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XIX. Addition and subtraction of fractions. To reduce them to a

common denominator. To reduce them to lower terms.

XX. Contractions in division.

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

common 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

fraction, when the purpose is to find how many times the
divisor 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 principle as that of dividing a number

INDEX TO PARTICULAR SUBJECTS.

Page. Example.

Miscellaneous examples

32

1....49

Miscellaneous examples 230

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1....25

20
96
109

43....50
65..113
43....74

235 58....68

80 130..142
244 110..113
30 102..106
37 34....38
109 33....41
234 52....57

56 158..166
240 85....86
241 87....92
242 53..109
237 69....72
238 73....84
81 1....49
95 56....64
107 13....26
249 141..144

109 28....32
255 181..187
256 188..198

Square and Cubic measure. Miscellaneous Examples

{

Duodecimals
Taxes
Measure of circles, parallelograms, triangles, &c.
Geographical and Astronomical questions

Exchange
Tables of Coin, Weights, and Measures
Reflections on Mathematical reasoning

257 198..204
258
262

ARITHMETIC.

PART I.

Addition.

The student may perform the following examples in his mind.

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

2. Charles bought 3 bunns for 16 cents, a quart of cherries for 8 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 dollars, a pair of boots for 5 dollars, and a vest for 7 dollars ; how niany dollars did the whole come to ?

4. A man bought a firkin of butter for 8 dollars, a quarter of veal 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

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