To reduce Spanish milled dollars to Livres Tournois. RULE. Multiply the dollars by 54, and the product will be livres. multiply them by 21, divide by 4, and the quotient will be livres. EXAMPLE. Reduce 100 Spanish dollars to livres.

To reduce New-England, &c. currency to Federal money

RULE.

1. If pounds only are given to be reduced, annex a cypher, and divide by 3; the quotient will be dollars. If there be a remainder, annex 3 cyphers thereto, and continue the division; the quotient will be cents and mills.

2. If pounds, shillings, pence and farthings are given, set down the pounds, and to the right hand write half the greatest even number of given shillings; then find how many farthings there are contained in the given pence and farthings, and if the sum exceed 12, increase it by 1, or if it exceed 36, increase it by 2, which sum set down to the right hand of half the even number of shillings before written, remembering to increase the second place, or the place next to shillings, by 5, if the shillings be an odd number, (as taught in reduction of decimals by inspection, to reduce shillings, &c. to the decimal of a pound.) To the whole sum thus produced annex a cypher, and divide the sum by 3, the same as before; cut off three right hand figures in the quotient, which will be cents and mills; the figures to the left will be dollars. 3. If there be no shillings, or only one shilling, in the given sum, so that there be no even number, write a cypher in place of half the even number of shillings, then proceed with the pence and farthings as before.

4. If pounds and an even number of shillings only be given, to the pounds annex half the even number of shillings, divide as before, and the quotient will be dollars.

EXAMPLE. Reduce £52 7 103 to dollars, cents, and mills.

3)523950

$174.65

Here to the right hand of the pounds, (52) I write 3, half the even number of the given shillings, (7) the farthings in 103d. (43) are inereased by 2, (45) because exceeding 36, and the second place increased by 5. because the sbillings were an odd number, make 95, which sum written to the right hand of the 3, a cypher annexed, and the sum divided by 3, gives the answer, 174 dollars, 65 cents.

EXAMPLE 2. Reduce £372 to dollars, cents, and mills.

3)3720

$1240 Ans.

To reduce Federal Money to New-England currency.

RULE. If the given sum be dollars only, multiply by 3 and cut off one figure. But if there be no mills, but dollars and cents, in the giv en sum, reduce it to mills by annexing cyphers; multiply the given sum by 3, cut off the four right hand figures, which will be decimals of a pound; the left hand figures will be the pounds.

To find the value of the decimals, double the first figure for shillings, and if the figure in the second place be 5, add another shilling; then call the figures in the second and third places, after deducting 5 in the second place, so many farthings, abating 1 when they are above 12, and 2 when they are above 36.

EXPLANATION. Having multiplied and cut off the four right hand figures, as the rule directs, to find the value of the figures cut off, I double the first figure, (3) which makes 6 for shillings; the figures in the second and third places,(21) abating 1 for being over twelve, (20) are to be considered so many farthings, which reduced to pence are 5. 3. In $432,45 how many pounds, 4. In 89 cents how many shit. shillings, pence and farthings? lings, pence and farthings?

To reduce New-York, &c. currency to Federal Money.

NOTE. The rule for reducing New-York, &c. currency to Feder al Money, is the same as that of New-England, only instead of dividing by 3 divide by 4, and proceed in every respect as in reduction of NewEngland currency.

EXAMPLES.

1. Reduce £47 7s. 10 d. to dollars, cents, and mills.

OPERATION.

4)47.3950

EXPLANATION. In this example, to the right of the pounds, (47) I write 3, half the even $118,48,7 number of given shillings, (7;) the farthings in 10 d. (43) increased by 2, (45 ;) because, exceeding 36. and the second place increased by 5, because the shillings were an odd number, make 95. which sum written to the right hand of the 3, a cypher annexed, and the sum divided by 4, gives the answer, 118 dollars, 48 cents, 71⁄2 mills.

To reduce Federal Money to New-York &c. currency. NOTE. Observe the same directions as in reducing to New-England currency, only instead of multiplying by 3 multiply by 4.

EXAMPLES.

1. Reduce 255 dollars, 40 cents, 6 mills, to pounds, shillings, pence, and farthings.

To reduce New-Jersey, Pennsylvania, Delaware, and Maryland curren

cy, to Federal Money.

RULE.

Reduce the given sum to pence, annex a cypher, divide these pence by 9, and add the quotient to the pence; from the sum point off three figures, which will be cents and mills; those to the left hand will be dollars. If there are farthings in the given sum, in the place of the cypher annex 2 for one farthing; 5 for 2 farthings; 7 for 3 farthings, and proceed as before. If the given sum be pounds only, multiply by 8, annex 3 cyphers to the product, and divide by 3; the quotient will be the answer, pointing of the three right band figures for cents and mills.

NOTE. The reason of dividing the pence by 9, when a cypher is annexed, is plain, as 9 pence is equal to 10 cents.

2. In £174 4s. 7d. how many dollars, cents and mills ?

174 4 7

20

3484

12

9)418150
46461

$464,611 Ans.

To reduce Federal Money to New-Jersey, Pennsylvania, Delaware and

Mary and currency.

RULE.

If there be no mills in the given sum, reduce it to mills by annexing cyphers; subtract one tenth of itself, the remainder, except the right hand figure, will be pence, which must be reduced to pounds; to find the value of the right hand figure, if it be 2 reckon it 2 farthings; if 7, reckon it 3 farthings.

EXAMPLE.

Reduce $42,456, to pounds, shillings, pence and farthings.

OPERATION.

$42,456

4,245

12)38211

EXPLANATION. Having subtracted one tenth of the given sum from itself, the right hand figure in the remainder (1) being reckoned 0 the other figures of the remainder (3821) being pence, I divide by 12, in doing which there is a remainder of 5, which are pence; these I also set down in the answer. £15 18 5 Ans. The shillings (318) dividend by 20, cutting off one figure from the divisor and one from the dividend, as is usually practised, give £15 18 5 which is the answer.

210)3118 5

1

COMPOUND MULTIPLICATION.

Compound Multiplication is when the multiplicand consists of several denominations. It is extremely useful in finding the value of goods, &c.

N. B. Observe one general rule in this, viz. multiply the price by the quantity, and as in Compound Addition we carry from the lowest denomination to the next higher, so we begin and carry in Compound Multiplication,

CASE I.

When the quantity does not exceed 12 yards, pounds, &c. set down the price of one yard or pound, and place the quantity underneath the lowest denomination for a multiplier. Begin by multiplying the lowest denomination, and carry from one denomination to another, as above directed.

EXAMPLES.

1. What will 5 yards of cloth come to, in old lawful and in Federal Money, at 9s. 4d. per yard?

OPERATIONS.

4 price of 1 yard,
5 yards.

Ans. £2 6 8 old lawful.
Here I 5 times 4 is 20 pence,
1s. 8d, i set down 8 and carry 1,
saying 5 times 9 is 45, and 1 1 carry
are 46 £2 6s.

CASE II.

Ans. $0,97,3

When the quantity exceeds 12, you must multiply by two such numhers as when multiplied together will produce the given quantity,