Let 1 rial be the 1st term, 10cts. the 2d. &c. multiply the marvadies by and add in the 16; reduce the first term the same, &c.

2. In 220 dolls. how many rials of plate? Ans. 2200 rials, Let the 10cts. be the 1st. term, and the given sum the 3d. or divide the cents in 220 dolls. by the cents in a rial.

CASE V.

With Portugal.

Accounts in Portugal. are kept in millreas, and reas. 1000 reas, make a millrea.

A millrea, is 1D. 24cts.

EXAMPLES.

1. If a bill of exchange be drawn upon Lisbon, for 7650 millreas, 97 reas; what is the value of the bill in dollars and cents, or Federal money? Ans. 9486D. 12cts. 28 rem. Make the given sum the 3d. term, 1 millrea the 1st. and the 2d. multiply the 3d. term by 1000, and add in the reas; reduce the 1st. term to the same name.

NOTE. When the reas are less than 100, place a cipher before them, or when less than 10, place two ciphers before them; thus, for the reas in the question, place 097.

2. If a bill of exchange be drawn upon a merchant in New York, for 2740D. 25cts. how much is it in millreas, &c, Ans. 2209 millreas 879 reas and 4 rem. Place the 124cts. for the 1st. term, 1 millrea the 2d. and 3d. if there be a remainder multiply by the reas in a millrea and di

vide again.

CASE VI.

With the United Netherlands.

for the

Accounts are here kept in guilders, stivers, groats and pen

1. Suppose a bill of exchange, for $295.60cts. be drawn upon a merchant in the United Netherlands; what is the value of this bill in guilders and stivers? Ans. 757G. 18st. 38 rem. Say as 39cts. is to 1 guilder, &c. If there be a remainder multiply it the stivers in a guilder, and divide again.

by

2. If a merchant, in the United Netherlands, has a bill of exchange for 360 guilders 14 stivers, to be paid by a mer

chant in Philadelphia; what is the value of this bill in Federal money? Ans. $140.67 cts, 3m. Say, as 1 guilder is to 39cts. so is, &c. Reduce the first and third terms to stivers.

CASE VII.

With Hamburgh.

Accounts in Hamburgh, are kept in marks, sous, and denierslubs, and by some rix dollars.

12 deniers-lubs, make 1 sous-lubs,

16 sous-lubs,

3 mark-lubs,

A mark-banco, is 33 cents.

EXAMPLES.

1 mark-lubs,

1 rix-dollar.

1. What is the value of 460 marks 9 sous in Federal money? Ans. 153D, 52cts. 4 rem.

Say, if 1 mark be 33 cts. &c. reduce the 1st. and 3d. terms, both into sous by then multiply the 33, by 3, and add in the one third; the answer will come in thirds, which divide by 3; to bring them into cents, &c.

2. If $750,25cts. be remitted to Hamburgh, what is the value of the bill in marks and sous? Ans. 2250 marks, 12 sous. Reduce the cents in the 1st. term to Reduce the cents in the 3d. term, to

Say, if 33 cts. be 1 mark, &c. thirds, as in the last example. thirds likewise, and proceed; multiply the remainder by 16, the sous in a mark, and divide again.

NOTE.-This case may be performed thus; divide the marks by 3, to bring them into dollars; and multiply the dollars by 3, to produce the

marks.

CASE VIII.

With the East Indies.

A tale of China is 148cts, a pagoda of India is 194cts. a rupee of Bengal is 55 cts. therefore to reduce East India money into Federal money, Observe.

Tales of China, multiply by 148 cents.

Pagodas of India,

Rupees of Bengal,

by 194

by 551

In this case, a statement by the Rule of Three, is unneces

sary.

EXAMPLES.

1. In 255 tales of China, how many dollars and cents.

Ans. 377D. 40cts.

nly by the number directed, and point off the dollars and cents ore taught.

2. In 80 pagodas of India, how many dollars and cents.

Ans. 155D. 20cts.

Multiply by 194 cents, the number directed.
3. In 86 rupees of Bengal, how many dollars?

Ans. $47.73cts. Multiply and take parts for, or you may multiply by 555 mills, and point off accordingly.

4. In 377 dollars 40 cents, how many tales of China?

Ans. 255 tales of China.

Divide the cents in the question by

ALLIGATION MEDIAL.

ALLIGATION MEDIAL is when the quantities and prices of several commodities are given to find the mean price of the mixture compounded of those things.

RULE.

As the whole composition is to its total value, so is any part of the composition to its mean price.

EXAMPLE FOR ILLUSTRATION.

gal. d. d. 10x 93 930 9x126=1134 12x 87=1044

1. If a merchant mixes 10 gallons of cherry wine, at 7s. 9d. per gallon, with 9 gallons of canary, at 10s. 6d. per. gal. 12 gallons of currant wine, at 7s. 3d. per gal. and 8 gallons of port wine, at 9s. 2d, per gallon; how may he sell this mixture per gallon? Ans. 8s. 61d. and 1 rem. For the 7s. 6d. in the price, I placed 93d. for the 10s. 6d. 126d, &c. setting all the prices down in pence; I then multiplied each quantity by its price; and added the whole quantity together; the sum was 39 gallons. I next added the value of each quantity together, and stated it, making the 39)3988( whole composition the 1st. term, the total value the 2d. and 1 gallon the 3d. When finished, it will bring 8s. 6d. 1qr. and 1 rem, which is the price of 1 gallon of this mixture. The learner may work it out, and see what the result is,

8x110= 880 gal,
: 3988

As.39

1

EXAMPLES.

2. Suppose a farmer mixes 20 bushels of rye, at 75cts. per bush, with 40 bush, of corn, at 60cts, per bush, and 30 bush. o

oats, at 35cts, per bush. what is the worth of 1 bush, of this mixture?

Ans. 55cts. Place the quantity and price as in the last example; set the first thus:

B.

cts.

20X75=1500 and so on.

3. If a grocer mix 3C, of sugar, at 75s, per C. with 2C, at 50s. and 1C, at 90s. per C. what is the price of 1C, of this mixture? Ans. 31. 9s. 2d.

Note-If the price of more than 1C. 1 bush, &c. be required, make such number the third term, and proceed as before,

4. If a dealer in tobacco mixes 40lbs, of tobacco, at 1s. 9d, with 16lbs. at 1s, 8d. and 19lbs, at 10d. what is the worth of a pound of this mixture? Ans, 1s, 6d. You may set the price down in pence, beginning thus. 40lbs. at 21 pence, &c.

5. Suppose a grocer would mix together three sorts of tea, viz, 20lbs. at 5s. with 35lbs, at 8s. and 25lbs, at 4s. what is the value of one pound of this mixture? Ans. 6 shillings. 6. Suppose a goldsmith melts together 12lbs. of silver bullion, of 9oz, fine, 14lbs. of 7oz. fine, and 14lbs. 4oz, fine; what is the quality, or fineness, of this composition? Ans. 6oz. 11pwts.

If, after dividing, there be a remainder, bring it into pennyweights, and divide again.

7. If 3lbs. of gold, of 20 carats fine. 2lbs. of 15 carats fine, and 1lb. of alloy to be melted together; what is the quality or fineness of this mass? Ans. 15 carats fine,

Placed thus: 3×20=60, &c. Place the alloy thus: 1X0= 8. Suppose a merchant wishes to mix some rum, as follows: 20 gals. at 10s. per gal, 50 gals. at 6s. and 10 gallons of water, at 0 per gal. what is the value of a gallon of this rum?

Ans. 6s. 3d,

VULGAR FRACTIONS.

A Fraction or broken number, is a part or parts of an unit or integer,* represented by two numbers, placed one above

teger means the whole of any thing.

the other, with a line drawn between them, thus;, one half, , four fifths, 1, eighteen twenty-sevenths.

18

The number below the line is called the denominator of the fraction; because it shows how many parts the unit or integer is broken or divided into, and is the divisor in division.

The number above the line, is called the numerator of the fraction; because it shows, or enumerates, how many of those parts are contained in the fraction, and is the remainder after division.

Try to remember which is the numerator, and which the denominator, they are as follows:

5 numerator,

6 denominator.

This fraction is called five-sixths; and, supposing it to be fivesixths of a yard, the denominator shows the number of parts the yard is to be divided into, and the numerator shows how many such parts are required to be considered.

4 8 145 59 168"

&c.

Vulgar fractions are proper, improper, compound, or mixed, A proper fraction is when the numerator (or upper figure,) is less than the denominator, (or lower figure,) as An improper fraction is when the numerator is greater than the denominator, as 2, 4, 672 A compound fraction is the fraction of a fraction, and may be known by the word of, between the parts, as of 1,3 of 1, of , &c.

3 15 148 &c.

1097

A mixed number, or fraction, is composed of a whole number and a fraction, as 31, 153, 12513, &c.

1

REDUCTION OF VULGAR FRACTIONS.

CASE I.

To reduce vulgar fractions, having different denominators, to fractions of equal value that shall have one common denomina

tor.

RULE.

Multiply each numerator, (taking them separately,) into all the denominators but its own, and the products will be the new numerators; then multiply all the denominators into one another for a common denominator.