 + 3 X 1 __ 4. 8 X 1 + 5 XI + 9 X 1 + 4 X 1 = 5. 7 X 1 + 7 X 1 + 7 X 1+7 X 1 = 6. 6 X 1 + 9 Xl + 4 X 1 + 5 X -j 7. 8 X 1 + 4 Xl + ? X 1 + 2 X 1 8. 9 X 1 + 9 Xl + 3 X 1 + 6 X "1 9. 7 X 1 + 5 Xl + 4 X 1 + 6 X 1 10. 8 X 1 + 7 Xl + 9 X 1 + 4 X 1 = 11. 9 X 1 + 8 Xl + 3 X 1 + 2 X 1 = 12. 7 X 1 + 9 Xl + 6 X 1 + 4 X 1 = 13. 5 X 1 + 8 Xl + 3 X 1 + 4 X -J 14. 9 X 1 + 7 Xl + 2 X 1 + 6 X 1 = 15. 8 X 1 + 5 Xl + 4 X 1 + 8 X 1 = 16. 7 X 1 + 9 Xl + 5 X 1 + 9 X 1 = 17. 9 X 1 + 6 Xl + ? X 1 + 3 X j 18. 8 X 1 + 8 Xl + 3 X 1 + 8 X 1 = 19. 2 X 1 + 9 Xl + 5 X 1 + 4 X 1 = 20. 7 X 1 + 6 Xl + 9 X 1 + 3 X 1 = 21. 3X2+2X2+3X2=8X2=16X1. 22. 4 X 2 + 3 X 2 + 2 X 2= - 23. 2X2 + 3X2 + 1X2 = 24. 3X2 + 1X2 + 1X2 = 25. 1X2 + 1X2 + 1X2 = 26. 2X2 + 1X2 + 1X2 = 14 SECOND-YEAR ARITHMETIC. 27. 3X2 + 3X2+4X2:= 28. 2X2 + 3X2 + 3X2 = 29. 3X2 + 4X2+2X2 = 30. 2X2 + 3X2 + 1X2 = 31. 4X2 + 4X2 + 2X2 = 32. 1 X2 + 1 X2+2X2= 33. 5X2 + 5X2 + 1X2 = 34. 2X2 + 2X2+2X2 = 35. 3 X 2 + 3 X 2 + 1 X 2 36. 5 X 3 + 2 X 3 + 1 X 3 37. 3 X 3 + 3 X 3 + 3 X 3 38. 4 X 3 + 3 X 3 + 2 X 3 39. 1 X 3 + 2 X 3 + 3 X 3 40. 2 X 3 + 1 X 3 + 2 X 3 41. 2 X 3 + 2 X 3 + 3 X 3 42. 3 X 3 + 2 X 3 + 2 X 3 43. 3 X 3 + 5 X 3 + 2 X 3 44. 7 X 3 + 1 X 3 + 1 X 3 45. 5 X 3 + 1 X 3 + 3 X 3 46. 3 X 3 + 1 X 3 + 5 X 3 47. 6 X 3 + 2 X 3 + 3 X 3 48. 3 X 3 + 5 X 3 + 2 X 3 49.. 2 X 3 + 2 X 3 + 4 X 3 50. 3 X 3 + 2 X 3 + 2 X 3 9X 3 :=: 9 X2 = 2 X 3 = 8X 2 = 5 X 3 = 4 X 2 = 6X 3 7 X 2~. 4X3 = SECOND-YEAR TEXT-BOOK. 15 5X2= 8X3= 2X2= 7x 3= 6X2= 3x 3 = LESSON IY. 1. James has 8 cts., George has 9 cts., and Kate has 10 cts.; how many cents have they all 3 Ans. They have 27 cents. 2. There are 2 pints in 1 quart ; how many pints in 7 quarts ? Ans. There are 7x2 pints, which are 14 pints. 3. How many pints in 9 quarts ? 5. A man paid $18 for a coat and $6 for a hat ; how much did he pay for both ? 6. There are 3 feet in 1 yard ; how many feet in 7 yards ? 7. How many feet in 4 yards ? 8. " " ' " " 9 " 9. What will 6 pencils cost at 3 cts. each ? 10. " " 12 " " " 2 " " 11. 9X1+6X1+4X1+5X1=24X1 12. 8X1 + 8X1 + 8X1 + 8X1 = 13. 7X1 + 6X1 + 7X1 + 5X1 = 14. 8X1 + 4X1+7X1 + 6X1 = 15. 9X1 + 9X1 + 8X1 + 7X1 = 16. 6X1 + 6X1 + 5X1 + 4X1 = 17. 7X1+8X1 + 6X1 + 5X1 = 16 SECOND-YEAR ARITHMETIC. 18. 10X1 + 6X1 + 6X1 + 5X1 = 19. 8X1 + 7X1 + 6X1+4X1 = 20. 7x1 + 6x1 + 7x1 + 8x1 = 9X4= 3X3= 7!X4= 8X3 = 5X4= 5X3= 8X4= 4X3= 11X4= 7X3 = 12X4= 12X3 = 2X4= 6X3= 6X4= 9X3= 10 X 4 = 10 X 3 = 7X4= 11X3 = 4X4 = LESSON V. 1. 8X1+6X1+3X1+1X1=18X1 2. 7X1+9X1+5X1+9X1= 3. 3X1+6X1+9X1+5X1= 4. 4X1+5X1+3X1+6X1= 5. 5X1+4X1+4X1+5X1= 6. 6X1+7X1+5X1+8X1= 7. 4X1+9X1+7X1+1X1= 8. 3X1+10X1+8X1+7X1= 9. 5X1+9X1+4X1+7X1= 10. 9X1+7X1+6X1+7X1= 11. 5X1+8X1+4X1+7X1= SECOND-YEAR TEXT-BOOK. 17 12. 9X1+9X1+7X1+5X1= 13. 6X1+^X1+8X1+3X1= 14. 7X1+5X1+4X1+9X1= 15. 8X1+8X1+5X1+7X1= 16. 3X2+3X2+2X2=8X2=16X1 17. 2X2+3X2+5X2= 18. 4X2+1X2+2X2= 19. 2X2+3X2+2X2= 20. 1X2+2X2+1X2= 21. 1X2+1X2+3X2= 22. 1X2+1X2+1X2= 23. 3X3+2X3+1X3 = 24. 3X3+3X3+3X3= 25. 2X3+3X3+1X3= 26. 1X3+2X3+4X3= 27. 3X3+2X3+3X3= 28. 1X3+3X3+6X3= 29. 3X4+2X4+3X4= 30. 2X4+3X4+4X4= 31. 1X4+1X4+2X4= 32. 2X4+1X4+3X4= 33. 1X4+1X4+5X4= 34. 2X4+4X4+4X4= 35. 1X4+1X4+3X4= 36. 2X4+3X4+5X4= 37. 1X4+2X4+4:X4= 38. 3X4+3X4+1X4= 18 SECOND- YEAR ARITHMETIC. 39. 40. 2X4+1X4+1X4= 41. IX= 46. XIV= 42. XXI= 47. XXIX= 43. XIX= 48. XVII= 44. XXXVIII= 49. XXIII= 45. XVI= 50. L= 10X4= 4X4= 7X3= 9X4= 3X4= 6X3= 8X4= 2X4= 5X3= 7X4= 10X3= 4X3= 6x4= 9X3= 3X3= 5X4= 8X3= 2X3= LESSON VI. 1. 3X5+2X5+3X5=8X5=40X1 2. 2X5+2X5+2X5= 3. 1X5+3X5+4X5= 4. 2X5+1X5+4X5= 5. 1X5+1X5+3X5= 6. 1X5+1X5+2X5= 7. 1X5+1X5+1X5= 8. 3x5+2x5+5X5= 9. 5X5+1X5+4X5= 10. 2X5+1X5+4X5= 11. 3X4+3X4+2X4= 12. 2X4+3X4+5X4= SECOND- YEAR TEXT-BOOK. 19 13. 3X4+1X4+1X4= 14. 2X4+2X4+3X4= 15. 1X4+1X4+1X4= 16. 3X4+3X4+4X4= 17. 2X4+1X4+2X4= 18. 4 X 4+4x4+1x4= 19. 3X4+2X4+1X4= . 20. 2X4+4X4+2X4= 21. 3X3+2X3+4X3= 22. 2X3+1X3+1X3= 23. 3X3+5X3+2X3= 24. 1X3+1X3+1X3= 25. 5X3+1X3+1X3= 26. 2X3+4X3+2X3= 27. 1X3+1X3+3X3= 28. 1X3+3X3+2X3= 29. 3X2+2X2+4X2= 30. 2X2+3X2+2X2= 31. 4X2+2X2+4X2= 32. 4X2+2X2+2X2= 33. 2X2+1X2+3X2= 34. 1X2+2X2+1X2= 35. 2X2+1X2+2X2= 36. 3X2+1X2+3X2= 37. 6X1+7X1+5X1+7X1+3X1=28X1 38. 7X1+7X1+5X1+4X1+5X1=: 39. 3X1+9X1+6X1+3X1+6X1= 20 SECOND-YEAR ARITHMETIC. 40. 7xl+5xl+7xl+5xl+7xl= 41. 6X1+6X1+6X1+7X1+5X1=: 42. 7X1+7X1+5X1+4X1+7X1=: 43. 9X1+5X1+3X1+8X1+4X1= 44. 8X1+4X1+8X1+4X1+3X1=: 45. 9X1+6X1+3X1+5X1+4X1= 46. 7 X1+7-X 1+5X1+4X1+3X1= 47. 8X1+8X1+8X1+8X1+4X1=: 48. 7X1+9X1+7X1+6X1+9X1= 49. 5X1+4X1+3X1+7X1+6X1= 50. 6X1+6X1+6X1+6X1+6X1= LESSON VII. 1. 2X5+2X5+2X5=6X5=30X1- 2. 3X5+3X5+3X5= 3. 4X5+4X5+2X5= 4. 3X5+3X5+2X5= 5. 2X5+2X5+1X5=: 6. 3X5+3X5+1X5= 7. 2X5+2X5+1X5= 8. 1X5+1X5+1X5= 9. 1X5+1X5+2X5= . 10. 3X6+2X5+2X6= 11. 4X6+5X6+1X6= 12. 1X6+3X6+1X6= 13. 2X6+6X6+1X6= 14. 6X6+1X6+1X6= 15. 1X6+2X6+3X6= SECOND-TEAR TEXT-BOOK. 21 16. 1X6+1X6+1X6= 17. 2X6+1X6+1X6=1 18. 3X6+5X6+1X6= 19. 1X6+3X6+4X6=: 20. 1X6+5X6+4X6= 21. 2X6+1X6+4X6=: 22. 3X4+2X4+3X4=: 23. 2X4+3X4+1X4=: 24. 1X4+4X4+4X4=, 25. 2X4+3X4+2X4= 26. 1X4+1X4+2X4= 27. 2X4+3X4+1X4=: 23. 3X4+3X4+3X4= 29. 3X3+2X3+4X3= 30. 1X3+2X3+1X3= 31. 5X3+1X3+2X3= 32. 2X3+4X3+1X3= 33. 1X3+4X3+5X3= 34. 2X3+1X3+2X3= 35. 2X3+2X3+2X3= 36. 1X3+1X3+1X3= 37. LIU = 44. LXXIY = 38. XLIY = 45. LXXXYI = 39. XXXI = 46. LXXYIII = 40. LX = 47. C = 41. LXXI = 48. XC = 42. LXIX = 49. CIX = 43. LXXY = 50. CY = SECOND-YEAR ARITHMETIC. LESSON YIII. 1. 3X6+1X6+1X6=5X6=30X1. 2. 1X6+2X6+3X6= 3. 1X6+1X6+1X6= 4. 2X6+4X6+3X6= 5. 3X6+2X6+2X6= 6. 1x6+1x6+2x6= 7. 3X6+4X6+1X6= 8. 4X6+4X6+1X6= 9. 2X5+3X5+1X5= 10. 3X5+4X5+2X5= 11. 2X5+3X5+3X5= 12. 3X5+2X5+1X5= 13. 2X5+1X5+1X5= 14. 1X5+1X5+1X5= 15. 3X4+2X4+2X4= 16. 7X4+1X4+1X4= 17. 1X4+4X4+1X4= 18. 2X4+2X4+4X4= 19. 3X3+3X3+3X3= '20. 1X3+1X3+3X3= 21. 1X3+3X3+3X3= 22. 3X3+2X3+5X3= 23. 1X3+1X3+1X3= 24. 2X3+2X3+1X3= 25. 1X2+5X2+4X2= 26. 2X2+5X2+1X2= SECOND-YEAR TEXT-BOOK. 23 27. 3X2+1X2+2X2= 23. 2X2+2X2+3X2= 29. 3xl+5Xl+6Xl+4Xl+7xl=25X 1- 30. 5X1+6X1+7X1+8X1+3X1= 31. 9X1+4X1+3X1+5X1+6X1= 32. 7X1+7X1+5X1+4X1+5X1= 33. 6X1+6X1+6X1+6X1+6X1= 34. 5X1+5X1+7X1+3X1+4X1= 35. 8X1+7X1+6X1+5X1+4X1= 36. 9X1+8X1+7X1+6X1+5X1= 37. 10X1+3X1+5X1+4X1+6X1= 38. 8X1+4X1+7X1+3X1+8X1= 39. 6X1+6X1+7X1+7X1+8X1= 40. 3X1+8X1+8X1+5X1+5X1= 41. 33=XXXIIL 46. 65= 42. 26= 47. 73= 43. 37= 48. 44= 44. 54= 49. 11= 45. 18= 50. 31= LESSON IX. 1. How many feet in 5 yards 1 Ans. There are 5X3 ft. which are 15 ft. 2. How many feet in 9 yards ? 3. How many pints in 7 quarts ? 4. Charlie has 9 cts., George has 11 cts., and Fred has 8 cts.; how many cents have the three boys together ? 24 SECOND-YEAR ARITHMETIC. 5. There are 4 quarts in one gallon; how many quarts in 4 gallons ? 6. How many quarts in 8 gallons ? 7. How many quarts in 9 gallons ? 8. There are 4 weeks in one month; how many weeks in 7 months ? 9. How many weeks in 4 months ? 10. I paid 12 cts. for a slate, 11 cts. for a book, 8 cts. for an eraser, and 7 cts. for a pencil ; how much did I pay for all ? 11. 9X1+8X1+7X1+6X1+5X135X1. 12. 8X1+8X1+7X1+7X1+6X1= 13. 11X1+11X1+7X1+6X1+10X1= 14. 5X1+5X1+8X1+7X1+5X1= 15. 6X1+7X1+3X1+9X1+7X1= 16. 9X1+6X1+6X1+6X1+9X1= 17. 7X1+8X1+9X1+10X1+3X1= 18. 8X1+6X1+4X1+10X1+6X1= 19. 7X1+7X1+9X1+8X1+7X1= 20. 6X1+7X1+8X1+8X1+8X1= 21. 7X1+8X1+10X1+5X1+7X1= 22. 6X1+10X1+8X1+7X1+5X1= 23. 9X1+9X1+9X1+9X1+9X1= 24. 8X1+7X1+8X1+7X1+6X1= 25. 11X1+10X1+9X1+3X1+4X1= LESSON X. 1. 9X1+7X1+6X1+5X1=27X1. SECOND-YEAR TEXT-BOOK. 25 2. 8X1+8X1+8X1+8X1= 3. 9X1+9X1+9X1+9X1 = 4. .7X1+7X1+7X1+7X1= 5. 6X1+6X1+6X1+6X1:= 6. 8X1+7X1+8X1+7X1= 7. 10X1+10X1+5X1+8X1= 8. 9X1+8X1+7X1+6X1= 9. 7X1+9X1+5X1+7X1= 10. 6X1+10X1+11X1+7X1= 11. 6X1+5X1+7X1+^X1= 12. 11X1+8X1+7X1+9X1= 13. 11X1+11X1+11X1+11X1= 14. 12X1+6X1+7X1+9X1= 15. 12X1+8X1+7X1+9X1= 16. 13X1+6X1+7X1+7X1= 17. 9X1+7X1+9X1+7X1= 18. 14X1+8X1+7X1+6X1 = 19. 13X1+10X1+5X1+7X1= 20. 6X1+11X1+7X1+9X1= 21. 3X6+2X6+3X6=8X648X1. 22. 2X6+5X6+2X6= 23. 1x6+1x6+2x6= 24. 2X6+3X6+1X6= 25. 3X6+5X6+2X6= 26. 2X6+1X6+2X6= 27. 2X6+4X6+1X6= 28. 3X6+5X6+1X6= 26 SECOND-YEAR ARITHMETIC. 29. 1X6+1X6+1X6= 30. 2X5+1X5+2X5= 31. 3X5+2X5+2X5= 32. 4X5+1X5+3X5= 33. 3X5+2X5+4X5= 34. 2X5+2X5+2X5= 35. 1x5+1x5+1x5= 36: 3X5+5X5+2X5= 37. 2X4+3X4+3X4= 38. 3X4+3X4+3X4= 39. 2X4+2X4+3X4= 40. 1X4+3X4+2X4= 41. 3X3+2X3+1X3= 42. 2X 3+3x3+4x3= 43. 3X3+1X3+3X3= 44. 5X2+1X2+4X2= 45. 2X2+2X2+3X2= 46. 3X2+3X2+2X2= 47. 2X2+2X2+1X2= 48. 1X2+1X2+1X2= 49. 3X2+1X2+1X2= 50. 2X2+4X2+3X2= LESSON XL 1. 6X1+6X1+6X1+5X1+3X1=26X1. 2. 7X1+6X1+9X1+8X1+4X1= 3. 9X1+7X1+6X1+5X1+3X1= SECOND-YEAR TEXT-BOOK. 27 4. 7X1+10X1+6X1+8X1+5X1= 5. 11X1+5X1+7X1+4X1+6X1= 6. 12X1+12X1+5X1+9X1+7X1=: 7. 8X1+11X1+5X1+7X1+6X1=: 8. 11X1+11X1+11X1+7X1+9X1= 9. 12X1+5X1+6X1+3X1+2X1=: 10. 8X1+7X1+5X1+4X1+4X1=: 11. 9X1+9X1+9X1+9X1+4X1=: 12. 7X1+6X1+5X1+4X1+3X1=: 13. 7X1+3X1+9X1+9X1+3X1=: 14. 5X1+6X1+8X1+7X1+6X1=: 15. 9X1+5X1+7X1+9X1+3X1=: 16. 11X1+7X1+7X1+7X1+5X1= 17. 10X1+7X1+5X1+5X1+2X1= 18. 12X1+7X1+9X1+6X1+7X1= 19. llxl+9xl+7xl+7xl+5xl= 20. 9X1+8X1+7X1+6X1+5X1= 21. 3x7+2x7+3x7=8x7=56x1. 22. 2X7+3X7+2X7=: S3. 4)^7+1x7+4x7= 24. 2X7+2X7+1X7= 25. 1X7+4X7+1X7= 26. 1x7+1x7+1x7= 27. 2X7+1X7+1X7= 28. 1x7+3x7+2x7= 29. 3x7+3x7+4x7= 30. 2X6+3X6+3X6= SECOND-YEAR ARITHMETIC. 31. 5X6+1X6+1X6= 32. 3X6+4X6+2X6= 33. 2X6+1X6+1X6= 34. 3X6+2X6+1X6= 35. 2X6+1X6+2X6= 36. 1X6+1X6+1X6= 37. 8X6+1X6+1X6= 38. 3X5+4X5+1X5= 39. 1X5+1X5+5X5= 40. 2X5+2X5+5X5= 41. 3X5+1X5+2X5= 42. 1X5+1X5+1X5= 43. 2X5+1X5+1X5= 44. 3X4+3X4+2X4= 45. 2X4+4X4+2X4= 46. 3X4+4X4+2X4= 47. 3X3+1X3+5X3= 48. 2X3+1X3+4X3= 49. 1X3+2X3+4X3= 50. 2X3+2X3+2X3= 10x7= 4X7= 7X*6= 9x7= 3x7= 6x6= 8X7= 2X7= 5X6= 7x7= 10X6= 4X6= 6X7= 9X6= 3X6= 5x7= 8X6= 2X6= SECOND-YEAR TEXT-BOOK. 29 LESSON XII. 1. 10X1+10X1+6X1+6X1=32X1. 2. 12X1+5X1+7X1+4X1= 3. 9X1+8X14-6X1+7X1= 4. 11X1+12X1+5X1+3X1= 5. 9X1+7X1+6X1+5X1=* 6. 8X1+8X1+8X1+3X1= 7. 9X1+6X1+5X1+8X1= 8. 8X1+9X1+5X1+4X1= 9. 11X1+6X1+6X1+5X1= 10. 10X1+5X1+10X1+5X1= 11. 10X1-5X1=5X1. 20. 7X1-5X1= 12. 9X17X1= 21. 9x15x1= 13. 10X1-8X1= 22. 10X1-4X1= ' 14. 10X1 6X1= 23. 10X19X1= 15. 8X1-3X1= 24. 9X1-6X1= 16. 9X13X1= 25! 10X1-7X1= 17. 10X13X1= 26. 8X14X1= 18. 8X15X1= 27. 10X1-1X1= 19. 9X14X1= 28. 9x11X1= 29. 5x7+1x7+2x7=8x7=56x1. 30. 2x7+3x7+4x7= 31. 3X7+1X7+1X7= 32. 1x7+3x7+2x7= 33. 3x7+4x7+1x7= 34. 1x7+1x7+1x7= 35. 2x7+4x7+4x7= 30 SECOND-YEAR ARITHMETIC. 36. 2X7+1X7+1X7= 37. 3X6+4X6+2X6:= 38. 3X6+1X6+3X6= 39. 1X6+1X6+1X6= . 40. 2X6+5X6+1X6= 41. 3X6+1X6+1X6= 42. 2x6+1x6+1^6= 43. 6x6+1x6+1x6= 44. 3X5+4X5+2X5= 45. 2X5+3X5+2X5= 46. 1X5+2X5+5X5= 47. 3X4+2X4+3X4= 48. 2X4+2X4+6X4= 49. 1x4+3x4+5x4= 50. 1X4+1X4+5X4= LESSON XIII. 1. 3X8+3X8+2X8=8X8=64X1. 2. 2X8+4X8+4X8= 3. 3X8+3X8+1X8= 4. 1X8+1X8+2X8= 5. 4X8+4X8+1X8= 6. 1X8+1X8+4X8= 7. 2X8+2X8+1X8= 8. 1X8+1X8+1X8= 9. 2X8+4X8+2X8= 10. 3x7+3x7+3x7= SECOND-YEAR TEXT-BOOK. 31 11. 2X7+1X7+3X7= 12. 3x7+3x7+4x7= 13. 2x7+1x7+4x7= 14. 1x7+1x7+2x7= 15. 3X7+2X7+1X7= 16. 1X1+3X7+1X7= 17. 5x6+2x6+1x6= 18. 3X6+3X6+3X6= 19. 2X6+1X6+3X6= 20. 5X6+4X6+1X6= 21. 3X6+2X6+2X6= 22. 2X5+1X5+1X5= 23. 3X5+4X5+2X5= 24. 4X5+1X5+3X5= 25. 3X5+4X5+3X5= 26. 2X5+2X5+3X5= 27. 1X5+1X5+1X5= 28. 4X4+1X4+1X4= 29. 3X4+3X4+2X4= 30. 2x4+4x4+3x4= 31. 3X4+1X4+2X4= 32. 3X3+3X3+1X3= 33. 1X3+1X3+6X3= 34. 2X3+4X3+3X3= 35. 2X2+2X2+4X2= 36. 2X2+5X2+2X2= 37. 3X2+3X2+1X2= 32 SECOND-YEAR ARITHMETIC. 38. CCXIY= 45. CLX1II= 39. CCXYI= 46. CLXXXYI= 40. CIX= 47. CCLXXYIII=: 41. CXXV= 48. CCIII= 42. CCLV= 49. CCCXC= 43. CXXXY1I=: 50_CCXCIX:= 44. CCXLVIII= LESSON XIY. 1. George earned 10 cts. and spent 4 cts. for a pencil ; how many cents had he left ? Ans. He had 6 cents left. 2. How many dollars will 8 sheep cost at $7 a head ? Ans. 8 sheep will cost 8 X $7 which are $56. 3. How many dollars will six sheep cost at $7 a head ? 4. A drover bought 13 cows and sold 9 of them ; how many cows had he left ? 5. There are 7 days in one week ; how many days in 7 weeks ? 6. How many quarts in 7 gallons ? 7. How many quarts in 9 gallons? 8. Mary is 6 years old, and her father is 7 times as old as she ; how old is her father ? 9. How many feet in twelve yards ? 10. How much will 4 lemons cost at 4 cts. each ? SECOND-YEAR TEXT-BOOK. 33 11. CCXVII= 21. 143=CXLIII. 12. CXCIY= 22. 226= 13. CCLXXXVI= 23. 118= 14. LXIII= 24. 139= 15. LXXVIII= 25. 211= 16. CCXIX= 26. 301= IT. CIII= 27. 110= 18. CXLII= 28. 1T5= 19. CYIII= 29. 382= 20. CLXYII= 30. 193= LESSON XV. 1. 18X1+10X1=28X1. 2. 25X1+9X1= 3. 16X1+11X1=- 4. 17X1+12X1= 5. 15X1+15X1= 6. 16X1+16X1= 7. 17X1+17X1= 8. 14X1+14X1= 9. 13X1+13X1= 10. 12X1+13X1= 11. 18X1+18X1= 12. 20X1+16X1= 13. 19X1+19X1= 14. 23X1+12X1= 15. 16X1+15X1 = 34: SECOND-YEAR ARITHMETIC. 16. 21X1+10X1= 17. 19X1+12X1= 18. 22x1+15X1= 19. 10X1+18X1= 20. 25X1+20X1= 21. 6x7+3x7+2x7=11x7=77x1 22. 5X7+3X7+2X7= 23. 1x7+5x7+1x7= 24. 2X7+1X7+3X7= 25. 3x7+3x7+2x7= 26. 1x7+2x7+4x7= 27. 3x7+2X7+2x7= 28. 1x7+1x7+2x7= 29. 3X6+1X6+1X6= 30. 2X6+2X6+5X6= 31. 1X6+1X6+2X6= 32. 3X6+4X6+1X6= 33. 1X6+1X6+4X6= 34. 3X6+2X6+5X6= 35. 2X6+3X6+2X6= 36. 1X6+1X6+1X6= 37. 3X5+2X5+4X5= 38. 2X5+2X5+3X5= 39. 1x5-1-1x5+2x5= 40. 4X5+3X5+1X5= 41. 1X5+1X5+1X5= 42. 3X5+1X5+1X5= SECOND-YEAR TEXT-BOOK. 35 43. 2X5+3X5+1X5= 44. 3X4+3X4+3X4= 45. 2X4+3X4+2X4= 46. 3X4+2X4+3X4= 47. 2X3+3X3+3X3= 48. 3X3+4X3+3X3= 49. 2X3+4X3+3X3= 50. 1X2+2X2+3X2= LESSON XVI. 1. 2x8+3x8+1x8=6x8=48x1. 2. 3X8+2X8+3X8= 3. 2X8+2X8+5X8= 4. 1x8+1x8+1x8= 5. 3X8+2X8+2X8= 6. 2X8+2X8+2X8= 7. 1X8+1X8+3X8= 8. 1X8+2X8+1X8= 9. 2x7+2x7+3x7= 10. 1x7+3x7+2x7=" 11. 3X7+3X7+2X7= 12. 2X7+1X7+1X7= 13. 3x7+4x7+3x7= 14. 2X7+3X7+4X7= 15. 2X6+2X6+4X6= 16. 3X6+1X6+5X6= 17. 3X6+2X6+2X6= 36 SECOND-YEAR ARITHMETIC. 18. 1X6+3X6+2X6= 19. ! X 6+lx6+3x6=r 20. 5X5+2X5+2X5= 21. 2X5+2X5+3X5= 22. 1x5+3x5+4x5= 23. 2X5+1X5+3X5= 24. 1X5+1X5+5X5= 25. 3X4+3X4+3X4= 26.- 1X4+1X4+2X4= 27. 3X4+3X4+2X4= 23. 2X4+3X4+2X4= 29. 6 Xl+Tx 1+5x1+3x1+7x1= 30. 9X1+9X1+9X1+7X1+5X1= 31. 11X1+11X1+11X1+9X1+6X1= 32. 12X1+9X1+3X1+7X1+7X1= 33. 10X1+8X1+7X1+9X1+8X1= 34. 9X1+7X1+10X1+9X1+11X1= 35. 8X1+7X1+6X1+10X1+9X1= 36. 7X1+9X1+5X1+8X1+11X1= 37. 12X1+6X1+7X1+9X1+5X1= .38. 11X1+7X1+8X1+5X1+9X1= 39. 10 X 1+10 X 1+10 X 1+10 X 1+10X1: 40. 8X1+7X1+6X1+9X1+7X1= 41. 9X1+8X1+7X1+6X1+5X1= 42. 6X1+5X1+8X1+4X1+5X1= 43. 9X1+8X1+7X1+6X1+4X1= 44. 101=01. 45. 253= SECOND-YEAR TEXT-BOOK. 3T 46. 328= 49. 190= 47. 147= 50. 119= 48. 239= LESSON XVII. (1) ( 2 ) (3) (*) (5) 6 3 9 7 8 5 7 3 5 3 3 4 8 5 9 8 6 6 5 4 4 5 4 5 6 26 (6) CO (3) (9) (10) 7 9 3 2 7 7 . 3 4 4 5 4 4 5 6 7 9 8 6 8 4 1 2 7 9 6 (11) (12) (13) (14) (15) 6 2 7 7 9 7 9 6 6 3 3 5 4 7 8 8 4 7 5 2 2 8 3 2 5 SECOND-YEAR ARITHMETIC. (16) (vn (18) (19) (20) 7 9 8 9 7 6 8 3 5 5 7 7 7 8 4 4 6 9 2 7 3 4 6 6 3 21. 4x7+3x337x1 (or 37). 22. 5x6+2x5= 23. 7x7+4x2= 24. 9x7+3x5= 25. 4X8+7X2= 26. 9x6+3x4= 27. 5X5+2X3= 28. 8X8+4X4= 29. 9X5+7X2= 30. 6X8+3X3=. 31. 9X7+2X8= 52. 6X6+5X3= 33. 7X10+3X4= 34. 5X9+4X5= 35. 8x7+3x6= 36. 7X9+4X2= .37. 6X7+3X5= 38. 1x8+3x8+2x8= 39. 3X8+2X8+4X8= 40. 2x8+1x8+1x8= 41. 3X8+4X8+1X8= SECOND-YEAR TEXT-BOOK. 39 42. 2X8+2X8+3X8= 43. 1X8+1X8+3X8= 44. 3x7+3x7+3x7= 45. 2x7+1x7+1x7= 46. 1X7+2X7+5X7= 47. 2x7+2x7+3x7= 48. 2x7+1x7+2x7= 49. 3x7+1x7+2x7= 50. 1x7+1x7+1x7= LESSON XVIII. 1. How many beets in 7 bunches, if there are 6 beets in each bunch ? Ans. There are 7x6 beets, which are 42 beets. 2. At 4 cts. each, what will 9 oranges cost ? 3. There are 4 pecks in a bushel ; how many pecks in 6 bushels ? 4. Hpw many pecks in 12 bushels ? 5. How many pints in 7 quarts ? 6. How many feet in 6 yards ? 7. How many quarts in 9 gallons ? 8. James paid 15 cts. for a slate, and 47 cts. for a book ; how much did he pay for both? 9. How many shoes does it take to shoe 4 horses ? 10. A beetle has 6 legs ; how many legs have 5 beetles ? 4:0 SECOND-YEAR ARITHMETIC. 11. 7X7+3X3=58X1 19. 10x6+3x8= 12. 6X8+4X5= 20. 6x7+5x4= 13. 7X5+3X6= 21. 8x6+5x3= 14. 6X9+5X3= 22. 7x11+^X3= 15. 8X5+3X7= 23. 8x3+7x5= 16. 5X9+4X6= 24. 4x8+6x2= 17. 7X3+3X7= 25. 9x5+5x9= 18. 9X2+8X7= LESSON XIX. 1. IX 9+2x9+3x9=6x9=54x1 (or 54). 2. 2X9+3X9+4X9= 3. 1X9+1X9+1X9= 4. 3X9+4X9+1X9= 5. 1X9+3X9+1X9= 6. 3X9+1X9+3X9= . 7. 1X9+1X9+4X9= 8. 2X9+1X9+1X9= 9. 1X8+3X8+1X8= 10. 1X8+2X8+4X8= 11. 2X8+2X8+4X8= 12. 1X8+1X8+4X8= ' 13. 2X8+1X8+7X8= 14. 1X8+1X8+7X8= 15. 1X8+1X8+1X8= 16. 2X8+1X8+1X8= 17. 1x7+1x7+1x7= IS. 2x7+2x7+2x7= SECOND-YEAR TEXT-BOOK. 41 19. 3X7+3X7+3X7= 20. 4x7+4x7+2x7= 21. 1x7+3x7+1x7=: 22. 2X7+1X7+1X7= 23. 1x7+1x7+5x7= 24. 2x7+3x7+3x7= 25. 1X6+1X6+1X6= 26. 2X6+1X6+1X6= 27. 3X6+4X6+2X6= 28. 2X6+2X6+3X6= 29. 1X6+1X6+6X6= 30. 3X5+2X5+2X5= 31. 2X5+4X5+2X5= 32. 1X5+1X5+6X5= 33. 2X5+1X5+1X5= 34. 3X4+3X4+1X4= 35. 2X4+1X4+5X4= 36. 2X4+3X4+5X4= 37. 1X4+5X4+3X4= 38. 2X3+3X3+2X3= 39. 1X3+1X3+7X3= 40. 1X3+1X3+6X3= 41. 1X3+3X3+2X3= ; 42. 3X9+4X5=47X1. 47. 7x7+3x3= 43. 7X6+3X3= 48. 8x5+5x3= .44. 9X7+4X2= 49. 8x4+3x3= 45. 9X9+7X2= 50. 9* 7+2x5= 46. 6X6+4X5= 42 SECOND-YEAR ARITHMETIC. LESSON XX. 1. 3 * 9+3x9+3x9=9x9=81 Xl. 2. 2X9+2X9+1X9= 3. 1X9+3X9+2X9= 4. 3X9+2X9+3X9= 5. 3X9+3X9+4X9= 6. 1X9+1X9+1X9= 7. 2X9+4X9+1X9= 8. 1x9+1x9+4x9= 9. 3X8+2X8+2X8= 10. 3X8+4X8+3X8= 11. 1X8+1X8+1X8= 12. 2X8+3X8+4X8= 13. 1X8+2X8+1X8= 14. 1X8+3X8+4X8= 15. 2X8+1X8+2X8= 16. 1X8+1X8+4X8= 17. 2x7+3x7+3x7= 18. 3X7+5X7+2X7= 19. 1X8+1X8+7X8= 20. 1X7+1X7+1X7= 21. 3x7+1x7+5x7= 22. 2x7+2x7+4x7= 23. 1x7+3x7+3x7= 24. 2X7+1X7+2X7= 25. 1X6+1X6+1X6= 2!6. 2X6+3X6+3X6= SECOND-YEAR TEXT-BOOK. 43 27. 3X6+2X6+4X6=: 28. 1X6+2X6+2X6= 20. 13X1+12X1+5X1+4X1+7X1= 30. 10X1+8X1+10X1+6X1+5X1= 31. 4X1+9X1+8X1+7X1+6X1= 32. 9X1+10X1+9X1+6X1+10X1= 33. 8X1+11X1+9X1+7X1+6X1= 34. 9X1+5X1+4X1+7X1+3X1= 35. 7X1+6X1+8X1+10X1+7X1= 36. 9X1+10X1+7X1+6X1+5X1= 37. 10X1+10X1+7X1+8X1+6X1= 38. 8X1+7X1+6X1+9X1+10X1= 39. 12X1+12X1+7X1+5X1+8X1= 40. 0X1+7X1+6X1+4X1+7X1= ' 41. 11X1+8X1+7X1+10X1+6X1= 42. 0X1+8X1+11X1+7X1+6X1= 43. 6X7+3X3=51X1. 44. 9X5+4X2= 45. 7X8+4X4= 46. 6x7+5x4=: 47. 8x10+3x4=: 48. 7X5+3X2= 49. 9X6+6X2= 50. 7X7+4X5= LESSON XXI. 1. 4 X 10+5 X 10+3 X 10=12 XK=120X1 (or 120). 44 SECOND-YEAK ARITHMETIC. 2. 3X10+2X10+5X10=: 3. 6X10+1X10+4X10:= 4. 2X10+3X10+3X10= 5. 3X10+1X10+2X10= 6. 5X10+2X10+2X10= 7. 2X10+2X10+3X10= 8. 3X9+1X9+1X9= 9. 2X9+1X9+4X9= 10. 3X9+2X9+4X9= 11. 2X9+3X9+6X9= 12. 3X9+6X9+3X9= 13. 2X9+3X9+5X9= 14. 3X9+3X9+2X9= 15. 4X9+1X9+1X9= 16. 2X9+1X9+1X9= 17. 4X8+4X8+4X8= 18. 3X8+3X8+3X8= 19. 2X8+2X8+2X8= 20. 3X8+3X8+2X8= 21. 2X8+2X8+1X8= 22. CCCI11= 29. CXLIX= 23. CCXXXYI= 30. CCCXYIL 24. CLXXXIY= 31. 104=GIV. 25. CC_CYII= 32. 202= 26. CCCI= 33. 222= 27. CCXXI= 34. 305= 28. CXCYIII= 35. 313= SECOND- YEAR TEXT-BOOK. 36. 156= 39. 260= 37. 276= 40. 333= 38. 318= 5X8= 12X8= 11X9= 3X9: 11X8= 7X9= 8X8: 4X8= 12X9= 7X8: 9X8= 6X9= 3X8: 5X8= 5X9= 6X8: 9X9=* 10X9= 8X9= 4X9= LESSON XXII. 1. How many days in 12 weeks? Ans. There are 12 X7 days, which are 84 days. 2. How many weeks in 56 days ? 3. " " " " 35 " ? 4. t: ^1+9X1+6X1+9X1+6X1+9X1= 11. 8X1+10X1+8X1+10X1+8X1+10X1= 12. 7X1+6X1+9X1+8X1+7X1+8X1:= 13. 9X1+11X1+7X1+9X1+10X1+9X1= 14. 13X14-8X1+7X1+10X1+9X1+8X1= 15. 8Xl+10Xl+8xl+llXl+8xl+10xl = 16. 12X1+6X1+9X1+7X1+8X1+8X1=- 17. 6X1+9X1+8X1+9X1+5X1+4X1=: 18. 8X1+8X1+6X1+6X1+7X1+5X1=: 19. 6X^+7X1+9X1+7X1+11X1+8X1=: 20. 5X1+12X1+6X1+12X1+8X1+6X1= 21. CCCXY= 31. 309= 22. CCLXXXVI= 32. 282= 23. CXYIII= 33. 111= 24. CCXCYII= 34. 358= 25. CLXIX= 35. 201= 26. CCCXXXII= 36. CCXI= 27. 276=CCLXXYI. 37. CCCXL= 28. 318= 38. XCYI= 29. 245= 39. CXLY= 50. 137= 40. CCXXI= SECOND-YEAR TEXT-BOOK. 55 LESSON XXIX. 1. 5X7+6X3=53X1. 2. 8X6+5X4= 3. 7X11+8X2= 4. 5X6+9X3= 5. 7X4+8X6= 6. 8X4+7X2= 7. 8X6+7X3= * 8. 9X6+6X3= 9. 5X8+8X7= 10. 7X3+9X2= 11. 5X11+11X3= 12. 8x6+4x3= 13. 9X5+5X4= 14. 3X12+12X3= 15. 7X6+3X8= 16. 5X11+4X4= 17. 6X6+5X5= 18. 4x8+8x5= 19. 7X6+9X3= 20. 8X7+5X4= 21. 3X9+8X2= 22. 7X6+6X4= 23. 2X8+9X7= 24. 5X3+6X8= 25. 7X7+5X4= 56 SECOND-YEAR ARITHMETIC. SUBTRACTION. (26) (27) (28) (29) (30) 836 914 763 646 928 271 812 312 314 814 115 (31) (32) (33) (34) (35) 779 890 945 675 810 246 370 810 345 700 (36) (37) (38) (39) (40) 546 298 989 967 789 324 137 787 824 362 LESSON XXX. (1) (2) (3) . (4) (5) 9 6 9 7 4 6 7 5 6 10 9 5 8 11 8 5 11 9 5 4 4 6 11 8 7 33 (6) (7) (8) (9) (10) 3 9 12 7 7 5 4 7 9 6 8 8 9 5 9 6 9 6 8 6 12 5 11 4 10 S^COND-YEAK TEXT-BOOK. 57 (15) 7 6 9 6 5 (11) 7 6 7 5 8 (12) 8 9 4 6 4 (13* 11 7 6 9 5 (14) 9 4 8 10 11 (16) (17) (18) (19) (20) 4 8 5 8 7 8 10 12 3 5 9 9 7 7 9 7 8 6 6 7 3 9 4 9 10 21. 5X5+2X5+3X5=10X5=50X1 22. 8X5+1X5+3X5= 23. 5X5+2X5+1X5= 24. 2X5+1X5+2X5= 25. 3X5+3X5+1X5= 26. 2X5+4X5+4X5= 27. 3X6+2X6+1X6= 28. 1X6+2X6+1X6= 29. 3X6+1X6+4X6= 30. 1x6+2x6+7x6= 31. 2X6+2X6+8X6= 32. 1X6+2X6+8X6= 33. 2X6+2X6+5X6= 34. 2X6+1X6+4X6= 58 SECOND-YEAR ARITHMETIC. 35. 2X7+3X7+4X7= 36. 1X7+2X7+3X7:= 37. 9X7+1X7+1X7= 38. 2X7+1X7+5X7= 39. 3X7+8X7+1X7=: 40. 2X7+1X7+7X7= 41. 1x7+1x7+5x7= 42. 3X8+1X8+5X8= 43. 1X8+2X8+1X8= 44. 2X8+2X8+8X8= 45. 1X8+3X8+3X8= LESSON XXXI. 1. 10X1+5X1+6X1+7X1+3X1+4X1= 35X1. 2. 9X1+8X1+7X1+6X1+5X1+4X1=: 3. 3X1+6X1+7X1+5X1+4X1+6X1= 4. 8X1+4X1+6X1+7X1+9X1+5X1= 5. 4X1+7X1+9X1+6X1+8X1+7X1=: 6. 11 X 1+6X1+7X1+5X1+4X1+8X1= 7. 10X1+10X1+6X1+7X1+5X1+4X1= 8. 9X1+8X1+10X1+6X1+7X1+3X1= 9. 11 X 1+11X1+9X1+7X1+5X1+4X1= 10. 6X1+7X1+6X1+7X1+6X1+7X1=: 11. 10X1-5X1=5X1. 12. 10X1-2X1= 13. 10X1-3X1= SECOND-YEAR TEXT-BOOK. 59 14. 10X16X1= 15. 10X14X1= 16. 10X1-8X1= 17. 10X1-1X1= 18. 10X19X1 = 19. 10X1-7X1= 20. 9X1-6X1= 21. 9X1-2X1= 22. 9X1-8X1= 23. 9X1-5X1= 24. 9X1-3X1= 25. 9X1-7X1= 26. 9X14X1= 27. 8X13X1= 28. 8X1-2X1= 29. 8X1-5X1= 30. 8X1-7X1= 31. 8X1-4X1= 32. 8X1-6X1= 33. 7X1-4X1= 34. 7X1-3X1= 35. 7X1-6X1= 36. 7X1-2X1= 37. 7X11X1= 38. 7X15X1= 39. 6X1-3X1= 40. 6X1-2X1= 60 SECOND-YEAR ARITHMETIC. 41. 6X1-4X1= 42. 6X1-1X1= 43. 6X15X1= 44. 5X1-1X1= 45. 5X1-2X1= 46. 5X1-4X1= 47. 5X1-3X1= 48. 4xl-lXl= 49. 4X1-3X1= 50. 4X1-2X1= LESSON XXXII. 1. How many lemons, at 4 cts. each, can be bought for 28 cts.? Ans. 7 lemons can be bought ; or 28 cts. will buy 7 lemons at 4 cts. each. 2. John had 17 cts.; he bought a present for his sister for 8 cts.: how many cents had he left ? 3. How many months in 11 years ? 4. How many pecks in 9 bushels?' 5. How much will a bushel of potatoes cost at 12 cts. a peck? 6. How many lemons, at 3 cts. each, can be bought for 15 cts.? 7. How many shoes will it take to shoe six horses ? SECOND-YEAR TEXT-BOOK. 61 8. Lucy had 10 roses, Kate had 12 roses, and Mary had 9 roses ; how many roses had the three girls ? 9. 7X1+8X1+6X1+5X1+7X1+4X1= 87X1. 10. 8X1+9X1+7X1+6X1+5X1+4X1= 11. 3X1+7X1+6X1+8X1+7X1+8X1= 12. 9X1+3X1+7X1+6X1+5X1+5X1= 13. 8X1+7X1+3X1+6X1+7X1+6X1= 14. 7X1+6X1+7X1+3X1+5X1+7X1= 15. 8X1+5X1+8X1+5X1+8X1+5X1= 16. 9xl+6Xl+3xl+6xl-f9Xl+3Xl= 17. 7X1+8X1+6X1+5X1+4X1+4X1= 18. 6X1+6X1+6X1+6X1+6X1+6X1= 19. 7X1+5X1+4X1+10X1+6X1+5X1 = 20. 9X1+9X1+8X1+8X1+7X1+7X1= 21. 10X1+9X1+8X1+7X1+6X1+6X1= 22. 7X1+5X1+8X1+6X1+3X1+7X1= LESSON XXXIII. 1. 10X1-3X1=7X1. 2. 10x1-2x1= 3. 10X1-9X1= 4. 10X1-5X1= 5. 10X1-4X1= 6. 10X1 6X1= 7. 10X1-1X1 = SECOND- YEAR ARITHMETIC. 8. 10X17X1= 9. 10X1 8X1= 10. 10X110X1= 11. 9X1-1X1= 12. 9X17X1= 13. 9X1-2X1= 14. 9X13X1= 15. 9X1-5X1 = 16. 9X14X1= 17. 9X1 6X1= 18. 9X1-8X1= 19. 9x1 9x1= 20. 8X1-1X1= 21. 8X13X1= 22. 8X1-5X1= 23. 8X1-2X1= 24. 8X1-4X1= 25. 8X1 6X1= 26. 8X17X1= 27. 7X16X1= 28. 7X1-3X1= 29. 2X12+3X12+2X12=7X12=84X1. 30. 3X12+1X12+1X12= 31. 1X12+3X12+5X12= 32. 3X12+3X12+4X12= 33. 3X12+2X12+3X12= 34. 3X12+3X12+6X12= SECOND-TEAK TEXT-BOOK. 35. 2X12+3X12+7X12= 36. 1X12+2X12+1X12= 37. 3xl2+3xl2+4xl2i 38. 3X12+4X12+4X12: 39. 2xil+3Xll+5xll:: 40. 3 Xll+^X 11+5X11- 41. 3X11+3XH+4X11: 42. 5X11+2X11+2X11= 43. 3X9+3X9+3X9= 44. 2X9+3X9+2X9= 45. 3X9+4X9+1X9= LESSON XXXIY. 1. 6X7+5X4=62X1. 2. 7X5+4X4= 3. 9X6+3X3= 4. 6X5+4X2= 5. 9X7+6X2= 6. 5X8+1X10= 7. 9X9+5X3= 8. 8X8+7X2= 9. 6X6+5X2= 10. 5X5+4X4= 11. 8X7+6X2= 12. 9.X 4+3x6= 13. 7X10+6X3= 14. 8X7+4X5= 15. 9X9+3X7= 64: SECOND-YEAR ARITHMETIC. 16. 91=XCI. 29. XCIII= 17. 175= 30. CCXY= 18. 264= 31. LXXXIX= 19. 183= 32. LXXYIII= 20. 372= "33. CCIY= 21. 256= 34. XCIX= 22. 147= 35. XCYI= 23. 328= 36. CCCXXI= 24. 239= 37. CCLXXXIIL 25. 106= 38. CCCXCYI= 26. LXXI= 39. CCLXI= 27. XLY= 40. CCCXCIX= 28. LXIY= LESSON XXXY. (1) 5 9 4 3 2 (2) 3 7 6 1 5 (3) 2 7 4 5 9 (*) 4 6 3 7 5 (5) 3 7 6 9 4 (6) 2 3 3 5 6 23 (7) (8) (9) (10) (11) (12) 3 ' 4 2 3 4 3 455447 577353 679755 786664 SECOND-TEAK TEXT-BOOK. 65 13. 3 X 12+2 X 12+3 X 12=8X12=96X1. 14. 2X12+4X12+3X12= 15. 3X12+1X12+1X12= 16. 4X12+5X12+3X12= 17. 2X12+1X12+2X12= 18. 3X12+4X12+4X12= 19. 1X12+1X12+1X12= 20. 3X9+4X9+3X9= 21. 2X9+3X9+3X9= 22. 3X9+4X9+2X9= 23. 2X9+3X9+1X9= 24. 2X8+2X8+3X8= 25. 2X8+2X8+2X8= 26. 2X8+4X8+3X8= 27. 2X8+3X8+2X8= 28. 1X8+1X8+3X8= 29. 2X^+3X7+3X7= 30. 3X7+4X7+2X7= 31. 2X7+1X7+1X7= 32. 2X7+3X7+1X7= 33. 1x7+1x7+4x7= 34. 2x7+3x7+5x7= 35. 1x6+1x6+1x6= 36. 3X6+2X6+3X6= 37. 2X6+3X6+4X6= 38. 2X6+1X6+2X6= 39. 1X6+3X6+2X6= 40. 2X6+3X6+2X6= 06 SECOND-YEAR ARITHMETIC. LESSON XXXYI. 1. 3X12+2X12+5X12=10X12=120X1. 2. 3X12+4X32+5X12= 3t 3X12+1X12+1X12= 4. 2X12+3X12+2X12= 5. 3X12+4X12+2X12= 6. 1X12+2X12+3X12= 7. 2X12+4X12+2X12= 8. 3X12+1X12+7X12= 9. 1X12+1X12+1X12= 10. 4X11+3X11+3X11= 11. 3X11+2X11+1X11= 12. 1X11+3X11+7X11= 13. 2X11+3X11+3X11= 14. 3X11+4X11+4X11= 15. 2X10+3X10+4X10= 16. 4X10+3X10+5X10= 17. 3X10+5X10+3X10= 18. 4X9+4X9+2X9= 19. 3X9+1X9+1X9= 20. 2X9+3X9+2X9= 21. 2X9+3X9+4X9= 22. 3X9+1X9+4X9= 23. 2x9+1x9+4x9= 24. 1X9+3X9+3X9= 25. 2X8+4X8+3X8= 26. 3X8+1X8+2X8= SECOND-YEAR TEXT-BOOK. 67 27. 1x8+4x8+3x8= 28. 3X8+2X8+2X8= 29. 3X8+4X8+5X8= 30. 2X8+3X8+6X8= 31. 1X8+1X8+1X8= 32. 7X7+3X7+2X7= 33. 2x7+1x7+4x7= 34. 3X7+1X7+5X7= 35. 1x7+1x7+1x7= 36. 1x7+2x7+1x7= 37. 2X7+3X7+2X7= 38. 1X7+4X7+3X7= 39. 3X6+2X6+2X6= 40. 2X6+2X6+3X6= 41. 3X6+1X6+8X6= 42. 2X6+3X6+4X6= 43. 1X6+1X6+1X6= 44. 3X6+3X6+2X6= 45. 1X6+1X6+9X6= LESSON XXXYII. 1. How many cents in 4 dimes? Ans. There are 4x10 cents, which are 40 cents. 2. How many dimes in 50 cents ? Ans. There are 5 dimes in 50 cents. 3. How many dimes in one dollar ? 4. How many inches in 12 feet ? 68 SECOND-YEAR ARITHMETIC. 5. How much will 8 pounds of sugar cost at 7 cts. a pound ? 6. How many pounds of sugar at 7 cts. a pound can be bought for 49 cents ? 7. John paid 40 cents for some firecrackers and 24 cents for some torpedoes ; how many cents did he pay for all ? 8. 7X6+5X5=67X1. 20. 6x6+3x4= 9. -9X3+3X5= 21. 8x9+5x3= 10. 8X7+6X2= 22. 11x6+3x5= 11. 7X11+5X4= 23. 8X7+5X4= 12. 6X8+3X7= 24. 7x7+6x3= 13. 5X9+4X6= 25. 9x5+4x6= 14. 6X8+8X3= 26. 8x6+6x5= 15. 7x7+5x5= 27'. 9x4+8X6= 16. 8X4+4X3= 28. 7x5+11x6= 17. 7X6+3X8= 29. 3x8+9x4= 18. 9X6+4X3= 30. 9x7+3x3= 19. 8X7+5X4= LESSON XXXVIII.' 1. 3X7+5X4=41X1 (or 41). 2. 7X5+6X2= 9. 7x11+4x2= 3. 9X8+7X2= 10. 8X7+5X3= 4. 8X7+3X3= 11. 7X6+3X6= 5. 6X9+4X4= 12. 9x7+5x2= 6. 7X7+3X4= 13. 6x8+4x4= 7. 8X5+9X2= 14. 5X7+2X3= 8. 10X6+3X5= 15. 6X6+5X5= SECOND- YEAR TEXT-BOOK. 69 16. 16X1+7X1+3X1+8X1+7X1+5X1= 46X1. 17. 10X1+9X1+7X1+6X1+5X1+4X1= 18. 11X1+11X1+7X1+5X1+9X1+3X1= 19. 9X1+8X1+7X1+6X1+5X1+4X1= 20. 12X1+12X1+12X1+7X1+6X1+5X1= 21. 8X1+7X1+6X1+9X1+8X1+6X1= 22. 7X1+5X1+5X1+8X1+7X1+8X1= 23. 9X1+6X1+10X1+5X1+10X1+6X1= 24. 11 X 1+11X1+7X1+6X1+8X1+5X1= 25. 6X1+10X1+8X1+7X1+9X1+7X1= 26. 8X1+7X1+6X1+7X1+5X1+8X1= 27. 6X1+8X1+7X1+9X1+4X1+3X1= 28. 11X1+7X1+9X1+10X1+6X1+5X1= 29. 3X7+5X7+4X7= 30. 2X7+1X7+6X7= 31. 2X7+3X7+4X7= 32. 5X7+1X7+1X7= 33. 1X7+1X7+2X7= 34. 2X7+2X7+1X7= 35. 3X7+1X7+6X7= LESSON XXXIX. 1. 10X1-7X1=3X1. 5. 10x1-10X1= 2. 10X1-2X1= 6. 10X1-3X1= 3. 10X1-9X1= 7. 10X1-5X1= 4. 10X1-6X1= 8. 10X1-8X1= '70 SECOND-YEAK ARITHMETIC, 9. 10X1-4X1=: 19. 9X1-5X1= 10. 10X12X1 20. 9X18X1= 11. 10X1-1X1= 21. 8X1-8X1= 12. 9X12X1= 22. 8X1-2X1= 13. 9X13X1= 23. 8X13X1= 14. 9X1-6X1= 24. 8X1-6X1= 15. 9X1-4X1= 25. 8X1-5X1= 16. 9X1-9X1= 26. 8X1-TX1= IT. 9X1-7X1= 27. 8X1-4X1= 18. 9X1 1X1= 28. 8X11X1= 29. 3X2+3X2+3X2=9X2=18X1. 30. 2X2+5X2+4X2= 31. 3X2+3X2+5X2= 32. 3X3+4X3+3X3= 33. 2X3+3X3+6X3= 34. 1X3+6X3+2X3= 35. 2X3+4X3+2X3= 36. 3X4+3X4+6X4= 37. 2X4+4X4+1X4= -38. 1X4+1X4+5X4= 39. 2X4+3X4+4X4= 40. 1X4+1X4+4X4= 41. 3X5+3X5+2X5= 42. 2X5+3X5+7X5= 43. 3X5+4X5+2X5= 44. 2X5+2X5+3X5= -45. 3X6+1X6+3X6= SECOND-YEAR TEXT-BOOK. 71 46. 2X6+2X6+2X6= 47. 3x6+lX6+lx6i= 48. 2X6+4X6+5X6= 49. 3X6+1X6+5X6= 50. 1X6+2X6+4X6= LESSON XL. 1. CIII=103. 11. 143=CXLIII. 2. XCY= 12. 372= 3. LXXXI= 13. 211= 4. XLIY= 14. 101= 5. CCYIII= 15. 364= 6. LXXY1I= 16. 110= 7. LXIX= 17. 396= 8. CCLYI= 18. 228= 9. CCXCIII= 19. 259= 10. CXIX= 20. 47= 21. 6X1+8X1+7X1+5X1+4X1+8X1+ 7X1=45X1. 22. 9X1+7X1+8X1+7X1+6X1+9X1+ 8X1= 23. 7X1+7X1+6X1+3X1+5X1+4X1+ 7X1= 24. 10X1+6X1+7X1+5X1+8X1+3X1+ 9X1= 25. 6X1+7X1+8X1+9X1+10X1+7X1+ 6X1= 72 SECOND-YEAR ARITHMETIC. 26. 11 X 1+11X1+7X1+6X1+5X1+9X1 27. 11X1+12X1+5X1+4X1+8X1+7X1 +6X1= 28. 10X1+10X1+7X1+5X1+6X1+3X1 +5X1= 29. 7X1+8X1+6X1+7X1+9X1+5X1+ 4X1= 30. 5X1+7X1+6X1+3X1+8X1= 31. 10X1+6X1+3X1+8X1+5X1= 32. 7xl+7xl+7xl+7xl+7xl= 33. 9X1+5X1+8X1+6X1+5X1= 34. 12X1+12X1+12X1+6X1+7X1= 35. 3X1+7X1+6X1+4X1+7X1= 36. 9X1+3X1+12X1+8X1+6X1= 37. 5X1+4X1+7X1+6X1+7X1= 38. 10X1+10X1+8X1+7X1+6X1= 39. 11X1+11X1+5X1+7X1+9X1= 40. 12X1+12X1+7X1+6X1+8X1= 41. 7X1+8X1+6X1+5X1+9X1= 42. 11X1+11X1+11X1+11X1+11X1= 43. 13X1+6X1+7X1+5X1+9X1= 44. 10X1+5X1+6X1+4X1+8X1= 45. 9X1+7X1+6X1+8X1+5X1= 9x7= 7X5= 6x6= 6X8= 9X8= 4X9= 12X5= 7X11= 6X3= SECOND-YEAR TEXT-BOOH. 73 12X9= 6X11= 9X6=: 5X8= 3X7= 4X12= 11X11=: 12X10= 10X11= LESSON XLI. 1. 7X7+6X3=67X1. 24, 7x1-3x1= 2. 9X6+4X4= 25. 7xl-2Xl= 3. 6X7+8X3= 26. 7x1-4x1= 4. 9X5+4X3= 27. 7x1-7x1= 5. 10X7+3X5= 28. 6x1-3x1= 6. 8X8+5X5= 29. 6x1-6x1= 7. 11x7+6x3= 30. 6x12x1= 8. 9X4+4X9= 31. 6x11X1= 9. 5X12+3X5= 32. 6x1-5x1= 10. 8X6+6X3= 33. 6x14x1= 11. 9X9+4X3= 34. 5xl-lXl= 12. 10X6+7X5= 35. 5x1-5x1= 13. 8X7+4X3= 36. 5x12x1= 14. 9X4+3X3= 37. 5x1-4x1= 15. 7X7+4X5= 38. 5x1-3x1= 16. 6X6+8X3= 39. 4x1-4x1= 17. 9X9+5X5= 40. 4xl-lXl= 18. 11X6+3X10= 41. 4X1-3X1= 19. 9X3+7X4= 42. 4x1-2x1= 20. 10X7+5X2= 43. 2xl-2Xl= 21. 7X1-6X1=1X1 44. 2X1-1X1= 22. 7X1-5X1= 45. 3x1-2x1= 23. 7X1-1X1= 74 SECOND-YEAR ARITHMETIC. LESSON XLII. 1. James has 16 cts., George has 9 cts., Fred has 7 cts., and James has 11 cts.; how many cents have all the boys together ? Ans. They have 43 cts. 2. How many days in 9 weeks ? 3. There are 8 wheels on a car ; how many wheels on 9 cars ? 4. How many weeks in 42 days ? 5. How many oranges, at 6 cts. each, can be bought for 48 cts.? 6. Lucy is 7 years old and her brother is 8 years older ; how old is her brother ? 7. How many months in 7 years ? 8. In 60 months, how many years ? 9. 9X1+7X1+8X1+6X1+10X1+9X1= 49X1. 10. 8X1+11X1+7X1+7X1+6X1+10X1= 11. 9X1+6X1+8X1+10X1+11X1+6X1= 12. V X 1+9X1+8X1+7X1+7X1+7X1= 13. 8X1+9X1+6X1+6X1+6X1+8X1= 14. 7X1+9X1+5X1+8X1+5X1+7X1= 15. 9X1+8X1+7X1+6X1+5X1+8X1= 16. 7X1+8X1+6X1+10X1+9X1+7X1= 17. 10X1+9X1+7X1+6X1+6X1+9X1= 18. 7X1+7X1+9X1+9X1+6X1+6X1= 19. 10X1+10X1+6X1+7X1+9X1+5X1= 20. 9X1+8X1+7X1+9X1+8X1+7X1= SECOND-YEAR TEXT-BOOK. 75 LESSON XLIIL 1. 3X12+2X12+1X12=6X12=72X1. 2. 4X12+3X12+2X12= 3. 1X12+3X12+8X12= 4. 3X12+2X12+2X12= 5. 2X12+3X12+5X12= 6. 4X12+1X12+3X12= 7. 3X12+1X12+1X12= 8. 2X12+3X12+6X12= 9. 1X12+1X12+1X12= 10. 1X12+1X12+2X12= 11. 2X11+3X11+3X11= .12. 3X11+2X11+1X11= 1 13. 3X11+4X11+4X11= :14. 2X11+4X11+4X11= 15. 3X11+2X11+4X11= 16. 1X11+1X11+10X11= 17. 3X10+3X10+1X10= 18. 2X10+3X10+6X10= 19. 3X10+1X10+6X10= 20. 2X10+2X10+8X10= 21. 3X9+3X9+3X9= 22. 1X9+1X9+3X9= 23. 3X9+2X9+2X9= 24. 2X9+3X9+1X9= 25. 3X9+4X9+5X9= 26. 1X9+1X9+1X9= 76 SECOND-YEAR ARITHMETIC. 27. 2X9+3X9+3X9= '28. 2X9+4X9+5X9= 29. 1X9+2X9+1X9= 30. 1X8+3X8+8X8= 31. 2X8+3X8+2X8= 32. 1X8+1X8+7X8= 33. 2X8+2X8+4X8= 34. 1X8+1X8+1X8= 35. 2X8+3X8+1X8= 36. 1X8+3X8+1X8= 37. 2X8+3X8+4X8= 38. 1X8+1X8+9X8= 39. 1X8+1X8+8X8= 40. 1X8+2X8+1X8= 41. 3x7+2x7+3x7= 42. 2x7+3x7+2x7= 43. 3x7+1x7+1x7= 44. 2X7+3X7+1X7= 45. 3X7+3X7+6X7= 46. 7X7+1X7+1X7= 47. 2x7+2x7+6x7= 48. 1X6+1X6+3X6= 49. 3X6+3X6+6X6= 50. 2X6+4X6+3X6= SECOND-YEAR TEXT-BOOK. 77 LESSON XLIY. 1. 9X9+3X4=93X1. 11- 6x8+7x2= 2. 10X10+7X3= 12. 9X5+4X4= 3. 9X8+6X5= 13. 3X8+3X4= 4. 4X7+8X2= 14. 5x12+4x6= 5. 9X6+7X3= 15. 3x7+5x4= 6. 8X7+4X4= 16. 9x8+3x6= 7. 6X6+5X5= 17. 7x7+3x3= 8. 7X5+4X6= 18. 8X9+4X2= 9. 8X8+6X4= 19. 9x6+3x4= 10. 10X7+5X6=. 20. 11X8+5X3= 21. 7X1+5X1+6X1+4X1+7X1+5X1= 34X1. 22. 6X1+8X1+7X1+8X1+6X1+9X1=: 23. 9X1+8X1+7X1+6X1+5X1+4X1= 24. 8 X 1+10 X 1+7 X 1+5x1+9*1+10x1= 25. 11X1+11X1+11X1+7X1 + 11X1 + 9X1= 26. 8X1+5X1+9X1+7X1+6X1+10X1= 27. 12X1+7X1+6X1+4X1+8X1+8X1= 28. 13X1+8X1+7X1+9X1+9X1+7X1= 29. 10X1+10X1+8X1+10X1+9X1+7X1= 30. 12X1+12X1+7X1+6X1+5X1+6X1= 31. 13X1+7X1+9X1+9X1+7X1+9X1= 32. 11 X 1 + 11 X 1+11 X 1 + 11 X 1+11X1+ 8X1= 33. 9X1+8X1+9X1+8X1+9X1+8X1= 78 SECOND-YEAR ARITHMETIC. 34 6 X 1+11 X l+Sxl+7Xl+9xl+5xl=r 35. 10X1+12X1+8X1+7X1+9X1+3X1= 36. 7X1+7X1+7X1+8X1+7X1+6X1= 37. 9X1+6X1+7X1+9X1+6X1+5X1= 38. 10X1+7X1+6X1+7X1+9X1+7X1= 39. 8X1+8X1+8X1+7X1+7X1+7X1= 40. 6X1+6X1+7X1+7X1+6X1+5X1= LESSON' XL Y. NOTE. The children are to be taught to write numbers from 400 to 1000. SUBTRACTION. (1) (2) (3) (4) (5) 376 724 546 665 448 124 113 413 104 135 (6) ' (7) (8) (9) (10) 243 437 576 993 876 131 426 132 172 544 (11) (12) (13) . (14) (15) 416 962 827 770 676 312 701 416 320 105 16. CCXXY= 20. XIY=: 17. CIX= 21. XXXYL= 18. XCIY=r 22. LXYII= 19. LXXXY1II= 23. CCXXIII= SECOND-YEAR TEXT-BOOK. 79 24. CCXCV= 30. 310= 25. CCXL= 31. 163= 26. 275= 32. 342= 27. 386= 33. 202= 28. 254= 34. 119= 29. 101= 35. 299= LESSON XLYI. SUBTRACTION. (1) (2) (3) (4) (5) 738 660 814 554 925 127 610 712 132 113 (6) (7) (8) (9) (10) 327 776 443 667 735 216 661 322 616 514 (11) (12) (13) (14) (15) 827 326 514 665 929 116 324 310 322 727 16. 7X7+3X5=64X1. 24. 7x6+4x3= 17. 9X6+4X4= 25. 9x9+3x2= 18. 10X8+3X10= 26. 11x6+5x4= 19. 9X7+6X3= 27. 7x9+6x2= 20. 8X9+7X2= 28. 8x8+4x4= 21. 7X6+3X8= 29. 11x7+3x5= 22. 6X6+5X5= 30. 9x10+4X6= 23. 9X8+5X7= 80 SECOND-YEAR ARITHMETIC. LESSON XLYII. (1) (2) (3) W (5) 6 7 3 5 5 5 6 9 7 5 8 4 10 2 5 7 7 7 6 5 10 11 12 U 8 (6) CO (8) (9) (10) 7 4 6 4 4. 3 6 6 4 4 6 10 - 7 7 5 11 7 7 6 10 13 15 6 9 12 (11) (12) (13) (14) (15) 7 9 3 13 10 3 2 6 7 9 6 9 7 6 6 4 3 13 4 3 8 9 12 12 14 16. 8X1+7X1+9X1+7X1+6X1+7X1= 44X1. 17. 11X1+7X1+9X1+10X1+7X1+6X1= 18. 12X1 + 12X1 + 7X1 + 7X1+10X1+ 6X1= 19. 13X1+11X1+7X1+6X1+5X1+7X1= 20. 14 X 1 + 10 X 1 + 7X1 + 6X1+6X1+ 10X1= SECOND- YEAR TEXT-BOOK. 81 21. ll!X 1+11X1 + 11 XI +11X1+HX1+ nxi= 22. 12X1+12X1+9X1+8X1+6X1+5X1= 23. 12X1 + 11X1 + 10X1 + 9X1+8X1+ 7X1= 24. 9X1+7X1+6X1+7X1+9X1+6X1= 25. 8X1 + 10X1 + 8X1 + 10X1+8X1+ 10X1= 26. 156=CLVI. 31. 183= 27. 294= 32. 62= 28. 127= 33. 237= 29. 255= 34. 148= 30. 378= 35. 107= LESSON XLYIII. 1. Fred sold 24 papers on Monday, and 37 papers on Tuesday ; how many papers did he sell during the two days? Ans. He sold 61 papers. 2. How much will 1 peck of peanuts cost at 5 cts. a quart ? Ans. They will cost 8x5 cents which are 40 cents. 3. How many feet in 9 yards ? 4. Kate ran 12 yards ; how many feet did she run ? 5. How many spools of thread at 5 cents a spool can be bought for 45 cents ? 82 SECOND-YEAR ARITHMETIC. 6. How many quarts in 6 gallons ? 7. Lucy is 15 years old and her mother is 25 years older ; how old is her mother ? 8. John paid 18 cents for some candy and 13 cents for some peanuts ; how much did he pay for both ? 9. 6X Y+7 X 6=: 18. 11X6+6X3= 10. 8X5+3X3= 19. 7X5+5X5= 11. 9X6+6X2= 20. 8X4+4X7= 12. 8X7+7X3= 21. 6x6+5x5= 13. 12X4+4X6= 22. 8x8+3x3= 14. 7X3+8X4= 23. 9x9+4x4= 15. 9X5+5X5= 24. 12x12+5x3= 16. 10X7+7X4= 25. 7x11+6x4= 17. 8X6+6X3= LESSON XLIX. 1. 7X5+6X2+3X1=50X1. 2. 8X7+4X4+2X2= 3. 9X4+6X4+3X3= 4. 10X6+7X3+6X2= 5. 6X9+9X2+4X4= 6. 8X8+5X5+1X6= 7. 9X7+6X5+3X4= 8. 7x7+5x7+6x1= 9. 9X10+3X8+1X10= 10. 5X11+7X4+2X1= SECOND-YEAR TEXT-BOOK. 11. 8X9+6X3+3X2= 12. 9X5+5X5+2X2= 13. 4X11+7X4+2X5= 14. 6X10+7X3+3X2= 15. 9X7+3X4+2X2= SUBTRACTION. (16) (17) (18) (19) (20) 756 994 864 660 526 136 632 322 550 416 (21) (22) (23) (24) (25) 437 360 673 928 875 126 250 661 716 661 (26) (27) (28) (29) (30). 384 956 726 676 963 273 325 114 506 721 (31) (32) (33) (34) (35) 846 749 676 952 676 726 627 676 752 624 LESSON L. 1. 5X12+3X12+2X12=10X12=120X1 2. 3X12+1X12+1X12= 3. 4X12+4X12+4X12= 4. 1X12+1X12+1X12= -84: SECOND-YEAK ARITHMETIC. 5. 3X12+2X12+2X12=: 6. 1X12+1X12+2X12= 7. 3X12+3X12+3X12= 8. 2X12+2X12+2X12= 9. 3X12+4X12+4X12= 10. 1X12+3X12+5X12= 11. 3X11+3X11+3X11= 12. 2X11+3X11+5X11= 13. 1X11+3X11+7X11= 14. 2X11+3X11+3X11= 15. 3X11+4X11+5X11= 16. 2X11+3X11+2X11= 17. 3X11+1X11+1X11= 18. 2X11+2X11+2X11= 19. 3X10+3X10+4X10= 20. 2X10+4X10+2X10= 21. 3X10+5X10+3X10= 22. 1X10+1X10+10X10=: 23. 2X10+2X10+2X10= 24. 3X9+3X9+4X9= 25. 3X9+1X9+1X9= 26. 1X9+1X9+1X9= 27. 3X9+2X9+2X9= 28. 2X9+1X9+1X9= 29. 3X9+2X9+3X9= 30. 2X9+4X9+6X9= -31. 3X9+3X9+5X9= SECOND-YEAK TEXT-BOOK. 85* 32. 1X9+3X9+2X9= 33. 2X8+3X8+3X8= 34. 3X8+4X8+5X8= 35. 1X8+1X8+1X8= 36. 3X8+1X8+1X8= 37. 1X8+1X8+5X8= 38. 2X8+2X8+2X8= 39. 3X8+1X8+5X8= 40. 1X8+7X8+3X8= LESSON LI. NOTE. The children are to be taught to add the first column and write the right hand figure of the sum un- der the first column, and add the left hand figure of the sum to the second column; proceeding thus with each column until the last column when the whole number of the sum is written. Nothing is said to the children of units, of tens, or of " carrying." (See*Nos. 21-32.) 1. 2X12+3X12+2X12=7X12=84X1- 2. 3X12+4X12+2X12= 3. 3X12+3X12+5X12= 4. 2X12+1X12+2X12= 5. 3X12+1X12+2X12= 6. 2X12+1X12+1X12= 7. 3X12+3X12+2X12= 8. 2X12+4X12+4X12= 9. 3X12+3X12+6X12= 10. 1X12+1X12+1X12= 86 SECOND-TEAE ARITHMETIC. 11. 7x7+5x5+3x3= 12. 9X9+5X6+3X2= 13. 7X8+5X7+6X1=: 14. 8X9+6X^+3X2= 15. 9X7+5X8+2X4= 16. 10X6+7X4+4X4= 17. 6X7+7X6+6X1= 18. 8X5+9X3+2X5= 19. 9X4+4X8+3X6= 20. 3X11+7X8+6X2= (21) (22) (23) (24) 325 114 386 136 134 411 168 163 268 141 144 212 74 114 . 221 122 (25) -(26) (27) (28) 139 330 135 314 283 303 72 413 72 333 164 134 6 33 8 25 (29) (30) (31) (32) 36 550 382 306 124 105 76 603 275 96 9 8 13 9 135 7 SECOND-YEAR TEXT-BOOK. 87 (33) (34) (35) (36) 134 212 316 414 6 75 67 144 152 134 127 94 71 63 8 4 LESSON LIL (1) (2) (3) (4) 275 514 114 327 133 73 206 54 246 164 138 6 74 9 110 131 (5) (6) m (8) 766 324 115 314 9 125 511 413 34 146 127 134 7 93 16 34 ff) (10) (11) (12) (13) 167 245 313 726 212 27 135 180 96 186 137 275 109 145 127 7 135 27 37 155 (14) (15) (16) (17) (18) 113 . 138 275 115 136 76 147 75 74 127 127 126 135 318 215 34 336 75 76 74 88 SECOND-YEAR ARITHMETIC. 19. 3X9+2X9+3X9=8X9=72X1. 20. 1X9+4X9+5X9= 21. 2X9+3X9+1X9= 22. 3X9+4X9+5X9= 23. 1X9+3X9+1X9= 24. 1X9+1X9+1X9= 25. 2X9+3X9+2X9= 26. 2x9+3x9+4x9= 27. 1X9+1X9+2X9= 28. 3X9+3X9+5X9= 29. 3X8+7X8+2X8= 30. 1X8+4X8+2X8= 31. 2X8+1X8+1X8= 32. 3X8+2X8+3X8= 33. 3X8+5X8+1X8= 34. 2X8+3X8+2X8= 35. 3X8+3X8+4X8= 36. 2X8+4X8+5X8= LESSON LIII. 1. 10X1+9X1+8X1+7X1+6X1+5X1 =45x1. 2. 9X1+7X1+6X1+6X1+7X1+7X1= 3. 8X1+7X1+9X1+9X1+9X1+6X1= 4. 11X1+11X1+11X1+9X1+7X1 + 10X1= 5. 9X1+9X1+9X1+9X1+9X1+9X1= SECOND-TEAK TEXT-BOOK. 89^ 6. 8X1+8X1+8X1+8X1+8X1+8X1= 7. 7X1+7X1+7X1+7X1+7X1+7X1= 8. 6X1+6X1+6X1+6X1+6X1+6X1= 9. 5X1+HX1+5X1+HX 1+*5X1 + 11X1= 10. 7X1+7X1+6X1+6X1+5X1+5X1= 11. 8X1 + 8X1 + 10X1+7X1+6X1+ 4X1= 12. 5X1+8X1+5X1+8X1+5X1+8X1= 13. 6X1 + 10X1 + 5X1+7X1+7X1+ 4X1= 14. 12X1+3X1+5X1+4X1 + 10X1 + 6X1= 15. 9X1+5X1+7X1+7X1+6X1+8X1= 16. 11X1 + 12X1+8X1+7X1+5X1 + 5X1= 17. 9*1+8X1+7X1+7X1+3X1+3X1= 18. 8X1+5X1+5X1+5X1+5X1+5X1= 19. 6X1+5X1 + 7X1+11X1+7X 2X1= 20. 9X1+3X1 + 12X1+5X1 + 6X 7X1= 21. CCLXYI= 26. 0011=: 22. CXC=i 27. CXIX= 23. CCCXXXIII= 28. CCCXY 24. LXXIY=: 29. CLXXIi= 25. XCVIII= 30. CCXLIII= 90 SECOND-YEAR ARITHMETIC. 31. CCCLVIIi= 36. 155= 32. CV= 37. 286= 33. LXIX= 38. 397= 34 274= 39. 143= 35. 321= 40. 369= LESSON LIT. 1. How many inghes in 8 feet ? Ans. There are 8x12 inches, which are 96 inches. 2. How many months in 9 years ? 3. How many pecks in 7 bushels ? 4. How many quarts in 12 pecks ? 5. In 6 gallons, how many quarts ? 6. How many feet in 36 inches ? 7. John shot an arrow 33 feet; how far would he have to go to get the arrow and bring it back ? 8. Sara is 7 years old and her father is 4 times as old ; how old is her father ? 9. 6X8+7X3=69X1. 10. 9X5+4X8= 18. 9X6+6X3= 11. 10X7+6X4= 19. 7X6+7X6= 12. 8X5+6X7= 20. 11x5+5x11= 13. 9x4+8x3= 21. 10x6+7x5= 14. 7X6+6X7= 22. 8x7+7x6= 15. 9X5+5X8= 23. 9x5+8x5= 16. 7X6+6X3= 24. 9x9+8x3= 17. 7x7+5x5= 25. 7x8+6x5= SECOND-YEAR TEXT-BOOK. 91 LESSON LY. 1. 9X8+6X6=108X1. 2. 5X9+8X6= 3. 3X7+6X12= 4. 8X8+5X5= 5. 4X4+3X12= 6. 9X2+8X6= 7. 7X5+8X3= 8. 2X12+3X6= 9. 9X4+2X8= 10. 7X5+8X3= 11. 9X6+7X7= 12. 8X3+6X5= 13. 7X4+8X2= (26) (27) 118 5 76 94 94 182 7 9 14. 3X12+8X10= 15. 9X2+10X0= 16. 7X5+3X12= 17. 9X4+7X7= 18. 6X6+3X9= 19. 9X2+8X7= 20. 6x5+5x7= 21. 4X12+3X0= 22. 5X7+6X4= 23. 7X2+8X3= 24. 12X12+5X4= 25. 3X11+8X2= (28) 101 296 87- 30 (29) 56 87 94 79 (30) 310 95 18 19 (31) 7 29 86 187 (32) 127 6 118 9 (33) 156 9 121 18 (34) 7 29 8 65 (35) 314 20 9 9 92 SECOND-TEAK ARITHMETIC. (36) (37) .(38) (39) , (40) 111 225 150 118 100 79 86 93 116 110 86 18 87 119 120 97' 81 9 117 119 - (42) (43) (44) (45) 9 187 212 19 220 59 59 120 118 202 87 8 86 127 9 196 126 95 59 18 (46) (47) (48) (49) (50) 375 416 372 516 284 124 105 141 113 181 LESSON LYI. 1. 45X1+18X163X1. 11. 66X1+44X1 = 2. 36X1+54X1= 12. 40X1+56X1= 3. 28X1+63X1= 13. 21x1+77x1= 4. 56 X 1+ 35 X 1= 14. 100 X 1+81 X 1= 5. 40X1+28X1= 15. 36X1+50X1= 6. 64X1+36X1= 16. 54x1+45x1= 7. 77X1+24X1= 17. 49x1+36x1= 8. 84X1+21X1= 18. 55X1+81X1= 9. 35X1+ 3 5X1= 19. 75X1+19X1= 10. 54X1+40X1= 20. 63X1+50X1= SECOND-TEAR TEXT-BOOK. 93 21. 3X7+2X7+3X7=9X7=56X1. 22. 2x7+2x7+5x7= 23. 1x7+1x7+1x7= 24. 3x7+3x7+4x7= 25. 2X7+1X7+2X7= 26. 1x7+2x7+1x7= 27. 2x7+3x7+1x7= 28. 1x7+1x7+5x7= 29. 2x7+2x7+3x7= 30. 3X7+3X7+2X7= 31. 3x7+3x7+5x7= 32. 2X7+4X7+6X7= 33. 1x7+1x7+7x7= 34. 2X6+3X6+3X6= 35. 3X6+1X6+1X6= 36. 2X6+7X6+2X6= 37. 1x6+1x6+1x6= 38. 3X6+1X6+2X6= 39. 1X6+3X6+5X6= 40. 2X6+2X6+3X6= 41. 3X6+3X6+6X6= 42. 1X6+2X6+1X6= 43. 3X6+2X6+4X6= 44. 3X6+1X6+6X6= LESSON LYII. 1. 6x7+5x7+3x3=86x1. 2. 9X9+6X3+1X2= y JUtt 94 SECOND-YEAR ARITHMETIC. LESSON LVIL 1. 6X7+5X7+3X3=86X1. 2. 9X9+6X3+1X2= 3. 10X5+6X7+3X2= 4. 9X5+7X4+4X1= 5. 5X8+9X6+1X5= 6. 7X7+6X6+2X2= 7. 8X8+7X7+1X3= 8. 9x5+6x7+3x3= 9. 12X7+7X5+3X2= 10. 9X6+6X9+5X2= 11. 7X6+3X11+12X1= 12. 10X7+7X8+3X4= 13. 11X6+6X9+3X3= 14. 12X5+7X9+5X1= 15. 8X8+8X8+2X3= SUBTRACTION. (16) (17) (18) . (19) (20) 775 958 876 953 887 121 148 304 100 663 (21) (22) (23) (24) (25) 736 584 735 518 376 616 504 615 413 145 (26) (27) (28) (29) (30) 729. 584 646 848 966 609 484 613 724 721 SECOND-YEAE TEXT-BOOK. 95 31. 124=CXXIY. 32. 207= S3. 356= 34. 143= 35. 256= 36. CI= 37. CCXYI= 38. CCCLXXXIY= 39. CXCYIII= 40. CCLX= LESSON LYIII. (1) (2) (3) (4) (*) 326 255 616 327 336 154 86 76 77 100 27 7 136 127 96 133 138 6 67 276 (6) (h (8) (9) (10) 167 100 354 716 325 155 69 86 85 76 200 184 9 9 148 73 96 2 13 9 (11) (12) (13) (14) 325 229 445 154 96 75 167 74 184 186 135 138 33 35 46 26 15. 3X12+3X12+3X12=9X12=108X1 16. 2X12+2X12+2X12= 17. 4X12+4X12+4X12= 96 SECOND-YEAK ARITHMETIC. 18. 1X12+1X12+1X12= 19. 2X12+2X12+1X12= 20. 3X12+3X12+2X12= 21. 2X12+2X12+7X12= 22. 1X12+1X12+2X12= 23. 3X12+2X12+2X12= 24. 2X12+2X12+6X12= 25. 1X12+2X12+1X12= 26. 3X11+3X11+3X11= 27. 2X11+5X11+4X11= 28. 3X11+5X11+2X11= 29. 2X11+2X11+2X11= 30. 3X11+4X11+5X11= 31. 3X11+5X11+1X11= 32. 2X11+3X11+2X11= 33. 1X11+1X11+3X11= 34. 3X11+1X11+2X11= 35. 2X10+3X10+4X10= 36. 3X10+4X10+5X10= 37. 1X10+2X10+3X10= 38. 2X10+3X10+2X10= 39. 4X10+4X10+3X10= 40. 2X10+3X10+5X10= LESSON LIX. 1. 3X9+4X9+2X9=9X9=81X1 2. 2X9+3X9+5X9= SECOND-YEAR TEXT-BOOK. 97 3. 1X9+2X0+4X9= 4. 2X9+4X9+6X9= 5. 3X9+2X9+6X9=: 6. 2X9+2X9+1X9= 7. 1X9+3X9+3X9= 8. 2X9+1X9+3X9= 9. 1x9+1x9+2x9= 10. 2X9+3X9+3X9= 11. 1X9+1X9+1X9= 12. 3X8+3X8+3X8= 13. 2X8+3X8+2X8= 14. 1X8+1X8+1X8= 15. 3X8+3X8+4X8= 16. 2X8+3X8+7X8= 17. 1X8+2X8+1X8= 18. 2X8+1X8+3X8= 19. 3X8+2X8+4X8= 20. 1X8+2X8+2X8= 21. 2X8+3X8+3X8= 22. 3X8+5X8+3X8= 23. 4X7+5X7+3X7= 24. 2X7+3X7+2X7= 26. 3x7+3x7+5x7= 26. 3X7+3X7+2X7= 27. 1x7+3x7+2x7= 28. 2x7+3x7+4x7= 29. 2x7+1x74-2x7= 98 SECOND-YEAR ARITHMETIC. 30. 3x7+5x7+1x7:= 31. 3x7+1x7+5x7= 32. 2X7+1X7+1X7= 33. 2x7+3x7+5x7= 34 3x7+2x7+4x7= SUBTRACTION. (35) (36) (37) (38) 725 984 609 927 014 723 102 16 (39) (40) (41) (42) 346 828 774 514 5 716 363 13 (43) (44) (45) (46) 675 544 476 373 613 322 133 253 (47) (48) (49) (50) 246 527 327 440 135 6 116 140 LESSON LX. 1. How many inches in 7 feet ? Ans. There are 7x12 inches which are 84 inches. 2. How many quarts in 8 pecks ? SECOND-YEAR TEXT-BOOK. 90 3. I paid 18 cts. for a book, 16 cts. for some paper, and 9 cts. for an eraser ; how much did I pay for all ? 4. Kate had 14 apples and ate 6 of them; how many had she left ? 5. How many oranges, at 6 cts. each, call be bought for 42 cts. ? 6. If one bunch of beets cost 8 cts., how muck will 9 bunches cost ? 7. How many quarts in 7 gallons ? 8. 9X6+6X4=78X1. 15. fx 11+6x6=- 9. 7X8+6X5= 16. 6x7+5x8= 10. 9X7+5X4= 17. 8X4+7X5= 11. 12X5+7X3= 18. 9X6+6X3= 12. 9X6+6X4= 19. 7X11+11X2= 13. 8X7+7X3= 20. 2X12+7X8=: 14. 6X9+5X5= LESSON LXI. 1. 9X5+6X3=63X1. 11. 10X7+7X6= 2. 8X7+5X6= 12. 11x6+8x4=:. 3. 5X7+9X4= 13. 8x8+9x5= 4. 8X3+7X5= 14. 7X9+8X7= 5. 9X6+7X7= 15. 6X12+7X5= 6. 8X8+6X6= 16. 5X11+11X6=: 7. 7X7+9X4= 17. 9X10+7X6= 8. 6X11+7X5= 18. 8X9+6X4= 9. 12X9+8X7= 19. 7X8+5X10 10. 9X5+5X9= 20. 9X4+5X7=- 100 SECOND- YE A B ARITHMETIC. (21) (22) (23) 1 (24) (25) 635 316 413 276 312 74 76 86 135 128 124 136 7 128 106 52 128 5 110 160 (26) (27) (28) (29) (30) 119 202 576 135 115 189 222 83 6 76 191 220 126 8 184 111 22 5 514 33 (31) (32) (33) (34) 376 576 316 275 76 35 76 161 6 114 56 44 136 141 96 33 LESSON LXII. 1. 9X5+8X3+2X2=73X1- 2. 7X6+6X5+4X2= 3. 8X7+5X4+3X2= 4. 10X6+7X5+4X3= 5. 9X4+8X7+3X1= 6. 6X8+7X7+5X2= 7. 9X5+8X4+3X3= :8. 7X6+6X7+5X3= SECOND-YEAK TEXT-BOOK. 101 9. 9X6+6X6+1X3=, 10. 7X9+5X8+4X2= 11. 8X7+6X4+3X1=^ 12. 9X9+7X5+3X2= 13. 7X6+6X7+3X3= 14. 5X9+9X7+1X4= 15. 4X8+7X2+2X5= SUBTRACTION. (16) (17) (18) (19) (20) 376 954 854 416 544 125 723 722 314 323 (21) (22) (23) (24) (25) 675 809 514 446 365 671 301 512 324 65 (26) (27) (28) (29) (30) > 514 330 514 376 418 114 320 413 4 11& (31) (32) (33) (34) (35) 372 514 376 728 518 212 413 215 613 114 LESSON LXIII. 1. 8X8+7X9+3X3=136X1. 2. 9X4+8X5+3X2= 102 SECOND-YEAR ARITHMETIC. 3. 7x7+6x5+4x1= 4. 8X9+3X7+2X5= 5. 9X4+3X3+7X2= 6. 7x7+5x7=: 7. 9X6+7X8= 8. 8X6+5X8= 9. 11X7+6X5= 10. 9x7+7x8= 11. 8X5+9X4= 12. 7X6+8X5= 13. 9X7+7X8= 14. 10X7+6X8= 15. 9X6+7X5= 16. CCLXYII= (27) (28) 336 225 184 146 125 38 64 135 17. CXCIX= 18. CCOXLYI= 19. CCLXXXIII: 20. CCCXXXIIL 21. 175= 22. 263= 23. 303= 24. 111= 25. 273= 26. 390= (29) 246 38 152 76 (30) 318' 165 27 141 LESSON LXIY. 1. 6 X 1+7X1+5X1+8X1+7X1+6X1+ 5X1=44X1. 2. 9X*1+8X1+7X1+6X1+5X1+4X1+ 3X1= -3. 10X1+6X1+6X1+6X1+5X1+5X1+ 5X1= SECOND-YEAR TEXT-BOOK. 103 4. 7 X 1+7X1+8X1+8X1+9X1+9X1+ 10X1= 5. 6 X 1+8X1+5X1+9X1+7X1+9X1+ 5X1= 6. 5X1+11X1+5X1+9X1+7X1+6X1+ 6X1= 7. 12 X 1 + 12X1+11X1+11X1+6X1+ 10X1+10X1= 8. Hxl + llXl + 7xl+7xM-7xl+ 6X1+6X1= 9. 10 X 1+10X1+8X1+7X1+6X1+7X1 +6X1= 10. 10X1+8X1+8X1+7X1+5X1+5X1+ 7+1= 11. 12X1+6X1+6X1+7X1+5X1+7X1+ 9X1= 12. 10X1 + 6X1 + 10X1+6X1+10X1+ 6X1+10X1= 13. 9X1+5X1+10X1+7X1+7X1+7X1+ 6X1= 14. 7 X 1+5X1+7X1+5X1+7X1+5X1+ 7X1= 15. 6 X 1+8X1+6X1+8X1+6X1+8X1+ 6X1= 16. 11 X 1 + 11 X1+11X1+HX1+11X1+ 11x1+11x1= 17. 9X1+9X1+9X1+9X1+9X1+9X1+ 9X1= 104 SECOND-YEAR ARITHMETIC. 18. 8X1+8X1+8X1+8X1+8X1+8X1+ 8X1= ' 19. 7 X 1+7x1+7x1+7x1+7x1+7x1+ 7X1= 20. 6 X 1+6X1+6X1+6X1+6X1+6X1+ 6X1= SUBTRACTION. (21) (22) (23) (24) (25) 676 375 544 350 273 135 * 144 104 120 100 (26) (27) (28) (29) (30) 416 549 927 676 276 114 136 114 135 136 LESSON LXY. 1. If one orange cost 5 cts., how many oranges can be bought for 45 cts.? Ans. 9 oranges can be bought for 45 cts.; or 45 cts. will buy 9 oranges. 2. James paid 16 cts. for a book, and 23 cts. for some paper ; how much did he pay for both ? 3. How many months in 8 years ? 4. George is 7 years old, how many months, old is he ? 5. James shot an arrow 53 feet ; he sent a boy after it ; how many feet would the boy have to go to get the arrow and bring it back to James ? SECOND-YEAR TEXT-BOOK. 105 6. 9X6+6X3=72X1. 7. 7X6+6X8= 8. 9X5+7X4= 9. 7x6+6x8= 10. 8X5+9X3= 11. 7X11+6X5= 12. 2X12+9X6= 13. 8X5+7X8= 14. 7X9+5X5= 15. 9X9+3X7= 16. 8X6+7X2= 17. 9X8+8X5= 18. 7x3+4x12= 19. 11X6+6X5= 20. 8X7+8X6= 21. 9X8+5X5= 22. 12X6+6X3= 23. 6xll+HX5= 24. 7X8+8X6= 25. 6X8+9X6= LESSON LXVI. (1) (2) (3) (4) 225 385 414 136 74 44 274 7 314 128 316 164 24 54 276 (5) 554 136 374 28 (6) 336 137 273 54 128 35 246 36 (8) 314 74 55 235 667 5 9 184 (10) 376 58 124 9 (11) 274 138 215 46 (12) 346 372 26 12 (13) 415 75 135 65 (14) 427 35 164 24 (15) 445 378 126 54 106 SECOND-YEAR ARITHMETIC. 16. 6X9+8X4=86X1. 17. 9X6+5X8= 18. 8X7+6X8=; 19. 5X9+9X5= 20. 7X6+6X7= 21. 6X11+7X5= 22. 9X8+7X7= 23. 12X6+6X5= 24. 8X8+6X6= 25. 9X9+7X4= 26. 12X6+6X5= 27. 9X10+10X4= 28. 5X11+11X5= 29. 8X7+7X7= 30. 9X6+5X7= LESSON LXYII. 1. 12X8+4X5=116X1. 2. 9X9+6X5= 3. 8X7+9X*= 4. 9X7+7X4= 5. 8X6+5X6= 6. 9X10+7X3= 7. 10X10+6X6= 8. 11x7+7x5= 9. 6X11+7X6= 10. 7X8+8X5= 11. 9X7+7X4= 12. 4X11+HX4: 13. 10X7+7X10: 14. 8x7+7x7= 15. 9x6+6x6= 16. 9x9+8x7= 17. 8X11+HX3: 18. 8X7+2X9= 19. 6X12+12X5: 20. : 7X5+5X7= (21) (22) (23) (24) (25) 376 275 134 276 275 154 145 109 310 146 123 135 196 209 109 143 295 209 111 76 SECOND-YEAR TEXT-BOOK. 107 (26) (27) (28) (29) (30) 346 427 567 376 254 37 96 27 27 13 126 137 128 9 134 147 34 54 124 66 (31) 376 64 134 94 (32) 427 96 136 276 (33) 276 136 256 196 (34) 346 27 154 35 (35) 416 76 136 25 LESSON LXYIII. 1. 3X12+2X12+3X12=8X12=96X1, 2. 2X12+4X12+4X12= 3. 1X12+1X12+1X12= 4. 3X12+2X12+2X12= 5. 2X12+1X12+2X12= 6. 3X12+6X12+3X12= 7. 1X12+1X12+2X12= 8. 1X12+3X12+2X12= 9. 3X12+2X12+6X12= 10. 1X12+3X12+5X12= 11. 2X12+3X12+2X12= 12. 3X9+4X9+5X9= 13. 1X9+2X9+3X9= 14. 2X9+3X9+4X9= r -^ 108 SECOND-YEAR ARITHMETIC. 15. 3X9+2X9+2X9= 16. 3X9+4X9+4X9= 17. 1X9+1X9+1X9= 18. 2X9+4X9+4X9= 19. 1X9+2X9+1X9= 20. 2X9+4X9+2X9= 21. 3X9+1X9+1X9= 22. 2X9+5X9+2X9= 23. 3X^+5X7+2X7= 24. 1x7+1x7+1x7= 25. 3x7+5x7+3x7= 26. 2X7+1X7+2X7= 27. 3x7+2x7+2x7= 28. 1x7+3x7+8x7= 29. 2X7+2X7+4X7= 30. 1x7+2x7+3x7= SUBTRACTION. (31) (32) (33) (34) (35) 355 724 518 767 500 123 613 114 316 100 (36) (37) (38) (39) (40) 646 327 276 534 779 101 13 10 321 32ft SECOND-YEAR TEXT-BOOK. 109 LESSON LXIX. NOTE. Teach the children to write numbers from 1,OCO to 10,000. 1. 9X6+5X8=94X1. 2. 7X8+4X9= 3. 8X9+6X5= 4. 9X9+4X8= 5. 7X6+6X7= 6. 8X9+5X6= 7. 6X11+4X5= 8. 5X7+8X6= 9. 4X12+12X4= 10. 9X8+7X3= (21) (22) (23) 448 326 16 144 514 376 44 154 134 138 64 52 11. 8X6+6X5= 12. 9X3+10X4= 13. 7X6+6X8= 14. 9X7+8X4= 15. 7X6+6X8= 16. 9x5+4x8= 17. 7x6+5x10= 18. 9X3+8X7= 19. 10x7+6x6= 20. 8X6+5X5= (24) (25) 374 376 152 154 54 13 138 124 ,(26) (27) (28) (29) (30) (31) 126 306 204 546 327 275 146 180 240 164 372 614 126 127 114 138 168 641 236 110 141 183 186 37 LESSON LXX. 1. 11 X 1+11 X 1+10 X 1+10 X 1+9 X 1+9 X 110 SECOND-YEAR ARITHMETIC. 2. 9X1+9X1+9X1+7X1+7X1 + 7X1+ 7X1= 3. 6X1+6X1+7X1+6X1+7X1 + 6X1+ 8X1= 4. 10X1+7X1+6X1+7X1+8X1+9X1+ 6X1= 5. 5X1+8X1+5X1+8X1+5X 5X1= 6. 7X1+6X1+8X1+7X1+9X 7X1= 7. 10xl+10xl+8xl+8Xl+6x 1+6X1= 8. 5X1+9X1+5X1+10X1+8X1+7X1+ 8X1= 9. 6X1+11X1+7X1+6X1+9X1+6X1+ 5X1= 10. 9X1+8X1+7X1+6X1+5X1+4X 3X1= 11. 12X1+12X1+8X1+7X1+10X 1+10x1= 12. 13X1+8X1+7X1+9X1+7X1+8X1+ 9X1= 13. 12X1+11X1+10X1+9X1 + 8X1+7X 1+6x1= 14. 7X1+7X1+6X1+7X1+9X1+8X1 + 7X1= 15. 8X1+7X1+8X1+7X1+8X1 + 7X1 + 8X1= SECOND-TEAK TEXT-BOOK. Ill 16. 6xl+6Xl+46 94 12,376 35 21,777 13,854 7 11,254 115 365 SECOND-YEAK TEXT-BOOK. 161 16. CCXCVI= 21. 327= IT. CCLXXXV= 22. 165= 18. 000X111= 23. 128= 19. CXVII= 24. 143= 20. CCCXLIli= 25. 279= LESSON CVIII. 1. 6X6+7X5+8X2=87X1. 2. 9X7+6X6+3X3= 3. 8X4+4X8+3X2= 4. 9X9+7X6+2X2= 5. 7X7+6X6+1X6= 6. 8X5+5X8+4X4= 7. 9X3+3X7+6X2= 8. 8X8+5X5+3X3= 9. 10X5+4X10+4X4= 10. 9x4+3x8+2*5= 11. 7X5+6X7+3X2= 12. 8X6+6X5+3X4= 13. 7X7+5X5+2X1= 14. 9X4+7X6+3X5= 15. 8X7+7X7+2X3= 16. 3X12+3X12+3X12= 17. 2X12+2X12+2X12= 18. 4X12+4X12+4X12= 19. 1X12+1X12+1X12= 20. 3X12+5X12+3X12= 162 SECOND-TEAR ARITHMETIC. 21. 1X12+5X12+1X12= 22. 1X12+2X12+1X12=: 23. 2X12+5X12+3X12= 24. 2X12+5X12+1X12= 25. 1X12+3X12+1X12= 26. 2X12+3X12+4X12= 27. 3X11+3X11+5X11= 28. 2X11+3X11+3X11 29. 2X11+1X11+2X11= 30. 1X11+1X11+2X11= 31. 2X11+3X11+2X11=: 32. 3X11+3X11+4X11= 33. 1X11+1X11+1X11= 34. 2X11+3X11+3X11= 35. 3X11+4X11+2X11= 36. 2X11+2X11+8X11= 37. 3X10+3X10+6X10= 38. 2X10+3X10+5X10= 39. 3X10+1X10+7X10= 40. 2X10+3X10+2X10= 41. 376= 42. 294= 43. 483= 44. 176= 45. 213= 46. 47. SECOND-YEAR TEXT-BOOK. 163 48. 49. 50. 12&6 106= LESSON CIX. 1. 6X7+6X5+3X3=81X1. 2. 9X5+8X4+7X1= 3. 8X1+7X5+2X2= 4. 9X0+5X6+4X3= 5. 8X'6+6X4+3X2= 7. 7X7+5X5+4X4= 8. 5X11+3X10+2X3= 9. 8X4+7X3+3X3= 10. 4X10+<:1X5+6X1= 11. 9X4+8X3+2X2= 12. 7X6+9X3+3X3= 13. 6X5+8X4+7X2= 14. 9X7+4X8+2X5= 15. 7X7+5X5+3X4= 16. 9X3+8X4+5X1= 17. 7X4+3X11+6X2= 18. 10X6+7X4+3X3= 19. 8X5+9X3+2X2= 20. 7X7+5X5+4X4= 21. I bought at one time 9 books, at another time 7 books, at another time 11 books, and at another time 6 books : how many books did I buy? Ana. I bought 33 books. 164 SECOND-YEAR ARITHMETIC. 22. James shot an arrow 21 feet ; he sent a boy after it ; how far would the boy have to go to get the arrow and bring it back to James? 23. There are 3 feet in one yard ; how many feet in 9 yards ? 24. There are 12 inches in one foot; how many inches in 12 feet? LESSON CX. . 1. 3X12-|-3X12+3X12=9X12=108X1. 2. 1X12+1X12+1X12= 3. 4X12+4X12+4X12= 4. 2X12+2X12+2X12= 5. 3X12+1X12+1X12= 6. 2X12+2X12+4X12= 7. 3X12+3X12+5X12= 8. 1X12+2X12+1X12= 9. 3X12+1X12+3X12= 10. 2X12+3X12+5X12= 11. 1X11+3X11+1X11 12. 2XH+3X11+ 4 5X11= 13. 3X11+4X11+5X11= 14. 1X11+3X11+6X11= 15. 2X11+3X11+4X11= 16. 3X10+2X10+3X10= 17. 3X10+4X10+4X10= 18. 4X10+7X10+1X10= SECOND- YEAR TEXT-BOOK. 165 19. 1X10+5X10+3X10= 20. 2X10+3X10+2X10= 21. 3X9+4X6+2X7= 22. 4x8+5x7+6x4= 23. 9X5+3X7+8X4= 24. 6X9+5X8+7X6= 25. 9X3+8X4+5X6= 26. 7x7+6x3+9x2= 27. 8x4+7x6+9x3= 28. 10x7+7x5+6x8= 29. 3x9+8x7+5x6= 30. 7X4+9X5+6X6= SUBTRACTION. (31) (32) (33) (34) (35) 37,625 76,385 85,727 96,386 .24,764 14,114 15,124 43,212 72,154 13,613 (36) (37) (38) (39) (40) 95,848 77,596 69,729 57,926 93,969 72,616 36,276 18,316 16,713 81,726 LESSON CXI. NOTE. Teacher may dictate these examples for slate- work. (1) (2) (3) (4) (5) 36,725 52,135 33,724 27,254 37,556 13,854 7,643 12,345 286 3,929 2,764 18,596 678 3,724 18,496 5,382 375 93 18,969 376 166 SECOND- YEAR ARITHMETIC. (6) (7) (8) (9) (10) 28,975 29,546 39,275 49,354 33,516 3,296 766 856 12,345 87 27,589 39 64 27,089 24,006 669 13,918 9 14,276 13,879 (11) (12) (13) (14) (15) 14,276 27,586 27,635 35,276 27,606 26,854 3,972 18,959 12,966 18,095 376 9,846 21,966 34,876 2,003 13,951 33,859 33,857 28,396 35,898 LESSON CXII. 1. 9X6-J-3X7+4X4=91X1. 2. 6X7+7X6+5X3= 3. 10X4+6X6+3X6= 4. 9X5+7X3+3X4= 5. 6X8+8X3+7X2= 6. 9X4+6X7+3X5= 7. 7X8+5X9+8X2= 8. 5X10+6X6+5X5= 9. 8X7+6X8+3X6= 10. 10X7+5X8+8X4= 11. 8X9+3X7+6X5= 12. 9X8+7X5+3X7= 13. 10X9+7X7+4X6= 14. 6X8+7X4+5X6= SECOND-YEAR TEXT-BOOK. 167 15. 8X7+7X6+3X8=: 16. 9X3+5X8+6X4=: 17. 3X10+9X5+3X6=: 18. 10X7+6X6+3X10= 19. 6X11+5X9+5X4= 20. 3X12+12X3+3X12= 21. 5X9+9X7+3X9= 22. 6X8+7X3+5X8= 23. 12X6+7X5+3X10= 24. 9X9+5X5+4X4= 25. 11X7+3X10+3X10= 26. 27. 28. \\xy 29. Qx 5#+4aj= 30. 31. 32. lly-9y+2y= 33. 12a? 6x 3a?= 34. 35. LESSON CXIII. 1. James has 11 cts., and George has 10 times as many cents, how many cents has George? Ans. George has 10 X 11 cts. which are 110 cts. 2. There are 12 girls in each of 9 rows, how many girls in the 9 rows ? 168 SECOND-TEAR ARITHMETIC. 3. I bought 2 quarts of peanuts at 10 cts. per quart, and 5 ounces of candy at 5 cts. per ounce, how much money did I spend ? 4. A man rode 8 miles an hour for 7 hours, how many miles did he ride ? 5. There are 11 girls in each of 12 rows, how many girls in the 12 rows? SUBTRACTION. (6) (7) (8) (9) (10) 32,751 46,789 68,950 51,964 95,876 11,321 13,327 27,840 31,723 72,341 (11) (12) (13) (14) (15) 27,586 58,667 76,392 89,699 27,676 13,316 23,542 54,181 73,248 16,354 (16) (17) (18) (19) (20) 54,849 48,379 34,567 78,901 58,946 13,726 27,164 12,345 67,801 37.005 LESSON CXIY. NOTE. Teacher may dictate to pupils at the board, or for slate work. (1) (2) (3) (4) (5) (6) 36,815 57,181 30,001 12,876 24,001 51,275 17,256 16,081 25,016 35,127 18,165 1,806 34,180 15,147 3,708 12,975 37,028 25,545 1,700 686 1,561 842 15,274 2,847 305 35 37 33,176 12,676 1,< SECOND- YEAR TEXT-BOOK. 169 (T) (8) (9). (10) (11) (12) 29 35,004 27,027 35,186 11,618 33.333 :J84 16,275 13,113 10,008 25,374. 18,105 14,256 2,876 12,002 30,030 12,156 24,267 18,524 364 10,010 25,176 13,241 1,382 32,576 85 1,515 18,255 876 12,500 13. 7X6+5X4+8X3= 14. 3X8+7X4+5X5= 15. 4X6+3X8+1X2= 16. 9X7+3X1+8X2= 17. 2X5+10X10+4X6= 18. 7X4+8X3+5X2= 19. 6X6+2X2+5X5= 20. 8X44-7X3+3X3= LESSON CXY. 1. 11X1+6X1+8X1+7X1+5X1+8X1 + 10X1+6X1= 2. 9X1+9X1+9X1+8X1+8X1 + 8X1 + 7X1+7X1= 3. 12X1+6X1+5X1+4X1+8X1+7X1 + 6X1+8X1= 4. 6xl + 7xl+8Xl+9xl-^3xl+4xl+5 X1+4X1= 5. 7xl+7xl+6xl+6xl+5Xl+5xl+4 Xl+4Xl= 6. 13xl+5xl+7xl+4xl+8>+9x 7+6x5+10x1= 32. 8X4+6X2+7X3+2X9= 33. 7X11+3X4+2X9+4X4= 34. 6X3+5X8+11X3+5X9= 35. 5X4+3X64-5X7+7X3= LESSON CXLIII. 1. 7X8+5X9+3X3= 2. 9X7+8X6+5X2= 3. 11x5+9x7+4x4= 4. 8x6+12x5+3x7= 5. 12X7+8X6+2X6= 6. 9x8+7x7+9x2= 7. 10x8+9x5+3^5= 8. 9X4+12X8+2X7= 9. 10X6+7X5+5X5= 10. 8X11+9X4+4X6= 11. 4X12+12X6+3X7= 12. 8X11+7X5+2X4= 13. 9X6+7X8+3X3= 14. 7X11+8X9+4X2= 15. 9X6+7X8+5X5= SECOND-TEAK TEXT-BOOK. 209 16. 5X8+4X9+3X7= 17. 11X12+12X4+5X2= 18. 7X3+11X11+4X3= 19. 9X6+6X5+3X7= 20. 4X8+8X7+2X6= (21) (22) (23) (24) (25) 363,517 240,351 345,162 437,216 518,464 124,121 126,148 127,143 143,182 327,110 (26) (27) (28) (29) 313,003 215,412 352,373 518,416 127,110 131,121 122,416 72,131 LESSON CXLIY. 1. 3X12+3X12+4X12: 2. 2X12+3X12+3X12: 3. 4X12+4X12+4X12: 4. 2X12+2X12+2X12: 5. 1X12+2X12+1X12: 6. 1X12+3X12+5X12: 7. 2X12+2X12+1X12: 8. 1X12+1X12+1X12: 9. 2X12+5X12+4X12: 10. 1X12+3X12+3X12: 11. 4X11+4XH+3X11: 12. 2XH+3X11+5X11: 13. 3X11+5X11+4X11: 210 SECOND-YEAR AlilTHMETIC. 14. 2X11+3X11+4X11= 15. 1X11+2X11+3X11= 16. 3X10+2X10+2X10=: IT. 2X10+3X10+5X10=: 18. 3X10+3X10+3X10=: 19. 2X10+1X10+2X10= 20. 1X10+5X10+6X10=: 21. 1X10+2X10+1X10= 22. 3X10+4X10+1X10= 23. 2X10+2X10+2X10=: 24. 1X10+1X10+1X10=. 25. 3X10+4X10+3X10=1 26. 2X10+4X10+5X10= 27. 3X10+4X10+5X10=: 28. 1X9+1X9+1X9= 29. 3X9+3X9+3X9= 30. 2X9+2X9+2X9= 31. 4X9+4X9+4X9= 32. 2X9+4X9+2X9= 33. 3X9+3X9+4X9= 34. 2X9+1X9+1X9=: 35. 1X9+2X9+2X9= 36. 3X9+2X9+2X9= 37. 4X9+5X9+2X9= 38. 4X8+3X8+^X8= 39. 4X8+4X8+3X8= 40. 2X8+5X8+3X8= SECOND-YEAR TEXT-BOOK. 211 41. 3X8+2X8+4X8= 42. 1X8+3X8+4X8= 43. 2X8+3X8+2X8= 44. 1X8+2X8+3X8= 45. 2X8+1X8+2X8= 46. 1X8+1X8+2X8= 47. 1X8+1X8+1X8= 48. 4x7+5x7+3x7= 49. 2x7+3x7+4x7= 50. 1x7+3x7+4x7= SUBTRACTION. (51) (52) (53) (54) (55) 3*67,218 738,646 416,067 276,375 570,050 149,146 133,493 133,819 118,416 133,126 (56) (57) (58) (59) (60) 676.003 116,764 439,376 356,164 518,473 128.004 31,396 183,727 163,276 125,146 LESSON CXLY. 1. 1x7+1x7+1x7= 2. 2X7+1X7+1X7= 3. 1x7+2x7+2x7= 4. 2X7+2X7+2X7= -5. 2X7+2X7+3X7= 6. 3X7+3X7+2X7= 212 SECOND-YEAR ARITHMETIC. 7. 4X7+4X7+1X7= 8. 3x7+3x7+4x7= 9. 2X7+3X7+6X7= 10. 3X7+3X7+6X7= 11. 1X6+3X6+1X6= 12. 3X6+5X6+4X6= 13. 1X6+1X6+1X6= 14. 2X6+3X6+4X6= 15. 1X6+2X6+3X6= 16. 1X6+1X6+1X6= 17. 3X6+2X6+2X6= 18. 4X6+4X6+2X6= 19. 3X6+3X6+3X6= 20. 3X6+3X6+2X6= 21. 1X5+3X5+4X5= 22. 2X5+2X5+1X5= 23. 3x5+3x5+5x5= 24. 1X5+1X5+1X5= 25. 2X5+3X5+2X5= 26. 4x5+5x5+3x5= 27. 1X5+2X5+1X5= 28. 2X5+3X5+1X5= 29. 3X5+2X5+4X5= 30. 3X5+3X5+5X5= 31. 2X5+3X5+7X5= 32. 1x4+4x4+5x4= 33. 2X4+3X4+7X4= SECOND-YEAR TEXT-BOOK. * 213 34. 1X4+3X4+5X4=: 35. 2X4+3X4+3X4= SUBTRACTION. (36) (37) (38) (39) (40) 370,064 414,814 295,004 164,376 557,467 59,184 37,326 137,106 25,138 138,149 (41) (42) (43) (44) (45) 726,676 519,460 846,827 337,386 418,418 484,359 39,184 139,134 29,147 137,137 46. 47. Qxy 5xy= 49. 50. 51. 52. 53. 54. 55. LESSON CXLYI. 1. James bought a book for 43 cts., some paper for 18 cts., and a slate for 15 cts.; how much did he pay for all 1 2. This class did 59 examples Monday and 87 SECOND-YEAK ARITHMETIC. examples Tuesday; how many examples were done during the two days ? 3. John bought 4 cts. worth of marbles at 7 for one cent, and 3 cts. worth at 5 for one cent ; how many marbles did he buy ? 4. A boy sold 16 papers Monday, 18 papers Tuesday, 14 papers Wednesday, 11 papers Thurs- day, 10 papers Friday, and 20 papers Saturday ; how many papers did he sell during the week ? (5) (6) (7) (8) ; (9) 367,518 227,386 518,466 216,326 346,367 493 159,443 37,518 95,466 25,676 23,614 276,345 376 316,376 3,918 293,724 113,726 134,415 254,246 467 1,864 234,376 217,348 123,356 35 SUBTRACTION. (10) (11) (12) (13) 376,464 254,376 514,376 370,005 186,137 35,418 133,007 110,006 (14) (15) (16) (17) 275,416 416,867 516,004 673,405 138,125 137,276 184,114 159,156 (18) (19) (20) 351,646 276,140 376,466 147,156 . 158,416 173,727 SECOND-YEAR TEXT-BOOK. 215 LESSON CXLYII. 1. 12X1 + 13X1+HX1+12X1+16X1+8 X1+12X1+16X1 2. 13X1+14X1+12X1+11X1+10X1+11 xi+nxi+ioxi= 3. 12X1+12X1+12X1+12X1+12X1+12 X 1+12X1+12X1= 4. 13X1+12X1+11X1+10X1+9X1+8X1 +7X1+6X1= 5. 11X1+13X1+15X1+17X1+19X1+21 X l+llxl+7xl= 6. 16X1+15X1+9X1+11X1+8X1+13X1 +14X1+15X1= 7. 12X1+13X1+14X1+12X1+13X1+14 X 1+12X1+13X1= 8. 11X1+10X1+12X1+11X1+8X1+HX 1+9X1+7X1= 9. 12X1+12X1+HX1+12X1+13X1+12 X l+HXl+12Xl= 10. 13X1+12X1+11X1+10X1+11X1+12 X l+13Xl+12xl= 11. 12X1+14X1+15X1+16X1+17X1+18 Xl+17xl+18xl= 12. 11X1+12X1+13X1+14X1+15X1+16 Xl+17xl+18xl= 13. 12X1+13X1+12X1+13X1+12X1+13 Xl+12xl+13Xl= 216 SECOND-YEAR ARITHMETIC. 14. 14 X 1+14X1+14X1+14-X 1+14X1+H X1+14X1+14X1= 15. 15X1+15X1+15X1+15X1+15X1+15 X1+15X 1+15X1= 16. 7X8+5X6+4X4= 17. 9X3+8X4+7X5= 18. 8X8+6X6+5X5= 19. 7X9+6X8+5X3= 20. 10X6+6X7+3X9= 21. 8X5+9X4+7X2= 22. 9X9+5X7+6X4= 23. 8X7+6X64-3X8= 24. 7X11+11X3+3X11= 25. 8X5+9X4+10X3= 26. 11 X 6+6X8+3XT= 27. 9X5+5X8+8X4= 28. 7X6+6X7+7X6= 29. 5X12+4X8+3X11= 30. 9X6+7X3+5X8= SUBTRACTION. (31) (32) (33) (34) (35) 276,643 751,643 646,346 336,185 435,270 128,153 125,716 187,173 144,217 183,16T LESSON CXLVIII. 1. 3X12+3X12+3X12= 2. 4X12+4X12+4X12= SECOND-YEAR TEXT-BOOK. 217 3. 2X12+2X12+2X12= 4. 1X12+3X12+7X12= 5. 2X12+3X12+5X12= 6. 3X12+3X12+2X12= 7. 2X12+3X12+2X12= 8. 1X12+2X12+2X12= 9. 1X12+1X12+1X12= 10. 1X12+2X12+1X12= 11. 2X11+3X11+6X11= 12. 2X11+3X11+7X11= 13. 2X11+3X11+5X11= 14. 3X10+5X10+3X10= 15. 2X10+3X10+7X10= 16. 1X10+3X10+6X10= 17. 3X9+5X9+4X9= 1.8. 2X9+3X9+5X9= 19. 3X9+3X9+5X9= 20. 2x9+3x9+4x9= 21. 3X9+3X9+2X9= 22. 2X9+1X9+4X9= 23. 3X9+1X9+2X9= 24. 1 X 9+1X9+3X9= 25. 2X9+1X9+1X9= (26) (27) (28) (29) (30) 335,146 127,217 415,014 133,216 446,738 218,375 514,637 123,716 325,791 106,187 218 SECOND- YEAR ARITHMETIC. (31) (32) (33) (34) (35) 276,376 726,938 286,676 335,725 193,761 149,728 95,146 137,158 144,873 128,376 (36) (37) (38) (39) (40) 543,210 506,709 297,386 333,333 275,186 123,456 183,185 138,487 123,043 166,276 (41) (42) (43) (44) (45) 345,678 218,617 514.376 214,006 376,413 134,546 154,396 25^413 73,864 185,575 276,375 376 115,735 128,726 36,656 145,184 1,543 94,366 35,376 7,284 376,354 245,376 3,736 218,444 966 LESSON CXLIX. 1. 12 X 1+13X1+14X1+15X1+16X1+17 X 2. 13X1+13X1+13X1+13X1+13X1+13 3. 15X1+14X1+15X1+14X1+15X1+14 Xl+15xl+14xl= 4. 16X1+HX1+15X1+13X1+12X1+12 X l+13Xl+15Xl= 5. 13X1+14X1+15X1+13X1+11X1+14 X l+15xl+13Xl= 6. 16X1+16X1+13X1+8X1+10X1+9X1 +13X1+13X1= SECOND-YEAK TEXT-BOOK. 219 * X 1+13x1+9x1= 8. 14X1+15X1+11X1+10X1+9X1+8X1 +7X1+6X1= 9. 12 X 1+13X1+MX1+13X1+10X1+13 X 1+16X1+13X1= 10. 14 X 1+1TX1+15X1+19X1+16X1+18 X1+14X1+12X1= 11. 13X1+14X1+11X1+8X1+9X1+11X1 +12X1+11X1= 12. 14X1+9X1+8X1+12X1+9X1+12X1 +9X1+12X1= 13. 13X1+12X1+WX1+13X1+12X1+14 Xl+13Xl+12Xl= Xl+14Xl+14Xl= 15. 9X1 + 10X1+11X1+12X1+13X1+14 X 1+15x1+16x1 = 16. llxl+HXl+llXl+llXl+12Xl+12 Xl+12Xl+12xl= 17. 9X1+9X1+10X1+10X1+11X1+11X1 +12X1+12X1= 18. 15 X 1+14X1+13X1+12X1+HX1+12 X 1+13X1+HX.1= 19. 16 X 1+13X1+15X1+13X1+12X1+13 Xl+12Xl+13Xl= 20. 14X1 + 13X1+12X1+11X1+9X1+H X1+9X1+12X1= 220 SECOND-YEAR ARITHMETIC. 21. 9X5+6X6+3X3= 22. 8X7+6X4+4X2= 23. 7x7+3x8+2x7= 24. 6X5+4X8+3X4= 25. 7X4+4X7+7X4= 26. 8x3+7x6+2x7= 27. 9X10+5X8+7X3= 28. 8X8+6X6+3X2= 29. 7X5+4X3+6X2= 30. 5X7+7X5+4X4= 31. 3X9+6X10+7X2= 32. 8X4+7X3+5X6= 33. 8X7+6X4+4X4= 34. 9X5+7X3+2X6= 35. 6X3+8X5+4X3= LESSON CL. 1. James is 18 years old and his sister is 5 years younger ; bow old is liis sister ? 2. Kate is 12 years old and her brother is 8 years older ; how old is her brother ? 3. George shot an arrow 12 feet and John shot an arrow 12 times as far as George did ; how far did John shoot the arrow ? 4. I bought 7 ounces of candy at 5 cts. per ounce, and 5 ounces of candy at 6 cts. per ounce ; how much did I pay for the candy ? SECOND-YEAR TEXT-BOOK. 221 5. How many days in 6 weeks ? 6. How many days in. 12 weeks ? 7. How many days in 9 weeks ? 8. How many weeks in 7 months ? 9. How many weeks in 9 months ? 10. How many months in 8 years ? 11. 9X6+3X7+5X5= 12. 4X8+8X4+4X8= 13. 7X6+5X4+9X2= 14. 6X9+3X8+7X3= . 15. 7X7+6X6+3X4= 16. 9X5+8X7+3X3= 17. 6X9+8X3+7X2= 18. 5X11+11X5+5X11=: 19. 6X4+7X3+2X6= 20. 8X5+6X7+3X8= LESSON CLI. (1) 764,346 182,719 (2) 646,309 128,107 (3) 375,184 127,616 (4) 814,617 17^,395 (5) 427,643 182,716 (6) 514,608 137,296 (?) 345,678 181,719 (8) 676,764 138,395 (9) 272,646 137,147 (10) 414,314 185,141 222 SECOND-YEAB ARITHMETIC. (11) (12) (13) (14) (15) 256,731 514,613 313,215 354,137 545,354 184,697 7,296 76,384 128,764 276,604 233,383 53,542 127,354 32,356 135,724 156,142 273,420 215,433 227,265 225,424 113,375 6,384 37,666 33,715 876,674 (16) (17) (18) (19) (20) 345,678 456,789 213,735 354,301 567,843 138,729 113,326 648 766 72 54,843 254,324 156,304 218,403 432,736 237,356 27,636 275,421 37,694 127,544 112,842 376 5,864 152,061 376,385 LESSON CLIL 1. 3X12+2X12+2X12=: 2. 4X12+3X12+1X12= 3. 2X12+1X12+1X12= 4. 1X12+1X12+1X12= 5. 1X12+2X12+2X12= 6. 3X12+4X12+2X12= 7. 2X12+1X12+3X12= 8. 3X12+3X12+4X12= 9. 2 X'12+3X 12+6X12= 10. 3X12+3X12+6X12= 11. 2X11+3X11+2X11= 12. 1X11+1X11+1X11= 13. 3X11+3X11+3X11= SECOND-YEAR TEXT-BOOK. 223 14. 2X11+3X11+5X11 = 15. 3X11+4X11+5X11= 16. 2X11+3X11+6X11= 17. 1X11+3X11+5X11= 18. 3X10+2X10+5X10= 19. 5X10+4X10+2X10= 20. 2X10+3X10+7X10= 21. 3X10+2X10+4X10= 22. 1X10+2X10+3X10= 23. 3X9+1X9+2X9= 24. 2X9+1X9+1X9= 25. 1X9+1X9+1X9= 26. 2X9+2X9+1X9= 27. 2X9+3X9+2X9= 28. 1X9+3X9+4X9= 29. 2X9+3X9+4X9= 30. 3X9+2X9+5X9= 31. 2X9+3X9+6X9= 32. 4X9+5X9+3X9= 33. 4X8+5X8+2X8= 34. 3X8+2X8+7X8= 35. 1X8+3X8+6X8= 36. 2X8+1X8+6X8= 37. 3X8+1X8+4X8= 38. 2X8+1X8+3X8= 39. 3X8+1X8+3X8= 40. 2X8+1X8+2X8= 41. 1X8+2X8+1X8= 224 SECOND-TEAR ARITHMETIC. 42. 1X8+1X8+1X8=: 43. 3X7+1X7+1X7= 44. 2x7+3x7+2x7= 45. 1x7+3x7+5x7= 46. 1x7+1x7+1x7= 47. 2x7+3x7+6x7= 48. 2X7+1X7+1X7= 49. 3X7+1X7+2X7= 50. 2x7+3x7+3x7= 5.1. 2X7+3X7+5X7= 52. 3X7+3X7+6X7= 53. 3X6+4X6+5X6= 54. 2X6+3X6+4X6= 55. 3X6+5X6+2X6= 56. 2X6+1X6+4X6= 57. 3X6+2X6+3X6= 58. 1X6+1X6+4X6= 59. 1X6+1X6+3X6= 60. 2X6+1X6+2X6= LESSON CLIII. 1. CMLXY= 11. 2,956: 2. MMCMXLYII= 12. 1,001: 3. MDCCXCYIII= 13. 3,574: 4. MMMCCCXXXIII= 14. 2,437: 5. MDCCCLXXXIY= 15. 1,010: 6. DCLXIX= 16. 3,333: 7. MDLXYI= 17. 4,268: 8. MMDCCLIY= 18. 1,616: 9. MCDLXX= 19. 2,770: 10. MMMCCCXXXITI= 20. 3,013: SECOND-YEAR TEXT-BOOK. 225 21. 6X9+5X7+3X4=: 22. 7X7+6X6+3X3= 23. 8X2+9X5+7X2=, 24. 6X8+3X7+2X5=: 25. 7X5+9X6+3X4=: 26. 8X7+6X4+4X3=: 27. 7X7+6X6+2X5=: 28. 3X8+7X*5+4X4=: 29. 9X5+5X9+3X3 30. 10x7+6x6+3 XS- SI. 5X8+7X11+6X2= 32. 8X4+4X8+2X7 33. 5X8+4X9+6X3= 34. 8X7+6X4+4X4=: 35. 9X5+8X6+3X3 36. 7X7+6X6+5X5=: 37. 8X6+6X7+4X4= 38. 9X11+11X3+2X11= 39. 3X10+6X8+7X2=: 40. 9X6+6X6+3X4=: LESSON CLIY. 1. I bought 3 packs of firecrackers at 8 cts. a pack, and 4 papers of torpedoes at 7 cts. a paper ; how much did I pay for all ? 2. How many marbles at 3 for one cent can be bought for 1 2 cents ? 226 SECOND-TEAR ARITHMETIC. 3. William lias 65 cents and Charles has 78 cents more than William ; how many cents have both boys ? 4. How many in 9 dozen ? 5. How many pecks in 7 bushels ? 6. 11 X 1+12X1+13X1+14X1+15X1+13 X1+15X1+13X1= 7. 15X1+14X1+13X1+12X1+HX1+10 X 1+9X1+SX1= 8. 21X1 + 16X1+8X1+13X1+14X1+15 Xl+llXl+12xl= 9. 13X1+13X1+14X1+14X1+15X1+15 X 1+16x1+16x1=: 10. 18Xl+15Xl+13Xl+18xl+llXl+16 xi+ioxi+nxi= 11. 12 X 1+14X1+12X1+17X1+13X1+17 12. 13X1+13X1+11X1+16X1+13X1+11 X 1+12X1+13X1= 13. 16X1+12X1+14X1+15X1+14X1+12 X 1+13X1+14X1= 14. 17 X 1+11X1+13X1+14X1+15X1+10 X1+14X1+15X1= 15. 14X1+10X1+12X1+13X1+16X1+11 X 16. 12X X 1+16X1+17X1= 8ECOND-YEAK TEXT-BOOK. 227 17. 13 X 1 +11 X 1+10 X 1+10 X 1+18 X 1+13 Xl+17xl+18xl=: 18. 18xl+16xl+9xl+18Xl+19Xl+i4: 19. 14X1 + 15X1+8X1+16X1+20X1+15 X l+HXl+15xl=: 20. 16 X 1+HX1+17X1+13X1+21X1+11 X1+12X1+16X1=: 21. 11 X 1+13X1+16X1+12X1+22X1+12 Xl+13Xl+17xl=: 22. 12x1+12x1+15x1+11X1+23x1+11 ' 23. 14 X 1+11 X 1+14 X 1+12 X 1+11 X 1+12 X 1+15x1+19x1= 24. 18X1+10X1+13X1+HX1+11X1+13 X 1+16X1+HX1= 25. 13xl+15xl+12xl+14Xl+llXl+12 Xl+lYX 1+13x1= LESSON CLY. (1) (2) (3) (4) (5) 326,731 456,789 200,257 116,876 356,160 184,167 376,198 146,137 114,917 184,437 (6) (7) (8) (9) (10) 437,126 566,676 514,376 320,006 250,676 187,299 187,696 182,767 166,861 184,395 228 fcECOND-YEAR ARITHMETIC. (11) 225,646 183,729 (12) 304,403 130,304 (13) 275,186 183,945 (14) '430,764 184,277 (15) 567,309 183,729 (16) 100,100 90,146 (17) 256,555 127,676 (18) 333,333 276,138 (19) 222,264 184,137 (20) 555,434 127,296 21. 9X6+8X7= 26. 9x6+10x7= 22. 8X9+7X6= 27. 11x8+8x11= 23. 9X5+8X8= 28. 12x6+7x10= 24. 7x6+10x8= 29. 12X6+11X5= 25. 11X5+8X4= 30. 9x9+7x7= LESSON CLYI. (1) (2) (3) (4) (5) 376,685 140,914 214,843 333,333 123,543 194,728 176,387 37,676 638 376,209 336 215,064 2,984 275,140 108,733 1,276 113,817 196 2,582 266,364 225,843 346,309 76 123,456 335,821 11. 7X6+6X5+3X4= 12. 8X6+6X7+5X3= 13. 7X9+8X4+3X2= 14. 6x6+8XlO+2x-5= 15. 9X7+6X6+6X3= 16. 8X10+7X6+6X2= 17. 7x11+11X5+4x4= SECOND-YEAR TEXT-BOOK. 18. 3X9+8X12+4X2= 19. 7X6+6X7+3X5=: 20. 3X11+12X9+2X10= 21. 9X6+6X5+8X4= 22. 8X7+10X4+6X3= 23. 9 x;5+!OX 11+3x3= 24. 7X6+9X12+4X2= 25. 8X11+11X5+7X3= LESSON CLYII. 1. 3X12+4X12+5X12= 2. 2X12+4X12+5X12= 3. 3X12+3X12+4X12= 4. 2X12+3X12+4X12= 5. 1X12+2X12+5X12= 6. 2X12+3X12+2X12= 7. 2X12+1X12+3X12= 8. 2X12+1X12+2X12= 9. 1X12+2X12+1X12= 10. 1X12+1X12+1X12= 11. 2X11+3X11+7X11= 12. 3X11+1X11+7X11= 13. 2X11+2X11+6X11= 14. 1X11+2X11+6X11= 15. 3X11+1X11+4X11= 16. 2X11+2X11+3X11= 17. 1X11+2X11+3X11= 18. 2X11+1X11+2X11= 230 SECOND-YEAR ARITHMETIC. 19. 1X11+1X11+2X11= 20. 1X11+1X11+1X11= 21. 3X10+1X10+8X10= 22. 2X10+1X10+6X10= 23. 2X10+3X10+7X10= 24. lx 10+4x10+5x10= 25. 2X10+2X10+7X10= 26. 2X10+3X10+3X10= 27. 2X10+3X10+2X10= 28. 1X10+2X10+1X10= 29. 2X10+3X10+1X10= 30. 1X10+2X10+2X10= - 31. 3X9-L2X9+7X9= 32. 2X9+4X9+5X9= 33. 3X9+3X9+3X9= 34. 2X9+3X9+4X9= 35. 3X9+1X9+4X9= 36. 1X9+3X9+3X9= 37. 2X9+2X9+2X9= 38. 1X9+2X9+2X9= . 39. 1X9+2X9+1X9= 40. 1X9+1X9+1X9= 41. 3X8+4X8+5X8= 42. 2X8+1X8+8X8= 43. 2X8+2X8+6X8= 44. 2X8+3X8+4X8= 45. 1X8+2X8+5X8= 46. 2X8+1X8+4X8= SECOND-YEAR TEXT-BOOK. 231 47. 1X8+2X8+3X8= 48. 2X8+2X8+1X8=: 49. 1X8+1X8+1X8= 50. 2X8+1X8+1X8= 51. 3X7+1X7+8X7= 52. 1x7+1x7+9x7= 53. 2X7+6X7+2X7= 54. 1x7+3x7+5x7= 55. 2x7+5x7+1x7= 56. 1X7+5X 7+1x7= 57. 2x7+2x7+2x7= 58. 1x7+3x7+1x7= 59. 2X7+4X7+2X7= 60. 1X7+1X7+2X7= LESSON CLYJII, 1. James ate 6 apples on Monday, 4 apples Tuesday, 3 apples Wednesday, 5 apples Thurs- day, 6 apples Friday, 4 apples Saturday, and 9 apples Sunday; how many apples did he eat during the week ? 2. There are 9 boys in each of 8 rows ; how many boys in the 8 rows ? 3. I bought 9 cents' worth of marbles at 5 for one cent ; how many marbles did I buy ? 4. Lucy bought a book for 65 cts., a slate for 15 cts., and an eraser for 9 cts.; how much money did she spend ? 232 SECOND-YEAK ARITHMETIC. 5. How much change should she receive from one dollar ? 6. 8X7+6X10+9X2= 7. TX+8X4+6X3= 8. 9X4+7 X 6+3x5= 9. 8X9+5X7+6X2= 10. 7X11+6X5+2X5= 11. 8X7+7X6+3X4= 12. 9X4+3X11+2X7= 13.'6X6+5X5+3X3= 14. 7X11+6X3+4X4= 15. 9X5+8X7+5X2= 16. 7X6+6X7+3X4= 17. 3X9+12X5+4X2= 18. 9X5+8X4+3X7= 19. 6X6+5X8+4X2= 20. 7X6+6X3+5X2= 21. 9X7+8X4+3X3= 22. 5X7+6X9+5X10= 23. 8X4+4X3+3X4= 24. 7X2+9X5+2X3= 25. 9X7+6X6+3X4= 26. 8x7+5x10+5x3= 27. 7X7+8X8+6X3= 28. 8X10+7X5+4X3= 29. 7X6+12X7+2X3= 30. 9X5+8X8+3X3= SECOND-YEAR TEXT-BOOK. LESSON CLTX. 233 (1) (2) (3) (4) (5) 327,666 504,700 276,675 416,256 314,273 183,729 133,116 184,317 181,176 124,281 (6) CO (8) C>) (10) 600,600 128,735 273,005 345,627 724,133 131,124 6,148 1,164 181,183 183,273 (11) (12) (13) (14) (15) 326,483 146,182 246,802 114,276 235,549 141,273 127,293 135,791 152,726 183,243 27,155 315,106 248,109 133,346 127,169 213,273 124,413 113,213 213,416 345,813 333 133,724 213,746 113,186 224,349 16. 48X1+56X1= 17. 35X1+81X1= 18. 77X1+64X1= 19. 55x1+70x1= 20. 42X1+72X1= 21. 48X1+99X1= 22. 35X1+76X1= 23. 96X1+32X1= 24. 72x1+88x1: 25. 35X1+72X1: 26. 50X1+56X1: 27. 56X1+49X1: 28. 81X1+T2X1: 29. 66X1+99X1: 30. 80X1+54X1= LESSON CLX. 1. 13X1+13X1+14X1+14X1+10X1+13 X1+15X1+16X1= 234 SECOND-YEAR ARITHMETIC. 2. 12 X 1 +14 X 1+ 16 X*+18X 1+20X1+22 xi+nxi+ioxi= 3. 13X1+11X1+14X1+11X1+15X1+H X 1+16X1+HX1= 4. 12X1+12X1+12X1+12X1+12X1+12 X1+12X1+12X1= 5. 14X1+14X1+14X1+14X1+14X1+14 X l+14xl+14Xl= 6. 15xl+15xl+15xl+15Xl+15xl+15 X 1+15x1+15x1= 7. 16X1+16X1+16X1+16X1+16X1+16 X 1+16x1+16x1= 8. 6X1+7X1+8X1+9X1+10X1+11X1+ 12X1+13X1= 9. 8X1+9X1+10X1+11X1+12X1+13X1 +14X1+15X1= 10. 11X1+15X1+16X1+HX1+18X1+12 Xl+llXl+12Xl= 11. 13X1+15X1+16X1+HX1+16X1+12 X1+15X1+14X1= 12. 14X1+13X1+15X1+16X1+14X1+13 Xl+15xl+16xl= 13. 12 X 1+12X1+14X1+UX1+16X1+16 Xl+18Xl+18xl= 14. 11*1+10x1+9x1+8x1+11X1+10x1 +9X1+8X1= 15. 15 X 1+11X1+15X1+12X1+15X1+13 X1+14X1+15X1= SECOND-YEAR TEXT-BOOK. 235 16. 13X1+HX1+11X1+13X1+13X1+11 X 1+11X1+11X1=: 17. 15X1+14X1+13X1+12X1+HX1+15 X 1+14X1+UX1= 18. 9X1+8X1+7X1+9X1+8X1+7X1+9 19. 8 X 1+11X1+9X1+10X1+7X1+12X1 +8X1+11X1= 20. 13 X 1+15X1+17X1+19X1+13X1+17 X 1+19X1+15X1= 31. 16 X 1+15X1+14X1+13X1+13X1+15 Xl+17xl+16Xl= 22. 21 X 1+20X1+19X1+18X1+17X1+16 X 1+15X1+14X1= 23. 17 X 1+17X1+17X1+17X1+17X1+17 Xl+17xl+17xl= 24. 9 X 1 + 9 X 1+9X1+9X1+9X1+9X1+ 9X1+9X1= 25. 8 X 1+9X1+8X1+9X1+8X1+9X1+8 X 1+9X1= 26. 14X1+15X1+HX1+12X1+13X1+16 Xl+13Xl+12Xl= 27. 7X1+8X1+9X1+9X1+9X1+8X1+8 X 1+8X1= 28. 16X1+13X1+9X1+8X1+15X1+HX1 +9X1+9X1= 29. 12X1+13X1+14X1+15X1+16X1+17 Xl+18Xl+19Xl= SECOND-YEAR ARITHMETIC. 30? 15X1+16X1+16X1+16X1+16X1+16 X1+16X1+16X1= NOTE. If the class can do more work during the year, give examples in algebra after the form contained in pre. vious lessons. -THE SCHOOL BULLETIN PUBLICATIONS.- Helps in Teaching Arithmetic, 1. First Steps Among Figures. A drill book in the Fundamental Rules of Arithmetic. By LEVI N. BEEBE. Cloth, 16mo, 3 editions. Pupils' Edition. pp. 140, 45 cts. Oral Edition, pp. 139, 50 cts. Teachers' Edition, including all in both the others, with additional parallel matter, Index, and Key, pp. 326, $1.00. 2. The Pestalozzian Series of Arithmetics. Teacher's Manual and First- Year Text-Book for pupils in the first grade. Based upon Pestalozzi's method of teaching Elementary Number. By JAMES H. HOOSE. Boards, 16mo, 2 editions. Pupils' Edition., pp. 156, 35 cts. Teacher's Edition, con- taining the former, with additional matter, pp. 217, 50 cts. J 3. The Word Method in Number. A series of 45 Cards, on which are printed all the possible Combinations of Two Figures. lu box. By H. R. SANFORD. Size 3*4x6 inches. Price 50 cts. It. A Work in Number for Junior Classes- in Graded Schools. By MARTHA ROE. Cloth, 16mo, pp. 116. Price 50 c*- 5. Intermediate Problems in Arithmetic for Junior Classes; containing more than 2,000 problems in Fractions, Reduction, and Decimals. By EMMA A. WELCH. Cloth, 16mo, pp. 96. Price 50 cts. 6. The Regents' Questions in Arithmetic, being the 1293 questions given rit the first 50 examinations held by the Regents of the University of the State of New York. Manilla, 16mo, pp. 93. 25 cts. Key, 25 cts. The same on Card-Board Slips, in Box., with Key, $1.00. 7. Dime Question Book, No. IS, Arithmetic. By ALBERT P. SOUTHWICK, Paper, 16mo, pp. 39. Price 10 cts. 8. A Manual of Suggestions for Teaching Fractions, especially designed to accompany a Fractional Apparatus for developing the Idea of Fractions. ByW. W.DAVIS. Paper, 16mo, pp. 43. Price 25 cts. Price of the Appa- ratus, net, $4.00. 9. 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Age- Cards, containing 9 columns of figures, to determine a person's age by adding the top numbers of those columns in which the number repre- senting the person's age is found. Heavy card-board, 4x6. Price 10 cts. 15. Cube*Boot Blocks, carried to 3 places. Size 3 inches, in box. $1.00. 16. Numeral Frames, with 100 Colored Balls, $1.25; with 150 Colored Balls, $1.50. 17. Algebra for Beginners. By O. S. MICHAEL. Cloth, 16mo, pp. 220. Price 75 cts. C. W. BARDEEN, Publisher, Syracuse, N. Y. - THE SCHOOL BULLETIN PUBLICATIONS. - Specialties in Arithmetic, I. Intermediate Problem* in Arithmetic for Junior Classes," containing more than 4000 problems in Fractions, Reduction, and Decimals. By EMMA A. WELCH. Cloth, 16mo, pp. 172. Price 75 cts. Key to Part II, pp. 30, 50 cts. In Syracuse and many other large schools, this takes the place of the small arithmetics in common use, forming with any larger or " practical " arithmetic a complete two-book series. The results obtained are in every instance far above those reached by the ordinary text-book. For city and graded schools no other collection of problems will compare with these in practical value and satisfactory results. S. A Work in Number for Junior Classes in Graded Schools. By MARTHA EOE. Cloth, 16mo, pp. 116. Price 50 cts. This is similar to the above, and was prepared expressly for the Cort- land State Normal School. S. The SO Possible Problems in Percentage, embracing a full and exhaust- ive discussion of the Theory of General Percentage, with 100 illustrative ex- amples. By W. H. BRADFORD. Manilla, 16mo, pp. 34. Price 25 cts. A. Latitude and Longitude, and Longitude and Time. Embracing a com- prehensive discussion, with over 100 illustrative questions and examples. By J. A. BASSETT. Manilla, 16mo, pp. 42. Price 25 cts. 5. Metric Tables and Problems: a comprehensive drill in the Metric System, with 175 Problems and Answers. By OSCAR GRANGER. Manilla, 16 mo, pp. 23. 25 cts. 6. 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Between the cups and the wire standards are grooves for holding arithmetical words and signs. It has a removable top ruled in inch squares, which serves as a conven- ient substitute for the ordinary ruled table, made for the use of blocks, splints, letters and words, in word and sentence building. Under the cover are five square spaces, employing five children at once. Each space contains five square and twenty cup-like receptacles for the articles found in the drawer, besides an oblong curved hollow for wire rods. Between the cups across the table from right to left are grooves for receiving printed cards bearing arithmetical words and signs, and between the grooves running from front to back are holes in which wires for hold- ing objects may stand. The drawer of the stand is divided into compart- ments, well filled with marbles, buttons, small spools, printed cards, small slates, and other apparatus for work. 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THE SCHOOL BULLETIN PUBLICATIONS.- Useful Appliances in Arithmetic. 1. The Word Method in Number. A series of 45 Cards, on which are printed all the possible Combinations of Two Figures. In box. By H. K. SANFORD, Institute Conductor. Size 3J4 x 6 inches. Price 50 cts. These cards need only to be seen, as the principle is familiar and ac- cepted. The type, in written figures, is large enough to be seen across the* room, and the combination on one side is given in reversed order on the- other, so that as the teacher holds the card before him he knows the figures presented to the class. The pupil is taught to look upon the combination. 4 + 9 as Itself 13, not as "4 and 9 are 13," just as he looks upon DOG as an entire word, not as D-O-G. Success is certain if new combinations are in- troduced only after those already given are thoroughly learned. Reviews should be constant. 2. A Fractional Apparatus. By W. W. DAVIS. A box of eight wooden balls, three and one-half inches in diameter, seven of which are sawn into 2, 3, 4, 6, 8, 9, and 12 parts respectively, while the eighth is left a sphere* Price $4.00. With this apparatus every principle and rule can be developed, and the pupils can be led to deduce rules for themselves. Many other expedients are resorted to, but they are all objectionable. Suppose a teacher takes a stick and breaks it in the middle, will the pupii perceive two halves of a stick or two sticks? In teaching fractions object- ively, that should be taken for unity from which if a part is taken unity i* destroyed. This is not the case with a stick or cube. Apples are objection- able for three reasons ; first because they cannot always be obtained ; sec- ond because they are perishable; and third,. because the attention of the pupils is diverted by a desire to know whether they are sweet or sour, etc. Nor can the teacher readily saw wooden balls into divisions even enough for the purpose designed, the charm of this method being the exact presentation to the pupil's eye of the fact illustrated. S. A Manual of Suggestions for Teaching fractions especially designed for accompanying the above apparatus. By W. W. DAVIS. Paper, 12mo, pp.43. 25 cts.- This accompanying manual gives probably the best arrangement of the subject into sixty lessons ever made, with practical suggestions which all teachers will find valuable. A. Cube Root Slocks, carried to Three Places. In box. $1.00. Our blocks are unusually large, the inner cube being two inches, and the additions each one-half inch wide. 5. 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The Word Method in Number, These cards need only to be- at once, as the principle is already fit- numbers are all printed in type like pnrtance of using script figures for this mated. ' ^^ The same figures are reversed if? upon the opposite J so that as the teacher lifts the ^J card he knows the , ures on the other side. As soon as the pupils com- j^r m e n c e reading, lessons in number, and the or first lesson si ionic! order to be \ntro-AF milkii 1 that liere shown, o T se cannot be side of the card sum of Equal gle figures. In this so much gf practice should pil when adding will learn ^^to look upon the " 13," not as " 4 and 9 are ^13," just as we learn to look up- on cat as an entire word v . t as c-a-t^ cat.*- ^qu;n subtraction, until combinations of two fig- nations of letters in words. At first add familiar objects, passing bers; write the simplest combinations on the cards, and write the answer in the times that the method of writing num- addition may be learned. Then use cards for drill, adding new cards from time to time, as new combina- veloped. Do not introduce new At every exercise, review all answers should be given imme- cards. Use the cards selected laneously, so that no answer ing. Pursue the same plan In subtraction when the readily add ten to the min- the usual manner. ^ Success will be cer- Betam if new combina- duced only after those al- H ready presented learned. Reviews should vk be constant. From scores of testi- we select the following: , they shoul be in combin be given that the pu- r combination \ ;.s itself _ readiness should fo: low in ures are as familiar as combl- afterward.-- to abstract num- the blackboard, as they are on proper place. Repeat this a few bers for tions are de- cards too rapid/,;/. cards previously lately on present- ^f ing the foraparticularexercise^^ miscel- can be guessed from the ^^^pr in subtraction and mulipli- smaller number is above,^^^pup uend, and give the re- ^flV mainder in r iions are int.ro- are thoroughly monials' received " Will you send me one-half dozen cases of Cards? I have many ^ inquiries for them, have been lavish in their praise of our work these sets are given away to try the card teen packages of the cards I have order- our class drills more, send Prof. San him more than he advertises." S. Q. Fulton, N. Y.. May 2, 1889, " During Normal we used Sanford's Number primary and intermediate depart- lent for quick work. Please send me three sets for our primary and prep-irv has once used them cannot Ph.D., headmaster Rutgers have frequently advised because I know from my Sanford's Number Some of our visitors with the cards. Two of work. This makes four- ed. After a few days, when ford down and we will show Clapp, principal Union School, several yeai's at the Potsdam Cards with great success in our ments. We found them excel- -epartments here. A teacher who afford to be without them. ".//. Cook, College grammar school, Jan. 31, 1890. "I , teachers to buy Sanford's Number Cards, _ own experience that they are very valuable in" aidfng'the teacher to'fix in the pupils' memory the results of the element- ary processes with numbers. ">Fw. J. Milne, LL.D., Ph.D., president New York State Teachers' College, Feb. 5, 1890. Sent post-paid in neat box, with directions, for 50 cts. C. W. BARDEEN, Publisher, Syracuse, N. Y.