Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

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

Ans. 701L. 1flo. 13 stiv. 13 pen.

23. In 290L. Ils. 10d. sterling, how many pounds Flemish; exchange at 33s. 10d. Flemish per pound sterling, and agio at 41 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?

- Ans.

2138 dols. 37 cts. 25. Amsterdam changes on London 34s. 3d. per L. sterling, and on Lisbon, at 52d. Flemish for 400 reas; how then ought the exchange to go between London and Lisbon ? Ans. 753d+sterling per millrça.

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, 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 1, 2, 7, &c.

3

An improper fraction is that of which the numerator is equal to, or greater than the denominator; as 4, 3, 12, &c. A compound fraction is a fraction of a fraction; as of 2, or of of %, &c.

A mixed number consists of a whole number and a frac tion; as 43, 73, &c.

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 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 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

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

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.

[blocks in formation]

2. Reduce, 2, and §, to a common denominator.

Result 3,4

32 48 40

3. Reduce,, and to a common denominator.

Result 144 192 240 252

288 288 288 288

4. Reduce,,, and to a common denominator.

Result 50' 340' 840° 560 504 720.

5. Reduce,,, and to a common denominator. Result 192 120 200 60 240 240 240 240

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 124 to an improper fraction.

Result 112.

new numerator.

12 × 9 + 4 = 132 denominator.

2. Reduce 1913 to an improper fraction.
3. Reduce 12 to an improper fraction.
4. Reduce 1001 to an improper fraction.
5. Reduce 514 to an improper fraction.
6. Reduce 473141 to an improper fraction.

CASE 4.

Result 354.

18

5.

Result 64 Result 5919. Result 8229,

59

16

[blocks in formation]

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.

[blocks in formation]

To reduce a compound fraction to a single one.

RULE.

Multiply all the numerators together for a new nume. rator, 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.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]

*. Reduce & of 7 of to a single fraction.

[ocr errors]

-

[ocr errors]

Result 1123

5. Reduce 11 of 1 of 2 to a single fraction.

Result 3093-111:

6. Reduce 12 of of to a single fraction.

CASE 6.

4872

Result 60

=

143. 232

To reduce the fraction of one denomination to the fraction of another, but greater, retaining the same value.

[merged small][ocr errors]

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.

[blocks in formation]

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

Results.

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

Result dol.

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

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

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

8. Reduce 10 of a minute to the fraction of a day.

CASE 7.

Result day.

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.

Note. This case and case sixth prove each other.

« ΠροηγούμενηΣυνέχεια »