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22. A merchant in Holland wishes to change 4376 florins currency into bank, the agio åt 4 per cento; how many pounds Flemish bank must he receive ?

Ans. 701L. Iflo. 13 stiv. 13 pen. 23. In 290L. 11. 10d. sterling, how many pounds Flem. ish; exchange at 33s. 10d. Flemish per pound sterling, and agio at 4 per cent.

Ans. 513L. 14s. Id. 24. A merchant in Philadelphia, receives per the ship London Packet from London, a parcel of goods, charged in the invoice at 450L. 10s. sterling, which he immediately sells at an advance of 78 per cent.: what is the amount in Pennsylvania currency; also in Federal money?

S 301L. 175.91d. Ans.

2138 dols. 37 cts. 25. Amsterdam changes on London 34s. 3d. per L. sterling, and on Lisbon, at 52d. Flemnish for 400 reas; how thien ought the exchange to go between London and Lisbon ?

Ans. 750+ sterling per millrea.

VULGAR FRACTIONS.

A vulgar fraction is a part, or parts of a unit or integer, expressed by two numbers, placed one above the other, with a line drawn between them; as one fourth, s two thirds.

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

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

Vulgar fractions are either proper, improper, compound or mixed.

A proper fraction is that of which the numerator is less than the denominator; as į , }, &c.

An improper fraction is that of which the numerator is equal to, or greater than the denominator; as $ 3, ii, &c.

A compound fraction is a fraction of a fraction; as į of or of 1 of 18, &c.

A mixed number consists of a whole number and a frac, tion; as 4, 7j, &c.

3

REDUCTION OF VULGAR FRACTIONS.

CASE 1.
To reduce a fraction to its lowest terms.

RULE.
Divide the greater term by the less, and that divisor bị
the remainder, till nothing be left; the last divisor will be
the common measure, by which divide both terms, for the
fraction required : or,

Divide the terms by any number that will divide them both without a remainder, and divide the quotients in the same manner, and soon, till no number greater than I will divide them; the fraction is then at its lowest terms.

Note.--If the common measure be 1, the fraction is already at its lowest terms. Ciphers on the right hand of both terms may be rejected; thus 400 *

EXAMPLES..

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12 25°

1. Reduce je to its lowest terins. 72)96(2

Or thus : 72

12) 2)

== Result. Com. measure 24)72(3

72 24= Result. 2. Reduce a to its lowest terms.

Result { 3. Reduce to its lowest terms.

Result 4. Reduce to its lowest terms.

Result, 34. 5. Reduce 60- to its lowest terms.

Result 2 6. Reduce 14 to its lowest terms.

Result 42 7. Reduce 2344 'to its lowest terms. Result 1:

CASE 2. To reduce several fractions to others, retaining the same value, and to have a common denominator.

RULE. Reduce the given fractions to their lowest terms; then multiply each numerator into all the denominators but its own, for its respective numerator; and all the denominators into each other, for a common denominator.

Note.This case and case 1, prove each other.

85

EXAMPLES.
1. Reduce , $, and to a common denominator.

3 X 5 X 6 90
4 X 4 X 6 = 96 Numerators.

5 X 4 X 5 100
4 X 5 X 6 = 120 Common denominator.

Result and 160 2. Reduce j , and , to a common denominator.

Result 32, 48, 40 3. Reduce j, s, and to a common denominator.

Result in ,24,252 4. Reduce não to, and to a common denominator.

Result 135, 560, 504, 720. 5. Reduce , 1, 5, and to a common denominator.

Result 192, 120-200

60 2479 240 2409 240

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CASE S. To reducé a mixed number to an improper fraction.

RULE. Multiply the whole number by the denominator of the fraction, and add the numerator to the product for a new numerator, which place over the given denominator.

EXAMPLES. 1.- Reduce 12 to an improper fraction.

Result 112. 12 x 9 + 4 =

new numerator. ?

denominator. 2. Reduce 1914 to an improper fraction. Result 354 3. Reduce 127 to an improper fraction. Result 64 4. Reduce 100to an improper fraction. Result 591 . 5. Reduce 5141 to an improper fraction. Result 823 6. Reduce 473177 to an improper fraction.

Result 397941.

CASE 4. To reduce an improper fraction to a whole or mixed number.

RULE.
Divide the upper term by the lower.
Note-This case and case 3 prove each other,

M2

5: 5919

16:

8400

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17 2. Reduce 31to its proper terms.

Result 164 3. Reduce 14 to its proper terms.

Result 817 4. Reduce to its proper terms.

Result 25 5. Reduce 3848 to its proper terms.

Result 1831 6. Reduce 12.25 to its proper terms.

Result 5611

CASE 5.
To reduce a compound fraction to a single one.

RULE.

Multiply all the numerators together for a new nume: Tator, and all the denominators for a new denominator

Note. Like figures in the numerators and denominators may be cancelled, and frequently others contracted, by taking their aliquot parts.

EXAMPLES 1. Reduce of of to a single fraction. Result 4. 2 X 3 X 4 = 24

2 Or, of of = jó = g: 3 X 4 X 5 60

3 4 Or cancelled, -of - of

ş as before. *

5 2. Reduce of of io to a single fraction.

Result 1 = 3. .Reduce of of 7 to a single fraction.

Result 1 = 1 . Reduce 4 of 7, of to a single fraction.

Result =

Result 60

5. Reduce ii of 1 of îl to a single fraction.

Result 300=143 6. Reduce 14 of of to a single fraction.

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S='s CASE 6. To reduce the fraction of one denomination to the fraction of another, but greater, retaining the same value.

RULE. Make the fraction a compound one, by comparing it with all the denominations between it and that to which it is to be reduced; which fraction reduce to a single one.

EXAMPLES 1. Reduce of a penny to the fraction of a pound.

of ty of t = = z of a pound. 2. Reduce of a penny to the fraction of a pound.

Result FöL. 3. Reduce of a farthing to the fraction of a shilling.

Result das 4. Reduce of a cent to the fraction of a dollar.

Result dodol. 5. Reduce of an oz. troy, to the fraction of a pound.

Result Álb. 6. Reduce of a lb. avoirdupois, to the fraction of a cwt.

Result zcwt. 7. Reduce is of a pint of wine to the fraction of a hhd.

Result yżshhd. 8. Reduce ti of a minute to the fraction of a day,

Result 15 day.

CASE 7. To reduce the fraction of one denomination to the fraction of another, but less, retaining the same value.

RULE. Multiply the given numerator by the parts of the denomination between it and that to which it is to be reduced, for a new.numerator, and place it over the given denomitor; which reduce to its lowest terms.

19te. This case and ease sixth prove each other.

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