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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. I lş. 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. 175.9 d. Ans.

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

Ans. 75 4+sterling per milliea.

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VULGAR FRACTIONS.

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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

An improper fraction is that of which the numerator is equal to, or greater than the denominator; as 4, 3, 14, &c.

A compound fraction is a fraction of a fraction; as į of Å, or sof of &c.

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

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å }, &c.

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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 by the remainder, till nothing be left; the tast 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 so on, 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. 1. Reduce je to its lowest terins. 72)96(1

Or thus : 72

12) 2 == Result.

* Com. measure 24)72(3

72

24) = Result. 2. Reduce zz to its lowest terms.

Results: 3. Reduce me to its lowest terms.

Result 4. Reduce 7 to its lowest terms.

Result, 4. 5. Reduce 60to its lowest terms.

Result 12 6. Reduce 84 to its lowest terms.

Result 42 7. Reduce 344 'to its lowest terms. Result 7

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 ), prove each other.

48

125

25

85

1536

96

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48 40

287 288 2884 288

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2409 240 2400 240

EXAMPLES
1. Reduce i, f, 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 19 and 100

90

120 120 2. Reduce , and go to a common denominator.

Result 2, 3. Reduce 1, s, and to a common denominator.

Result 144, 192, 240, 25 2 4. Reduce , o to, and to a common denominator.

Result 356, 3908409 810*

560 504 720. 5. Reduce $, in, and to a common denominator.

Result 192, 120.-200

CASE S. To reduce 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

new numerator. 12 x 9 + 4 = 112

denominator. 2. Reduce 1915 to an improper fraction. Result 35 4 3. Reduce 127 to an improper fraction.

Result 4. Reduce 1001; to an improper fraction. Result 5919 5. Reduce 5141 to an improper fraction. Result 82%. 6. Reduce 473100 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.

18 64 5

16

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EXAMPLĖS. 1. Reduce 19 to its proper terms.

17)219(1214

17

Result in

49
34

15

19

18

17 2. Reduce 3117 to its proper terms.

Result 1616

Result 811 3. Reduce 44 to its proper terms. 4. Reduce 126 to its proper terms.

Result 2 m

Result 18341 5. Reduce 3848 to its proper terms. 6. Reduce 12.15 to its proper terms.

Result 5611

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

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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 2 X 3 X 4 = 24

Or, jof of == : 3 X 4 X 5 = 60

2

3 4 Or cancelled, of - of

šas before. 3 *

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

Result = 16 3. Reduce of ofto a single fraction.

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

Result 1:11. - =

2

140

3003
4872

1 4

168

5 14

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5. Reduce 11 of 11 of z, to a single fraction.

Result = 113 6. Reduce ii of of į to a single fraction.

Result 60

= 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.

8 1 16

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

Result zöol.
3. Reduce į of a farthing to the fraction of a shilling.

Result 76s. 4. Reduce of a cent to the fraction of a dollar.

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

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

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

Result ahhd. 8. Reduce îi 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 deno. mination between it and that to which it is to be reduced, for a new. numerator, and place it over the given denomi. tor; which reduce to its lowest terms.

Nøte. This case and ease sixth prove each other.

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