20. Change 794 guilders, 15 stivers, current money, into bank florins, agio 43 per cent.

Result 761guild. Sstiv. 11 pennings. 21. Change 761 guilders, 9 stivers bank, into current money, agio 43 per cent.

Result 794guild. 15stiv. 4 pennings. 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. 13stiv. 13pen. 23. In 290L. 11s. 10d. sterling, how many pounds Flemish; exchange at 33s. 10d. Flemish bank per pound sterling and agio at 44 per cent.? Ans. 513L. 14s. 1d.

24. A merchant in Philadelphia receives 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?

801L. 17s. 94d.

Ans. 2138dols. 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. 75 d. +sterling per millrea.

VULGAR FRACTIONS.

A vulgar fraction is a part, or parts of a unit or integer expressed by two numbers, piaced one above the other, with a line drawn between them; as 4 one fourth, two thirds.

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

The denominator denotes the part, and the numerator informs how many of that part are designed to be expressed.

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.

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

A compound fraction is a fraction of a fraction; as of 3, or off of, &c.

A mixed number consists of a whole number and a fraction; 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. Divide both terms by the common measure, and the quotients will be the numerator and denominator of 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 1 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 #88=4.

CASE 2.

To reduce several fractions to others, of the same value, and having a common denominator.

RULE.

Multiply each numerator into all the denominators but its own, for its respective numerator; and all the denominators into each other, for a common denomi

nator.

Result,,.

3. Reduce,, %, and 7 to a common denominator.

Result 금, 금융, 금융, 금융중.

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

504 560

Result 7, 8, 894, 728.

5. Reduce,,, and to a common denominator. Result 18, 18, 228, 178.

CASE 3.

200

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, under which place the given denomi

nator.

EXAMPLES.

1. Reduce 12 to an improper fraction. Result 142. new numerator. 112 denominator. 9

12×9+4=112

2. Reduce 1918 to an improper fraction.
3. Reduce 124 to an improper fraction.
4. Reduce 100 to an improper fraction.

354

Result 5.
Result.

ខ.

Result 5.

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.

2. Reduce 1 to its proper terms. 3. Reduce to its proper terms. 4. Reduce 126 to its proper terms. 5. Reduce 3848 to its proper terms. 6. Reduce 15 to its proper terms.

48

ΣΤ

CASE 5.

Result 16.
Result 8

Result 28.

Result 183

Result 56

To reduce a compound fraction to a single one.

RULE.

Multiply the numerators together for a new numerator, 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 3. 2333

of 1 of 2 to a single fraction.

5. Reduce Result 3893-11. 6. Reduce of of to a single fraction.

372

CASE 6.

Result 60

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. 5 of 11 of of a pound. 2. Reduce of a penny to the fraction of a pound.

20 14.

Result L.

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

Results.

4. Reduce of a cent to the fraction of a dollar. 90

Result dol.

Result lb.

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