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5. CLOTH MEASURE.
1. In 95 yards, how many quarters and nails ?

Ans. 380 qrs. 1520 na. 2. In 341 yards, 3 qrs. 1 na. how many nails ?

Ans. 5469. | 3. In 3783 nails, how many yards ?

Ans. 236 yds. 1 qr. 3 na. 4. In 61 Ells English, how many quarters and nails ?

Ans. 305 qrs. 1220 na. %. In 56 Ells Flemish, how many quarters and nails? 1416.

Ans. 168 qrs. 672 na. 6. In 148 Ells English, how many Ells Flemish ? 16.1% 06

Ans. 246 E. F. 2 qrs. 7. fu 1920 nails, how many yards, Ells Flemish, a Ells English ? Ans. 120 yds. 160 E. F. and 96 E. E.

8. How many coats can be made out of 364 yards broadcloth, allowing 14 yards to a coat ? Ans. 21.

9. DRY MEASURE. how man! 1. In 136 bushels, how many pecks, quarts and pints

Ans. 544 pks. 4352 qts. 8704 pts. 2. In 49 bush. 3 pks. 5 qts. how many quarts ? Ans. 1597 3. In 8704 pints, how inany bushels ?

Ans. 136. 4. In 1597 quarts, how many bushels ?

Ans. 49 bush. 3 pks. 5 qts how many

5. A man would ship 720 bushels of which hold 3 bushels 3 pecks each, how many bar

Ans. 192

Ins. 5099. -573440.

892245. 40%. Il dr.

Ans. 1.

- 16. 50%.

corn in barre

15084.

4 cut.

h 8 cwt sining 1 get?

S. 284,

7. WINE MEASURE. 1. In 9 tuns of wine, how many hogsheads, gallons Jarts ?

Ans. 36 hhds. 2268 gals. 9072 qts 2. In 24 hhds. 18 gals. 2 qts. how many pints?

Ans. 12244 3. In 9072 quarts how many tuns ?

Ans. 4. In 1905 pints of wine, how many hogsheads?

Ans. 3 hhds. 49 gals. 1 p6 In 1789 quarts of cider, how many barrels ?

Ans. 14 bls. 25 qt F2

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6. What number of bottles, containing a pint and a hall vach, can be filled with a barrel of cider? Ans. 168.

7. How many pints, quarts, and two quarts, each an equal number, may be filled from a pipe of wine! Ans. 144.

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8. LONG MEASURE. 1. In 51 miles, how many furlongs and poles ?

Ans. 408 fur. 16320 poles. 2. In 49 yards, how many feet, inches, and barley-corns ?

Ans. 147 ft. 1764 inch. 5292 b. c. 3. How many inches from Boston to New-York, it being 248 miles ?

Ans. 15713280 inch. 4. In 4352 inches, how many yards ?

Ans. 120 yds. 2 ft. 8 in. 5. In 682 yards, how many rods?

Ans. 682 X2-11=124 rods. 6. In 15840 yards, how many miles and leagues?

Ans. I m. 3 lea. 7. How many times will a carriage wheel, 16 feet and 9 inches in circumference, turn round in going from Newe York to Philadelphia; it being 96 miles ?

Ans. 30261 times, and 84 feet over. 8. How many barley-corns will reach round the globe, it being 360 degrees ?

Ans. 4755801600.

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9. LAND OR SQUARE MEASURE. 1. In 241 acres, 3 roods, and 25 poles, how many square rods or perches?

Ans. 38705 perches. 2. In 20692 square poles, how many acres ?

Ans. 129 a. lr. 12 po. 3. If a piece of land contain 24 acres, and an enclosure of 17 acres, 3 roods, and 20 rods, be taken out of it, how many perches are there in the remainder ?

Ans, 980 perches. 4. Three fields contain, the first 7 acres, the second 10 acres, the third 12 acres, I rood; how many shares can they be divided into, each share to contain 76 rods ?

Ans. 61 shares and 44 rods over.

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10. SOLID MEASURE. 1. In 14 tons of hewn timber, how many solid inches

Ans. 14 x 50 x 1728=120960 2 In 19 tons of round timber, how many inches?

Ans. 13132€ 3 In 21 cords of wood, how many solid feet ?

Ans. 21 X 128=268 4. Iu 12 cords of wood, how many solid feet and ind

Ans. 1536 ft. and 2654208 in 5. In 4608 solid feet of wood, how many

cords ?
Ans. 36 c

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11. TIME. 1. In 41 weeks, how many days, hours, minutes seconds? Ans. 287 d. 6888 h.413280 min. and 24796800 2. In 214 d. 15 h. 31 m. 25 sec. how many seconds

Ans. 18545485 3. In 24796800 seconds, how many weeks? Ans. 41 u 4. In 184009 minutes, how many days ?

Ans. 127 d. 18 h. 49 5. How many days froin the birth of Christ, to mas, 1797, allowing the year to contain 365 days, 6 h

Ans. 656354 d. 6. Suppose your age to be 16 years and 20 days inany seconds old are you, allowing 365 days and 6 to the year?

Ans. 506649600 7. From March 2d, to November 19th following, sive, how many days ?

Ans.

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12. CIRCULAR MOTION. 1. In 7 signs, 15° 24' 40', how many degrees, m and seconds ?

Ana. 225o 13524' and 8114 2. Bring 1020300 seconds into signs.

Ans. 9 signs, 13

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Questions to exercise Reduction. 1. In 1259 groats, how many farthings, pence, s and guineas, at 288. ? Ans. 20144qrs. 5036d. 419.

and 14 guineas. 27

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2. Borrowed 10 English guineas at 28s. each, and 34 English crowns at 6s. and Ed. each; how many pistoles at 22s. each, will pay the debt?

Ans. 20. 3. Four men brought each 171. 10s. sterling value in gold into the mint, how many guineas at 21s. each must they receive in return?

Ans. 66 guin. 14s. 4. A silversmith received three ingots of silver, each weighing 27 ounces, with directions to make them into spoons of 2 oz., cups of 5 oz., salts of 1 oz., and snuff-boxes of 2 07., and deliver an equal number of each ; what was the number?

Ans. 8 of each, and 1 oz. over. 5. Admit a ship's cargo from Bordeaux to be 250 pipes, 130 hhds. and 150 quarter casks, [i hhds.] how many gallons in all; allowing every pint to be a pound, what burden was the ship of ? Ans. 44415 gals. and the ship's burden

was 158 tons, 12 cut. 2 qrs. 6. In 15 pieces of cloth, each piece 20 yards, how many French Ells?

Ans. 200. 7. In 10 bales of cloth, each bale 12 pieces, and each piece 25 Flemish Ells, how many yards ? Ans, 2250.

8. The forward wheels of a wagon are 141 feet in cir: cumference, and the hind wheels 15 feet and 9 inches; how many more times will the forward wheels turn round thau the hind wheels, in running from Boston to New-York, it being 248 miles ?

Ans. 7167. 9. How many times will a ship 97 feet 6 inches long, sail her length in the distance of 12800 leagues and ten yards?

Ans. 2079508. 10. The sun is 95,000,000 of miles from the earth, and a cannon ball at its first discharge flies about a mile in 71 seconds; how long would a cannon ball be, at that rate in flying from here to the sun ? Ans. 22 yr. 216 d. 12 h. 40m.

11. The sun travels through 6 signs of the zodiac in half a year; how many degrees, minutes, and seconds ?

Ans. 180 deg. 10800 min. 648000 sec. 12. How many strokes does a regular clock strike in 365 days, or a year?

Ans. 56940. 13. How long will it take to count a million, at the rate o 60 a minute ? Ans. 333 h. 20 m. or 13 d. 21 h. 20 m.

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14. The national debt of England amounts to about millions of pounds sterling; how long would it take to co this debt in dollars (4s. 6d. sterling) reckoning withou termission twelve hours a day at the rate of 50 dols. a nute, and 365 days to the year?

Ans. 94 years, 134 days, 5 hours, 20 me

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FRACTIONS. FRACTIONS, or broken numbers, are expression any assignable part of a unit or whole number, an general) are of two kinds, viz.

VULGAR AND DECIMAL. A Vulgar Fraction, is represented by two numbers pi one above another, with a line drawn between them,

&c. signifies three fourths, five eighths, &c. The figure above the line, is called the numerator zat below it, the denominator ;

5 Numerator.

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Thus, { Denominator.

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The denominator (which is the divisor in division) how

many parts the integer is divided into; and the rator (which is the remainder after division) shows hony of those parts are meant by the fraction.

A fraction is said to be in its least or lowest terms, it is expressed by the least numbers possible, as wh duced to its lowest terms will be , and ia is equal to

PROBLEM I.
To abbreviate or reduce fractions to their lowest t
RULE.—Divide the terms of the given fraction by any numbe
will divide them without a remainder, and the quotients agai
same manner; and so on, till it appears that there is no
greater than 1, which will divide them, and the fraction will b
Jeast terms.

EXAMPLES.
1. Reduce 144 to its lowest terms.

(3) (2)
8)/1===the Answer.
2. Reduce to its lowest terms.

An 3. Reduce to its lowest terms.

An 4. Reduce Me to its lowest terms.

An

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