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worth of cherries; how many centshow many cents must you have had be left ?

back? 19. Take eight and three from 26. A person rode twenty miles sisteen, what remains ?

n three hours ; the first hour be 20. George has pine inerits, and rode seven miles, the second six, John five and Charles two; hou how many miles did be ride the many more bas George than both third buur? the others ?

| 27. A man owed another twenty 21. Sarah had nineteen plumbs five dollars of which he paid at one and gave five of them to Lucy and time nine dollars, and at another four to Mary ; bow many bad she seven dollars, how much remains Jeft?

due ? 22. Five and four from nineteen, 28. Take nine and six from wbat remains ?

wenty and what remains ? 23,, Eighteen periods are in a 29. A boy is thirteen years old room, but only seven are sitting, and his sister is eighteen what is how many are standing

the difference of their ages ? 24. A boy bad twenty centand 30. Twenty four puunds of sulost six of them, bow many bad ke gar are put into three boxes, one left?

box contains seven pounds anothe 25. If you buy a slate for twelveer nine, what does ihe other cona cenis and a sponge for six and give tain ? a lwenty cent piece, or pistareene,

DIVISION 10. 1. Iftwo pears cost fourl 11. Twenty cents are put into cents, how much is that a piece ? four equal piles, how many cents

2. Two oranges cost six cents ;fare there in each pile? . bow much is that a piece?.

12. If live oranges cost twenty 3. Three leinons cost oine cents, live cents; how much is that a how much is that a piece ?

piece; 4 If ten apples are divided el 13. In twenty how many times qually between two boys, how four? many will each have?

| 14. In twenty how many times 5. How many thimbles at five five ? cents a piece can you buy for ten 15. In twenty-five how many cents ?

times live? 6. Divide twelve apples between 16. In twenty how many times. two boys, how many will each ten ? have ?--between three boys ?-be. 17. If I have eight apples and a in een four boys?

give you half of them, bow many 7. Fourteen cants were divided shall I give you? between two poor boys, how many 18. In thirty bow many times did eacli have?

ten ?-how many times five 8. If I buy four books for sixteen how many three? cents, how much do I give for one 19. In eighteen how many times book ? '

Inine ?-how many times six ? 9. I sold nine quills for eighteen three ?-two? bents, how much is thai a piece? 21. If a boy owes an another

10. If twenty men ride in two twenty-one cents and pays him 00aches how many will be in each three cents every day, how many coach?

days will it take to pay the debt.

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22. In twelve how many times vided among nine girls, how many one? how mpauy times two ? how will each have? many times three?-four I-six ? | 19. In thirty-two how many

23. I bought five oranges for fif times eight ? teen cents, how much was that al 30 In thirty bow many times piece ?

live? how many times six ? ten! 24. At twelve cents a dozen fifteen? what will half a dozen apples cost 31. In a garden are forty-nine

25. Iftwenty-eight cents be di-hills of corn planted in severi equal vided between four boys, how ma-rows, how many hills are there in ny will each have ?

26. If a quire of paper cost twen 32. Divide thirty-nine cbesnuts ty-four cents, how much is that between ihree boys, how many sheet?

vill each have? 27 If twelve sheets of paper 33 Divide ninety-one cants hecost twenty-four cents, bow much is even children, how many is that a sheet?

wi have?
28. If thirty-six cherries be di-

FRACTIONS.
The following questions s onid ve iliustraied by dividing an apple

before the pupils according to the conditions of each question.' 11. 1. If an apple be divideofapples will give two boys just one into two equal parts what are those pple a piece, and that one apple parts called ? A. Halves.

vill give them half of an apple a 2. If an apple be divided into iece, so that three apples will give three equal parts what are those i wo boysone apple anda balf each. parts called ? A. Tbirds.

12. Divide five apples between 3 li an apple be divided into four boys, how many will each four equal parts what are thoselliave? parts called? A. Fourtbs, or quar 13. Divide ten cents between tlrree ters.

boys, how many will each bave. 4. How many halves in a whole 14. Divide one apple and a half apple ?

Jof an other between six boys, how 5. How many thirds in a wbole much will each receive ? applet

15. How many quarters in three 6. "How many fourths in a whole apples ?

16 How many thirds in three 7. Which is most one half of an apples ? apple, or one third of an apple?--'17. To how many apples are *. one third or one fourth ?

eight quarters equal ? 8. In two whole apples how ma- 18. To how many apples are py halves? how many thirds? bow twelve halves equal ? mang fourths ?

19. How many apples will ten 9. Eight quarters of a dollar are thirds make? how many whole dollars ?

20. How many apples will fifteen 10. Seven halves of a dollar are quarters make how many whole dollars ?

21. Divide eleven apples be11. If ihree apples be divided when four boys; how many will between two boys how many will each receive ? each bave ?

- 22. How many quarters are one The pupil will observe that twothalt and one quarter!

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12. 1. If a pear is worth two dollars, and it be cut into two'e. . tents, what is one half of it worth ? qual parts, what are each of these A. One cent, because, if two cents parts worth? le divided into two equal parts, 8. If a yard ot cloth is worth i one of the parts is our cent. four dollars, what is half a yard

2. If a lemon is worth three worth ?-one quarter of a yard ? cents, what is one third of it wortb three quarters two thirds of itp

| 9. If one pound of tea is worth 3. If three shillings will buy a one dollar, what is half a pound bushel of rye, what part of a bush - worth ? a quarter of a pound ? el will one shilling buy?-will troone third of a pound?-two thirds? shillings buy?

10. If one quarter of an orange 4. If you can buy a barrel of ci-is worth one cent, what is a whole der for two dollars how much can orange worth? - what is an orange you buy for three dollars ? for one and a half worth?. dollar for half a dollar? ! 11. Two apples are what part of

5. What is meant by. flthree apples? A. Two times one o a thing ?*

Third, or two thirds of three apples. 6. What is meant by

o ird 12. Two apples are what part of of a thing? what hy two thirds four apples ? what by one fou th? by two 13. Three apples are what part Tourths ? by three fourths ? fof four apples.

7. If a yard of cloth cost two!

SECTION III. 13 The pupils having by this time learned to form and decom. pose numbers with considerable facility, may now be taught the metbod of expressing numbers by characters. For this purpose they should be furnished with slates, upon wbich they should be required to form the characters at the same time they are learning them By this exercise they will learn the characters, and the method of expressing numbers by tbem, much faster than by any other means, and will at the same time be learning to write. The method of writing the num. bers from one to one hundred is as follows: One is written 1 | Fourteen : 14 | Twenty seven '- 27 Two . . . 2 Fifteen . . 15 | Twenty eight - 28 Three

3 Sixteen . 16 Twenty nine 29 Four

4 Seventeen : 17 | Thirty - - 30 Five . . . 6 Eighteen

18 | Thirty one - 31 Six . 6 i Nineteen

19 Thirty two, &c. 32 Seven 7 | Twenty

20 | Forty : - 40 Eight

Twenty one - 21 Fifty • - 50 Nine . . . 9 Twenty two . 22

22 Sixty . . 10 Twenty three - 23 Seventy . . Eleven - · 11 Twenty four • 24 Eighty · · 80 Twelve . . 12 Twenty five • 25 Ninety . . 90 Thirteen . . 23 Twenty six . 26 One Hundred 100

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Questions of this kind should be frequently repeated, that the pupil may have a clear idea of the meaning of the different expressions used.

14.

PAMILIAR QUESTIONS.

17

As the pupils advance, these exercises should be extended beyond the numbers contained in the foregoing table, and repeated till they become familiar with the laws of potation.

14. When numbers are applied to any particular things, as men, dollars, &c. they are called concrete numbers, but when numbers are used without refering them to any particular things, they are called abstract numbers. Hitherto the numbers employed bave mostly been concrete. The following tables are made up of abstract numbers and upon these the pupils should be exercised repeatedly until they are made perfectly familiar with them and have the various results all treasured up in their memories. In exercising the pupils, the teacher should put the table into an interrogative form ; thus, 0 and 1 are low many? A. one, &c. After the pupils can answer all the questions in the order in which they arise they should be proposed promiseuously from all parts of the table until they can all be answered without hesitation.

ADDITION TABLE.

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O and 1 an .D and 2 are

O and 3 are O and 4 are land 5 are O and 6 are O and hy are O and 8 are O and 9 are O and 10 are 3 and I are 3 and 2 are 3 and 3 are 3 and 4 are 3 and 5 are 3 and 6 are 3 and 7 are 3 and 8 are 3 and 9 are 3 and 10 are 6 and. 1 are 6 and 2 are 6 and 3 are 6 and 4 are 6 and 5 are 6 and 6 are 6 and 7 are 6 and 8 are 6 and 9 are 6 and 10 are

111 and 1 are
21 and 2 are
31 and 3 are
41 and 4 are
51 and 5 are
61 and 6 are
71 and try are
81 and 8 are
91 and 9 are
10 1 and 10 are

4,4 and I are
54 and 2 are
64 and 3 are
74 and 4 are.
8 4 and 5 are
9 t and 6 are
10 4 and 7 are
11'4 and 8 are
12 4 and 9 are
134 and 10 are
77 and 1 are
817 and 2 are
97 and 3 are
107 and 4 are
1117 and 5 are
12/7 and 6 are
137 and are
147 and 8 are
15 7 and 9 are
167 and 10 are

212 and 1 are
32 and 2 are
42 and 3 are
52 and 4 are
62 and 5 are
1712 and 6 are
82 and 7 are
92 and 8 are
102 and 9 are
112 and 10 are
5,5 noc iure
6 5 and 2 are
75 and 3 are
85 and 4 are
95 and 5 are
10j5 and 6 are
11 5 and 7 are
125 and 8 are
13 6 and 9 are
14!5 and 10 ore
8.8 and 1 are
9 8 and 2 are
108 and 3 are
118 and 4 are
128 aod 5 are
138 and 6 are
14.8 and 7 arc
15'8 and 8 are
16 8 and 9 are
178 and 10 are

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17 13

9 and I are:
9 and 2 are
9 and 3 are
9 and 4 are
9 and 5 are
9 and 6 are
9 and 7 are

1019 and 8 are
11 9 and 9 are
129 and 10 are
13 10 and I are
14 10 and 2 are
15 10 and 3 are
16 10 and 4 are

17/ 10 and 5 are 18 10 and 6 are 19 10 and are 1110 and 8 are 12 10 and 9 are 13110 and 10 are 141

15. The following table must also be put into the interrogative form by the teacher, when exercising the learuer ; thus one taken from one, or one from one, what remains ? A. Nothing. One from two, what remains ? A. One. Or thus ; one lessened one, or one less one are how many? A. Notning. Two less one are how many ? A. One. If the latter method be used, the pupil should be made to understand clearly that two less one means the same thing as one taken from or oul of two

SUBTRACTION TABLE. 1 from 1 remains 0 2 from 2 remains 0 | 3 from 3 remains 0 1 from 2 remains 1 | 2 from 3 remains 1 3 from 4 remains 1 I from 3 remains 2! 2 from 4 remains 2, 3 from 5 remains 2 1 from 4 remains 3 2 from 5 remains 3 3 from 6 remains 3 1 from 5 remains 4 | 2 from 6 remains 4 3 from any remains 4 1 from 6 remains 5.2 from 7 remains 5 3 from 8 remains 5 1 froin 7 remains 6 | 2 trom 8 remains 6 3 from 9 remains 6 1 from 8 remains og 2 from 9 remains og 3 from 10' remains ? I from 9 remains 82 from 10 remains 83 from 11 remains 8 1 from 10 remains 92 from 11 remains 9. 3 froin 12 remains 9 4 from 4 remains 0.5 troin 5 remains 016 from 6 remains 0 4 from 5 remains 115 from 6 remains 1/6 from y remains i 4 from 6 remains 2.5 from 7 remains 2,6 from 8 remains 2

remains 3/5 froto 8 remains 36 from 9 remains 3 4 from 8 remains 4/5 from 9 remains 4' 6 from 10 remains 4 4 from 9 remains 5/5 from 10 remains 56 from 11 remains 5 4 from 10 remains 65 from 11 remains 66 from 12 remains 6 4 from 11 remains 75 from 12 remains 76 from 13 remains ? 4 from 12 remains 85 from 13 remaios 8/6 from 14 remains 8 4 from 13 remains 95 from 14 remains 9 6 from 15 remains 9

from 7 remains 0,8 from 8 remains 019 from 9 remains 7 from 8 remains 118 from 9 remains 19 from 10 remains 7 from 9 remains 28 from 10 remains 2,9 from 11 remains 2 7 from 10 reinains 3/8 from 11 remains 39 from 12 remains 3 7 from 11 remains 48 from 12 remains 4 9 from 13 remairs

from 12 remains 5 8 from 13 remains 59 from 14 remains 5 7 from 13 remains 68 from 14 remains 6'9 from 15 remains 6 thing from 14 remains 78 from 15 remains 7,9 from 16 remains 7 7 from 15 remains 88 from 16 rentains 89 from 17 remains 8 7 froin 16 remains 98 from 17 remins 9'9 from 18 remains 9 10 from 10 remains 0; 10 from 14 remains 4:19 from 17 remains 7 10 trom 11 regains 1/10 from 15 remains 51' (rom 18 retains 8 10 from 12 remains 210 from 16 remains 6/10 from 19. remains 9 10 from 13 remains 31.

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