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The chapter of Miscellaneous Examples will afford a valuable and thorough drill to the advanced student of arithmetic or algebra. They contain a great variety of principles, and while they may be considered difficult, yet the full analysis given of every principle, and the selection of numbers so adapted to the conditions of the question as to produce results free from large and difficult fractions, will render a mental solution of them comparatively, easy.

In conclusion, it gives me pleasure to state, that this work has been mostly prepared by Mr. D. W. FISH, of Rochester, N. Y, whose long experience as a teacher, as well as his extensive and intimate acquaintance with the teachers and schools of the country, has eminently qualified him to prepare such a work; and it is hoped that in it the teacher will find a desideratum long sought in this department of science, affording the means of mental discipline and development furnished by no similar treatise.

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SUGGESTIONS TO TEACHERS. Pupils of nearly the same degree of advancement should be classed together. Regular exercises should be assigned to the class, and sufficient time allowed them to thoroughly examine their lesson before being called upon to recite.

The use of the book at the time of recitation should be strictly prohibited, except, perhaps, in some of the more difficult lessons in the latter part of the work.

Each example should be read but once, slowly and distinctly, the pupils called upon promiscuously, who should arise, stand erect, repeat the example, and then give the analysis. This will ecure close attention.

Every question should be clearly and thoroughly analyzed, and the pupil required to adhere strictly to the forms of solution given, unless better ones can be substituted; and in no case should he be allowed to omit the conclusion, commencing with “ Therefore."

The class should be encouraged to detect and correct errors in statement or analysis, to criticise and make proper inquiries, all of which should be signaled by the uplifted hand.

It is suggested that the class be occasionally exercised upon “Ringing the Changes," as explained in the Appendix, and which may be applied to a great number and variety of examples. It will not only afford a valuable drill, but a pleasant and enlivening exercise.

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INTELLECTUAL ARITHMETIC,

CHAPTER I.

ADDITION.

how many

1. 1. JAMES had 1 cent, and his father gave him 1 more ;

had he then ? 2. If a slate pencil cost 2 cents, and a steel pen 1 cent, how many cents will both cost ?

3. George spent 2 cents for candy, and had 2 cents left; how many cents had he at first ?

4. A farmer sold a calf for 3 dollars, and a pig; for 2 dollars; how many dollars did he receive foi: both ?

5. Mary gave 2 cents for some tape, and 5 cents for a thimble; how many cents did she give for both ?

6. Martin gave John 3 apples, and kept 4 for himself; how many apples had he at first ?

7. There are 4 books on one desk, and 2 books on another; how many books on both desks?

8. If a lemon cost 3 cents, and an orange 5 cents, how many cents do both cost ?

9. In à certain class there are 5 girls and 4 boys; how many pupils in the class ?

10. Samuel had 3 marbles, and his brother gave him 3 more; how many did he then have ?

11. Bought a barrel of apples for 2 dollars, and a cord of wood for 4 dollars; how many dollars did both cost?

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? 2 : 1. and 2 are how many

? 3. - 2 and 2 are how many

? 4..2 2. a'id 3 are how many

? 5. 2 and 4 are how many ? 6. 2 and 5 are how many

? 7. 2 and 6 are how many

? 8. 2 and 7 are how many

? 2 and 8 are how many

? 10. 2 and 9 are how many

? 11. 3 and 3 are how many

? 12. 3 and 4

are how many

? 13. 3 and 5 are how many

? 14. 3 and 6

are how many

? 15..3 and 7 are how many

? 16. 3 and 8 are how many

? 17. 3 and 9 are how many ? 18. 3 and 10 are how many ? 19. 4 and 2 are how many

? 20. 4 and 3

are how many

? 21. 4 and 4 are how many ? 22. 4 and 5 are how many ? 23. 4 and 6

are how many

? 24. 4 and 7 are how many

? 25. and 8 are low many ? 26. 4 and 9 are how many

? 27. 4 and 10

are how many

? 28. 5 and 1 are how many

? 29. 5 and 2 are how many

? 30. 5 and 3

are how many

? 31. 5 and 4 are how many ? 32. 5 and 5 are how many

? 33. 5 and 6

are how many

? 34. 5 and 7 are how many

? 35. 5 and 8 are how many

? 36. 5 and 9 are how many ?

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3. 1. A man bought a calf for 7 dollars, and sold it for 3. dollars more than he gave for it; how much did he sell it for ?

2. Bought a barrel of cider for 2 dollars, and 20 bushels of apples for 8 dollars ; how many dollars did the whole cost?

3. If a coat cost 10 dollars, and a pair of pantaloons 5 dollars, what will be the cost of both ?

4. A merchant bought 4 boxes of black tea, and 7 boxes of green tea ; how many boxes did he buy of both kinds ?

5. A farmer sold 5 sheep to one man, and 9 to another ; how many did he sell to both ?

6. Ralph walked 4 miles and rode 10 miles; how many miles did he go?

7. Philip answered 8 questions in geography, and Oliver 5; how many questions did both answer ?

8. If a quart of chestnuts cost 10 cents, and a quart of walnuts 4 cents, what will be the cost of one quart of each ? 9. 6 and 3 are how many

? 10. 6 and 4 are how many ? 11. 6 and 5 are how many ? 12. 6 and 6 are how many ? 13. 6 and 7 are how many ? 14. 6 and 8 are how many ? 15. 6 and 9 are how many ? 16. 6 and 10

many

? 17.7 and 4 are how many

? 18. 7 and 5

are how many ? 19. 7 and 6 are how many

? 20. 7 and 7 are how many

? 21. 7 and 8

are how many

? 22. 7 and 9

are how many

? 23. 7 and 10 are how many ? 24. 8 and 3 are how many ?

are how

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25. 8 and 4 26. 8 and 5 27. 8 and 6 28. 8 and 7 29. 8 and 8 30. 8 and 9 31. 8 and 10 32. 9 and 4 33. 9 and 5 34. 9 and 6 35. 9 and 7 36. 9 and 8 37. 9 and 9 38. 9 and 10 39. 10 and 4 40. 10 and 5 41. 10 and 6

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4. 1. Eli paid 9 shillings for a pair of skates, and 6 shillings for a cap; how many shillings did he

pay for both ?

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ANALYSIS. He paid the sum of 9 shillings and 6 shillings, which is 15 shillings. Therefore, since Eli paid 9 shillings for a pair of skates, and 6 shillings for a cap, he paid 15 shillings for both.

2. A farmer sold some oats for 7 dollars, and a ton of hay for 9 dollars; how many dollars did he receive for both ?

3. Paid 8 cents for some raisins, and 6 cents for
some cloves; how many cents did both cost?

4. Nancy is 10 years old; how old will she be
5
years

from this time ?
5. A lady paid 7 dollars for a shawl, and 6 dol-
lars for a dress; what was the cost of both ?

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