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TABLE OF CONTENTS.

(This Table equally refers to Parts I. and II.)

ways to multiply, and two ways to divide, a fraction.
XIX. Addition and subtraction of fractions. To reduce them to

common denominator. To reduce them to lower ternis

XX. Contractions in division.

XXI. How to find the divisors of numhers. To find the grea

mun divisor of two or more numbers To reduce fra

their lowest terms.

XXII. To find the least common multiple of two or more

To reduce fractions to the least common denominator.
XXIII. To divide a whole number by a fraction, or a fract

fiuction, when the purpose is to find how many times
Bur is contained in the dividend. To find the ratio of a

and a wholo number, or of two fractions.
XXIV. To divide a whole number by a fraction, or a fractio-

fraction; a part of a number being given to find the
This is on the same princi, le as that of dividing a numb

pa.ts.
XXV. Deciinal Fractions. Numeration and notation of them.
XXVI. laddition and Subtraction of Decimals. To change a co

fraction to a decimal.

XXVII. Multiplication of Decimals.

XXVIII. Dirision of Decimals.

XXIX. Circulating Deciinals.

Proof of multiplicacion and division by casting out 8.

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jon.

in by a whole numbor. To multiply a fraco

action by dividing the denominator. Two
nd two ways to divide, a fraction.
action of fractions. To reduce them to
or. To reduce them to lower terras

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Compound Multiplication

Allifirion
Subtraction

Disisiun
Interest, Simple
Commission
Insurance
Duties and Premiums
Discount, Common
Coinpound Interest
Discount

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Barter

Loss and Gain

Fellowship, Simple . .
Fellowship, Compound .
Equation of Payments
Alligation Medial .
Alligation Alternate ...

215 58....68

78 130..142
224 110..113
38 102..106

34....38
103 33...41
214 52..7
58 158..) 66

85....86
221 87....92
202 103..109
218 69....72
218 73....81
9 1....49
91 50....64
101 13....26
223 141..444
103 28....32
233 181..187
234 188..138
235 199..205
236
240

Bquare and Cubic Measure. Miscellaneous Examples

Duodecimals
Tases .
Measure of circles, parallelograms, triangles, &c.
Geographical and Astronomical questions .
Exchange .
Tables of Crin, Weights, and Measures
Rollections on Mathematical reasoning

ICULAR SUBJECTS

ARITHMETIC.

PART I.

Pago. Example llaneous examples 37 laneous eramples 211 1...

ADDITION. The student may perform the following example mind.

1. James has 3 cents and Charles has 5; how m they both ?

2. Charles bought 3 bunns for 16 cents, a quart ries for 8 cents, and 2 oranges for 12 cents ; how ma did he lay out ?

3. A man bought a hat for 8 dollars, a coat for 2 a pair of boots for 5 do'lars, and a vest for 7 dulla many dollars did the whole come to ?

4. A man bought a firkin of butter for 6 dollars, of vcal for 45 cents, and a barrel of cider for 3 dullas cents; how much did he give for the whole ?

5. A man sold a horse foor 127 dollars, a load of h dolars, and 3 barre!s of cider for 12 dollars ; how he receive for the whole ?

6. A man travelled 27 miles in one day, 15 miles day, and 8 miles the next ; how many miles did he the whole ?

7. A man received 42 dollars and 37 cents of one 4 dollars and 68 cents of another, and 7 dollars and of a third ; how much did he receive in 1!:e whole !

8. I received 25 dollars and 58 cents of urie man lars and 83 cents of another, and 8 dollars and 39 c third; how much did I receive in the whole ?

The two last examples may be performed in the they will be rather difficult. A more convenient will soon be found.

29 43....50

99 65..113 104 43...74

215 58...68

78 130..142 224 110..113 30 102..106

43 34....38 103 33....41 314 52...57 58 108..JG6

65....86

87....92 202 103..109 218 61... 218 73....81

ng 1...49 teous Examples 91 56.64

101 13....26
229 141.J44

103 28....32

. 233 181..187 ns.

234 188..148
235 199..206
236
240

ngles, &a

NUMERATION. 1. Write in words the following numbers. 1 27/24

10 000 2 85125

20,10 3 58126

50,705 4 63/27

67,083 5 7023

309,050 6 84 29

470,099 7

96 30

707,720 8 100131

1,001,370 303 32

5,600,073 10

110/33

8,081,305 11

11:34

59,006,341 12

127135

305,870,400 13

305 36

7.7

590,047,608 14

520,37

1,000,000,000 15

7:51:38

3,670,07020,387 16

1,000139

45,007,070,007 17

1,001 40

680,930,100,700 18

1,010 41 50,787,6-57,000,500 19

1,100 4:2 270,060,8:38,00;3,908 20 1,018 43

68,907,605 21

2,107|44

56,000,034,750

3 2:50 45 6,703,720,000,857 23

5,790 Write in figures the following numbers. 1. Thirty-four. 2. Fifty-seven. 3. Sixty-three. 4. Eighty. 5. One hundred. 6. One hundred and one. 7. One hundred and ten. 8. Three hundred and eleren. 9. Five hundred and seventeen. 10. Eight hundred and fifty. 11. Nine hundred and eighty-six. 12. One thousand and one. 13. One thousand and ten. 14. Three thousand, one hundred and one. 15. Five thousand and sixty.

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