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XX. Contractions in division.

XXI. How to find the divisors of numbers. To find the greatest com-

mon divisor of two or more numbers To reduce fractions to

their lowest terms.

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

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

fi action, when the purpose is to find how many times the divi.
sor is contained in the dividend. To find the ratio of a fraction

and a whole number, or of two fractions.
XXIV. 'To divide a whole number by a fraction, or a fraction by a

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

paits.

XXV. Deciinal Fractions. Numeration and notation of them.

XXVI. Addition and Subtraction of Decimals. To change a common

fraction to a decimal.

XXVII. Multiplication of Decimals.

XXVIII. Dirision of Decimals.

XXIX. Circulating Decimals.

Proof of multiplication and division by casting out 8

INDEX TO PARTICULAR SUBJECTS

{

Compound Multiplication)

Page. Example
Addition Miscellaneous examples 37 1....49
Subtraction

Division Miscellanoous examples 211 1....25
Interest, Simple
Commission

23 43....50
Insurance

92 65..113
Duties and Premiums

104 43....74
Discount, Common
Compound Interont

215 58....68

78 130..142
Discount

224 110..113

30 102..106
Barter

42 34....38

103 33....41
Loss and Gain

914 52....57

58 158..166
Fellowship, Simple . .

220 85....86
Fellowship, Compound .

221 87....92
Equation of Payments

103,109
Alligation Medial .

218

69....72
Alligation Alternate ..

218 73....84

79 1....49
Square and Cubic Measure. Miscellaneous Examples 91 56....64

101 13....26
Duodecimals

229 141..144
Taxes ...

103 28....32
Measure of circles, parallelograms, triangles, &c. 233 181..187
Geographical and Astronomical questions

234 188..198
Exchange

235 199..205
Tables of Coin, Weights, and Measures

236
Reflections on Mathematical reasoning

240

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ARITHMETIC. .

PART I.

ADDITION The student may perform the following examples n bis mind.

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

2. Charles bought 3 bunn for 16 cents, a quart of cherries for S cents, and 2 oranges for 12 cents ; how many cents did he lay out ?

3. A man bought a hat for 8 dollars, a coat for 27 dolars, a pair of boots for 5 dollars, and a vest for 7 dullars; how many dollars did the whole come to ?

4. A man bought a firkin of butter for 6 dollars, a quarier of vcal for 45 cents, and a barrel of cider for 3 dollars and 25 cents ; how much did he give for the whole ?

5. A man sold a horse for 127 dollars, a load of hay for 15 dollars, and 3 barrels of cider for 12 dollars ; how much did he receive for the whole ?

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

7. A man received 42 dollars and 37 cents of one person, 4 dollars and 68 cents of another, and 7 dollars and 83 cents of a third ; how much did he receive in the whole ?

8. I received 25 dollars and 58 cents of one man. 45 dollars and 83 cents of another, and 8 dollars and 39 cents of a third; how much did I receive in the whole ?

The two last examples may be performed in the mind, but they wiil be rather difficult. A more convenient method will soon be found.

11

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NUMERATION.
1. Write in words the following numbers.
27124

10.000 35/25

20. uro 3 58/26

50,705 4 6327

67,083 5 70/23

300,050 6 84 29

476,099 96 30

707,720 8 100131

1,000,370 9 103 32

5,600,073 10

110 33

8,081,305 113 34

59,006,341 12

127 35

305,870,400 13

308 36

590,047,608 520 37

1,000,000,000 15

738 38

3,670,000,387 16

1,000!39

45,007,070,007 17

1,001 40

680,930,100,700 18

1,010 41

50,787,657,000,500

1,100 42 270,000,838,003,908 20 1,018 43

68,907,605 21

2,10744

56,000,034,750 3 250 45

6,703,720,000,857 5,796 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 eleven. 9. Five hundred and seventeen. 10. Eight hundred and fifty. - Jl. Nine hundred and eighty-six.

12. One thousand and one.
13. One thousand and ten.
14. Three thousand, one hundred and one.
15. Five thɔusand and sixty.

19

16. Ten thousand and five.
17. Thirty thousand, five hundred, and four.
18. Sixty-seven thousand, and forty.
19. Five hundred thousand, and seventy-one.
20. Two hundred and seven thousand, six hundred.
21. Four millions, sixty thousand, and eighty-four.

22. Ninety-seven millions, thirty-five thousand, eight hun dred and five.

23. Fifty millions, seventy thousand, and eight. 24. Three hundred millions, and fifty-seven.

25. Two billions, fifty-three millions, three hundred and five thousand, two hundred.

26. Fifty billions, two hundred and seven millions, sixtyseven thousand, t:vo hundred.

27. Eighty-seven millions, and sixty-three.

28. Six hundred billions, two hundred and seven thousand, and three.

29. Thirty-five trillions, nine millions, and fifty-eight.

30. Six hundred and fifty-seven trillions, seven billions, ninety-seven thousand, and sixty-seven.

31. Seventy millions, two hundred and fifty thousand, three hundred and sixty-seven.

32. Four hundred and seven trillions, and eighty-seven thousand.

33. Thirty-fi.e billions, ninety-eight thousand, one hundred.

34. Forty millions, two hundred thousand, and seventyfour.

35. Eighty-three millions, seven hundred and sixty-three thousand, nine hundred and fifty-seven.

ADDITION

II. 1.* A man bought a watch for fifty-eight dollars, a cane for five dollars, a hat for ten dolla:s, and a pair of boost for six dollars. What did he give for the wiole ?

2. In an orchard there are six rows of trees; in the two first rows, there are fiftcen trees in each row; in the Third row, seventeen ; in the fourth row, eleven; in the fifth row,

* See First Lessons, seci. I.

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