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INTRODUCTION.

That frequent exercise in mental computations have a happy influence upon the mind, by inducing habits of attention, by strengthening the inemory, and by producing a promptness of recollection, is, at present, universally admitted. And, that exercises of this nature should be more extensively introduced into our primary schools, is acknowledged and even urged by many of our most experienced and successful instructers. The success, which has, in most cases, attended the introduction of Mental Arithmetick, would doubtless appear incredible to those unaccustomed to it. But experience has shown, that children may, in this way, be made acquainted with the first principles of Arithmetick, at as early an age as they can be taught the Alphabet and its most simple combinations. Classes of children under nine years of age, by the force of memory and the aid of a few plain rules, without the assistance of pen or pencil, have been taught to multiply seven or eight figures by an equal number, enumerate and announce accurately the product, amounting to quintillions; and then extract the square root of this large product, and state the root. and remainder, without varying a figore from the truth.

In the ordinary course of instruction, Arithmetick has been studied only by the boys ; and it has usually been deferred by them to the last portion of their attendance at school. The consequence has been, that few have become familiar with its first principles, before they have been obliged to quit school, and enter upon the business of life. Commencing the study of Arithmetick at this advanced period, the scholar is sensible he has but little time to devote to it, but, being determined to cipher through his book, he applies himself with diligence, yet he hurries on from rule to rule with such rapidity, that he learns nothing as he ought. He may indeed reach the end, and thus accomplish his principal purpose; but, of what he has gone over, scarcely a trace remains upon his mind. He has not even made himself thoroughly acquainted with any of the elements of the science ; por has he made himself so familiar with the rules, as to derive from them any considerable practical advantage. It is asserted with confidence, that children, after having learned to talk, cannot too soon be made acquainted with numbers, and exercised in mental computations. But care should be taken, that these exercises be adapted to the age and capacity of the child - that the questions proposed, be such as the child can fully comprehend. And as very young children are scarcely capable of the exercise of abstraction, the instructer will derive much advantage from the employment of sensible objects. The child will find no difficulty in conceiving sensible objects, that are before Lim, to represent such as are absent, even at an age when they could form no conception of abstract numbers. After making the child acquainted with the nature of the several operations by means of these objects, he should be directed to perform the same by the force of memory, and he will, in this way, soon become familiar with fundamental principles of Arithmetic, and his judgment, as it becomes matured by age, will direct him in the application of these principles to practical purposes. ' He will at the same time be acquiring habits of attention, and a promptness of computation, which will be of inestimable value to him in after life. All this may be done as an amusement, and a relaxation

to the young mind, without interrupting, in the least, its other pursuits ; and thus may every boy and girl, of ordinary capacity, be made more thoroughly acquainted with the elements of Arithmetick, before they arrive at the age of ten years, than most of our scholars are on leaving school, after having plodded through the whole Arithnetick in the ordinary way. A knowledge of Arithmetick, at the present day, is scarcely less necessary to the female sex than to our own, and if the course be adopted, which is here recommended, it is believed, they will not be found less capable of proficiency in this science It is hoped that our teachers, both male and female, will take this subject into consideration, and use their exertions to bring about a reformation sọ desirable in the course of arithmetical in, struction.

ADDITION. 1. I have two cents in one hand, how much do I give for the cow and and one in the other; how many have sheep? I in both ?

18. Eight and four are how many ? 2. How many fingers have you on

19. Nine and five are how many one hand? 3. How many on both ?

20. Seven and seven are how many? 4. If you count your thumbs with 21. Seven & eight are how many? your fingers; how many will it make? 22. Nine & eight are how many

? 5. George has three apples in one

23. Nine & ten are how many ? pocket and two in the other; how

24. Nine & nine are how many

? many has be in both ?

25. Eleven & nine are how many ? 6. How many are three and two ?

26. Twelve & pine are how many ? 7. Henry has four cents and Geo. 27. A boy gave to another boy six two; how many have both ?

peaches, to another four, and had 8. David gave three cents for a three left; how many bad he at first? lemon and five for an orange ; how 28. A boy bought a slate for 22cts. many did he give for both ?

a pencil for three, and a sponge for 9. Three and five are how many ? six; how much did they all cost?

10. Peter had six cherries, and 29. A man gave seven dollars for Dick gave him four more; how many a sleigh, gave'six dollars for ironing had he then ?

it, and four dollars for painting it; 11, John had seven nuts and Peter what did the whole cost ? gave him two more ; how many had 30. A drover bought twenty-three he then ?

sheep of one man, seven of another, 12. A man bought a barrel of flour and five of another; how

many

did for seven dollars, and a barrel of soap he buy of the three? for four dollars ; how much did they 31. A lady bought some pins for both cost?

eleven cents, a comb for twenty-five, 13. A man has six cows at one and some tape for eight cents; what barn, and eight at another; how ma did they all cost ? ny has he at both ?

32. Nine and eight and six are hop 14. Eight and six are how many? j many?

15. A person bought a hundred 33. Five and three and eleven are weight of sugar for ten dollars, and

how many ? a barrel of flour for seven dollars ; 34. Seven and four and twelve are how much did he give for both ?

how many? 16. A man travelled four miles the 35. Thirty-five and six and four Ürst hour, three the next, and two are how many ? the next; how far did he travel in 36. Forty-seven and three and the three hours ?

seven are bow many ? 17. If I give pine dollars for three 37. A man bought a cow for sevsheep, and ten dollars for a cow, enteen dollars, a hog for five dollars,

and three sheep for six dollars; what | half; how much did he give for the did they all cost ?

three? 38. From Burlington to Montpe 40. How many are nineteen, and lier it is thirty-eight miles, and from nine, and twenty-nine ? Montpelier to Woodstock it is forty 41. A boy paid ten cents for a. seven miles; how far is it from Bur. card of gingerbread, six cents for a lington to Woodstock ?

pint of plumbs, lost twenty-eight 39. A man bought a horse for cents at play, and had eleven cents, forty eight dollars, a yoke of steers left; how many had he at first? for twenty-three dollars and a half, 42. How many are seventeen and and a cow for fourteen dollars and a

seven and seventy-six ?

SUBTRACTION. 1. David had six plums, and gave

17. Twenty-seven less eleyen are two of them to George; how many

how many ? had he left ?

18. A man owed seventy-five dol. 2. A boy had eight cents and lost lars, of which he paid at one time three of them; how many had he left? | fifteen, and at another twenty five

3. A man bought a barrel of flour dollars; how much remains to be for eight dollars, and sold it again paid? for twelve dollars; how much did he 19. Twenty-five less eight and six. gain by the trade?

are how many ? 4. A person bought nineteen lbs. 20. A person bought a horse for of rice, and having lost a part of it, sixty dollars, a saddle for twenty found he had nine pounds left; how dollars, and a bridle for two dollars. much did he lose ?

and a half, and sold them all toge5. A boy having twenty cents, ther for eighty-six dollars; did he. bought one quart of plums for six gain or lose? and how much? cents, and a pound of figs for ten 21. Twenty-one and eight and seve cents; bow many cents had he left ? en less seventeen are how many ?

6. A man bought a cow for sixteen 22. Thirty and forty less twenty dollars, and sold it again for twelve and twenty-five are how many? dollars ; how much did he lose? 23. A lady bought two yards of

7. Seven less three are how many ? calico for sixty-two cents, a yard of 8. Eight less three are how many? ribbon for twenty-one cents, and 9. Eleven less four are how many? | two skeios of silk for eight cents,

10. Twenty-one less four are how and gave a dollar bili; how much many ?

should she receive back? 11. Thirty less six are how many ?

24. A barrel containing thirty12. Six and ten less four are how two gallons of cider, sprung a leak, many ?

and nine gallons run out; how much, 13 Nine and fifteen less eight are

was there left ?

25. A man sold a drover seren 14. A lady bought a comb for thir-¡ sheep for twelve dollars, a yoke of ty-three cents, some tape for eight oxen for sixty-eight dollars, two cents, and some peedles for six cts. cows for twenty-six dollars, and re.. She gave fifty cents ; how much ceived in payment one hundred dol. change must she receive ?

lars; how much remains his due ? 15 Peter had twelve cents, and 26. If I buy a horse for seventyJohn gave him ten more, with which dollars, and a saddle for nineteen he bought eleven cents worth of dollars, and sell them both for ninecake; how many cents had he left? ty-five dollars, do I lose or gain, and

16 Twenty-one less nine are how how much? mapy?

how many ?

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MULTIPLICATION. 1. What cost two apples at one hour, how far will he travel in six *cent a piece ?

hours ? 2. What cost two lemons at two 8. What will eight yards of cloth cents a piece ?

cost at four dollars a yard? 3. What cost four yards of tape 9. What will six pounds of raisins at two cents a yard?

cost at pine cents a pound? 4. What cost three barrels of ci 10. What will seven yards of shirtder at three dollars a barrel ? ing cost at three shillings a yard ?

5. At four cents a piece what will 11. What will sixteen yards of three oranges cost?

shirting cost at ten cents a yard? 6. At four cents a yard what will 12. If four bushels of wheat make four yards of ribbon cost?

a barrel of four; how many bushels 7. If a man travel three miles an will it take to make eight barrels ?

Multiplication 'Table.

How many are Two times two ?

Four times five ?

Six times twelve ? Two times three ?

Four times six ?

Seven times seven? Two times four?

Four times seyen ? Seven times eight? Two times five ?

Four times eight? Seven times nine ? Two times six ?

Four times nine ?

Seven times ten ? Two times seven ?

Four times ten ?

Seven times eleven ? Two times eight?

Four times eleven ? Seven times twelve ? Two times nine ?

Four times twelve ? Eight times eight? Two times ten ?

Five times five ? Eight times nine ? Two times eleven?

Five times six ? Eight times ten? Two times twelve ? Five times seven? Eight times eleven? Three times three ? Five times eight ? Eight times twelve? Three times four?

Five times nine ?

Nine times nine? Three times five?

Five times ten ?

Nine times ten ? Three times six ?

Five times eleven? Nine times eleven ? Three times seven ? Five times twelve ? Nine times twelve ? Three times eight? Six times six ?

Ten times ten ? Three times nine ?

Six times seven? Ten times eleven ? Three times ten?

Six times

Ten times twelve ? Three times eleven? Six times nine ?

Eleven times eleven? Three times twelve ? Six times ten?

Eleven times twelve ? Four times four ?

Six times eleven? Twelve times twelve ? .13. What will twelve pounds of 18. A certain room has four winbutter cost, at twelve and a half dows, each containing eighteen cents a pound?

panes of glass; how many panes are 14. If a person earn five dollars a there in the whole ? week, how much does he earn in 19. A ream of paper contains twelve weeks ?

twenty quires, of twenty-four sheets 15. If a person earn seven shil. each ; how many sheets in a ream? lings a day, how much does he earn 20. What will nineteen bushels in nine days?

of potatoes cost, at eighteen cents a 16. At twelve cents a pound, bushel ? what will eleven pounds of sugar 21. What will twenty-one barrels cost?

of cider cost, at seventy-five centa 17. Peter has fifteen cents, and a barrel ? John has three times as many; how 22. What will fifty sheep cost, at many has John?

one dollar twenty cents a piece ?

eight?

DIVISION. 1. If two apples cost four cents, 14. At twelve ćents a dozen, how how much is that a piece ?

much will half a dozen apples cost ! 2. If three lemons cost nine cents, 15 If five pounds of sugar cost fifty how much is that a piece?

cents, what is that per pound ? 3. A lad had twelve plums, which 16. If twenty yards of cloth cost he divided equally among six boys; six dollars, what is that a yard? how many did each have?

17. In a certain cornfield are eight 4. If you divide twenty dollars e rows forty hills long ; how many hills qually among four men; how much are there? will each have ?

18. A certain corpfield contains 5. In fifteen how many times five ? three hundred and twenty hills, and

6. In twenty-one how many times the rows are forty hills long; how geven?

many rows are there? 7. In sixteen how many times four? 19. In five hundred, how many 8. In thirty how many times five ?

times twenty? 9. In twenty-four how many times 20. If a bushel of wheat cost eight?

eighty cents, how much is that a 10. In eighteen how many times quart; there being four pecks in a two?

bushel, and eigh quarts in a peck ? 11. If a quire of paper cost twelve 21. In two dozen and a half, how cents, how much is that a sheet?

many half dozen? 12. If five lemons cost thirty cents, 22. In a certain village are two how much is that a piece ?

hundred and eighty-five persons, and 13. If fifty-four cherries be divid the average number in each family ed among six girls, how many will is five; how many families are there? they have a piece ?

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