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1. Divide 23lb. 70z. 6dwt. 12gr. by 7.

Ans. 3lb. 40z. 9dwt. 12gr.

2. Divide 13lb. 1oz. 2dr. 10gr. by 12.

Ans. 1lb. 1oz. 2sc. 1ogr.

3. Divide 1061cwt. 2qrs. by 28.

Ans. 37cwt. 3qrs. 18lb.

4. Divide 375mls. 2 fur. 7pls. 2yds. 1ft. 2in. by 39.

Ans. 9mls. 4fur. 39pls. 2ft. 8in.

5. Divide 571yds. 2qrs. inl. by 47.

6. Divide 120L. 2qrs. ibu. 2pe. by 74.

Ans. 12yds. 2nls.

Ans. 1L. 6qrs. ibu. 3pe.

7. Divide 120mo. 2w. 3d. 5h. 20′ by III.

Ans. Imo. 2d. 10h. 12.

DUODECIMALS.

DUODECIMALS.

DUODECIMALS are so called because they "decrease by twelves, from the place of feet toward the right hand. Inches are sometimes called primes, and are marked thus '; the next division, after inches, is called parts, or seconds, and is marked thus ; the next is thirds, and marked

thus"; and so on.

Duodecimals are commonly used by workmen and artificers in casting up the contents of their work.

MULTIPLICATION of DUODECIMALS; or,

CROSS MULTIPLICATION.

RULE.

1. Under the multiplicand write the same names or de nominations of the multiplier; that is, feet under feet, inches under inches, parts under parts, &c.

2. Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write each result under its respective term, observing to carry an unit for every 12, from each lower denomination to its next superior.

3. In the same manner multiply every term in the multiplicand by the inches in the multiplier, and set the result of each term one place removed to the right of those in the multiplicand.

4. Proceed in like manner with the seconds and all the rest of the denominations, if there be any more; and the sum of all the lines will be the product required.

Or

Or the denominations of the particular products will be as follows:

Feet by feet, give feet.

Feet by primes, give primes.
Feet by seconds, give seconds.
&c.

Primes by primes, give seconds.
Primes by seconds, give thirds.
Primes by thirds, give fourths,

&c.

Seconds by seconds, give fourths,
Seconds by thirds, give fifths.
Seconds by fourths, give sixths.

&c.

Thirds by thirds, give sixths,
Thirds by fourths, give sevenths,
Thirds by fifths, give eighths.
&c.

In general thus:

When feet are concerned, the product is of the same denomination with the term multiplying the feet.

When feet are not concerned, the name of the product will be expressed by the sum of the indices of the two factors.

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7. Multiply 44f. 2' 9" 2"

Ans. 745f. 6′ 10′′ 2′′′′ 4ive 4iv. by 2f. 10' 3".

Ans. 126f. 2' 10" 8" Ioiv. IIV.

8. Multiply 24f. 10' 8" 7" 5iv. by 9f. 4′ 6′′.

Ans. 233f. 4′ 5" 9"" 6iv. 4v. 6vi, 9. Required the content of a floor 48f. 6' long, and 24f. 3' broad.

Ans. 1176f. 1' 6". 10. What is the content of a marble slab, whose length is 5f. 7, and breadth 1f. 10?

Ans. 1of. 2′ 10′′. 11. Required the content of a ceiling, which is 43f. 3′ long, and 25f. 6′ broad.

Ans. 1102f. 10' 6".

12. The length of a room being 2óf. its breadth 14f. 6', and height 1of. 4', how many yards of painting are in i, deducting a fire place of 4f. by 4f. 4', and two windows, each 6f. by 6f. 2? = 69 27

3.2.

6927

Ans. 73 yards. 13. Required the solid content of a wall 53f. 6' long,

12f. 3 high, and 2f. thick.

Ans. 1310f. 9',

VULGAR

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VULGAR FRACTIONS:

FRACTIONS, or broken numbers, are expressions for any assignable parts of an unit; and are represented by two numbers, placed one above the other, with a line drawn between them.

The figure above the line is called the numerator, and that below the line, the denominator.

The denominator shews how many parts, the integer is divided into, and the numerator shews how many of those parts are meant by the fraction.

Fractions are either proper, improper, single, compound, or mixed.

1. A proper fraction is when the numerator is less than the denominator: as,,, &c.

2. An improper fraction is when the numerator exceeds the denominator: as,, &c.

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3. A single fraction is a simple expression for any number of parts of the integer.

4. A compound fraction is the fraction of a fraction: as of, of, &c.

5. A mixed number is composed of a whole number and a fraction as 8, 173, &c.

NOTE.

Any whole number may be expressed like a fraction by writing I under it as 3.

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6. The common measure of two or more numbers is that number, which will divide each of them, without a remainder. Thus 3 is the common measure of 12 and 15 and the greatest number, that will do this, is called the greatest common measure.

7. A number, which can be measured by two or more numbers, is called their common multiple; and if it be the

least

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