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XIX. Addition and subtraction of fractions. To reduce them to a
common denominator. To reduce them to lower terms.

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

into parts.

XXV. Decimal 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. Division of Decimals.

XXIX. Circulating decimals.

Proof of multiplication and division by casting out 9s.

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

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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 many 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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