5. In 1789 quarts of cider, how many barrels?

Ans. 14bls. 25qts. 6. What number of bottles, containing a pint and a nalf each, 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.

corns ?

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

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

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

Ans. 15715280inch. 4. In 4352 inches, how many yards ?

Ans. 120yds. 2ft. Sin. 3. In 682 yards, how many rods ?

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

Ans. Om. Slea. 7. How many times will a carriage wheel, 16 feet and 9 inches in circumference, turn round in going from New-York to Philadelphia ; it being 96 miles ?

Ans. 30261 times, and 81 feet over. 8. How many barley-corns will reach round the globe it being 360 degrees :

Ans. 4755801600

a

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

Ans. 58705perches. 2. In 20692 square poles, how many acres ?

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

Ans. 980 perches. 4. Three fields contain, the first 7 acres, the second 10 res, the thad 12 acres, 1 rood, how many shares como be divided into, each share to contain 76 rods ?

Ans. 61 shares, and 44 rods ocor.

1. In 14 tons of hewn timber, how many sold inches

Ans. 14x50x1728=1209600. 2. In 19 tons of round timber, how many inches?

Ans. 1313280. 3. In 21 cards of wood, how many solid feet?

Ans. 21x128=2688. 4. In 12 cords of wood, how many solid feet and inches?

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

Ans. S6cds.

11. TIME. 1. In 41 weeks, how many days; hours, minutes, and conds :

Ans. 287d. 6888h. 413280min, and 24796800 sec. 2. In 214.1. 15h. 31m. 258ec. how

many

second's ?

Ans. 18545485sec. $. In 24796800 seconds, how many weeks?

Ans, 4f weeks. 4. In 184009 minutes, how many days?

Ans. 1278. 18h. 49 min. 3. How many days from the birth of Christ, to ChristM, 1797, allowing the year to contain 365 days, 6 hours.

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

Ans. 506649600sec. 7. From March 20, to November 19th following, inusive, how many days?

Ans. 262.

12. OIROU'LAR MOTION. 1. In 7 signs, 15° 24' 40" how many degrees, minutes, und seconds ?

Ans. 22.50 13524' and 811480" 2. Bring 1020300 seconds into signs.

Ans. 9 signs, 19° 250

QUESTIONS TO EXERCISE REDUCTIOI. 1. In 1959 gruato, how many farthings, pence, shilling ad guineas *98.

Ans. 20144grs. 30365 410% 94. od 14 gwinean, sfs. Nd.

2. Borrowed 10 English guineas at 288. each, and 24 English crowns at 6s. and sil. each ; how many pistoles at 22s. each will pay the debt?

Ans. 20. 3. Four men brought cach 1:1. ins. sterling value in gold into the mint, how many guive:13 at 91s. cach must ines recrive in return;

Aus. 66 min. 145. to a sier mit received there ingois of silvera rach weighing unrices, with direriinds 10 mehe 01.0! into apoons of 2017.. cups of 30%. salts of 1 07. 20 stuttbuses

2017.. and deliver an equal number of each ; wiat was the womber

Ans. 8 of rail, anul 1 ozeurer. 5. Admit a ship's cargo from Bordeaus to be 230 pipes, 130 hlids. and 1.50 quarter casks!) hlids.) how uang gallons in all; allowing every pint to be a pound, what burilen was the sirip of: Ans. 44415 muls, and

the ship's burilen n'as 158 tons, 12cwl. 2yrs. 6. In 15 pieces of cloth, each piece 20 yds, how many French Eils :

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

8. The forward wheels of a waygon are 14 feet in vircumference, and the hind wheels 15 feet 9 inches, how many more times will the forward wheels turn round than the kind wheels, in running froin Boston to New-York, it being 248 miles:

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

dis. 2079308.' 10. The sun is 95,000,000 of miles from the earth, and a rannon ball at its first discharge flies about a mile in :? seconds; how long woulgl a cannon ball be, at that rute in Hying from here to the sun :

Jus. 221r. 216d. 19h. 40m. 11. The Sun travels through 5 signs of the Zuliac in halt a year ; how many degrees, minutes and seconds :

1.. 1801.pr. 10800min. 648601sri. 2. llow many strokes dues a regular clock strike in dars, or a rear :

ons. 56940. 3. How loving will it take to count a million at the rate ill. a minute Aros. 335h. 20m. 'ur 15d. 214. 20enn.

14. The national debt of England amounts to about 279 millions of pounds sterling; how long would it take to count this debt in dollars (4s. 6d. sterling) reckoning without intermission twelve hours a day at the rate of 50 dollars a ninute, and 365 days to the year ?

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

Thus, Denominator

FRACTIONS. FRACTIONS, or broken numbers, are expressions fo.

, . any assignable part of an unit or whole number, and (ir general) art of two kinds, viz..

VULGAR AND DECIMAL. A Vulgar Fraction, is represented by two numbers pla ced one above another, with a line drawn between thern thus, i, j, &c. signities three-fourths, five-eights, &c.

The figure above the line, is called the numerator, apo hat below it, the denominator,

S5

3 The denominator (which is the divisor in division) shews how many parts the integer is divided into; and the numerator (which is the remainder after division) shews how niany of those parts are meant by the fraction.

A fraction is said to be in its least or lowest terins, when it is expressed by the least numbers possible, as when reduced to its lowest terms will be d, and is equal to }, &c.

PROBLEM I. 'To abbreviate or reduce fractiuns to their lowest terms

RULE. Divide the terms of the given fraction by any number which will divide them without a remainiler. an' the quotients again in the same manner: and so on, tillit appears that there is no number greater than I, which will divide chem, and the fractun will be in its least terins

EXAMPLES.

Aris.

1. Reduce 11% to its lowest terms.

(3) (2)

8)!*4=16= the Answer. 2. Reiluce to its lowest torms.

Ans. } 3. Reiluce 1% to its lowest leims.

Als is 4. Reduces to its lowest terms. dus. 5. Abbreviate as much as possible. Jus. 6. Reduce $1 to its lowest termis. Jus. 7. Reoluce ii to its lowest terins.

Aus. 8. Recluce 32 to its lowest terins.

Aus. . 9. Reduce 171 to its lowest terms. 10. Reduce to its lowest terins. Aus.

PROBLEM II. To find the value of a fraction in the known parts of the intover, as to coin, weight. ineasure, &c.

RULE. Multiply the numerator by the common parts of the integer, and divide by the denominator, &c.

EXAMPLES.
What is the value off of a pound sterling ?

Numer.

20 shillings in a pound.

Denom. 3)40(15s. 4d. Ans.

3

10
9

1

.12

5)1204

12 2. What is the value of 1 of a pound sterling?

Ans. 18s. 5d. grs. 3. Reduce of a shilling to its proper quantity,

Ansi 4 d. 4. What is the value of of a shilling? Ans. 4jd. 5. What is value of 1* of a pound troy? Ans. 90%.