3. What is the amount of the following sums?

Compound Subtraction is taking a sum of different denominations, and of less value, from a sum of different denominations, and of greater value.

RULE.-Place the numbers as in compound addition, and, commencing at the right hand, subtract the figure in the right-hand column from the figure above it in the minuend, and place the remainder directly under the right-hand column. If the figure in the minuend be less than the figure under it, in the subtrahend, add to it the figure above it, and from that amount subtract the figure in the subtrahend, and place the remainder directly below. Whenever the number above the minuend is added to it, 1 must be added to the next left-hand figure in the subtrahend before subtracting.

PROOF.-Add the remainder to the subtrahend, and if the work is right, the amount will agree with the minuend.

1. From £82 1 s. 1 d. 1 qr. take £81 19 s. 11 d. 3 qrs.

2. A note bearing date Dec. 28, 1826, was paid Jan. 2, 1827; how long was it at interest?

OPERATION. 12 30

1827 0 2 1826 11 28

0 0 4

In this example, I set down the later date, 1827, and 2 days on the next year. As there are only 2 days on the year after 227, I place a cipher in the column of months. Under this date I write the former one, 1826 years, 11 months, and 28 days, and subtract according to the rule.

3. What is the difference of time between the 13th day of June, 1838, and the 27th day of April, 1841 ?

Ans. 2 yrs. 10 mo. 14 days.

COMPOUND MULTIPLICATION.

Compound Multiplication teaches to repeat a compound number a certain number of times, or as many times as there are units and parts of units in the multiplier.

RULE.-Place the multiplier under the right-hand column of the multiplicand, and multiply the figures of the lowest denomination by the multiplier, setting down as in addition. Multiply the figures of the next higher denomination, by the multiplier, and to this product add the figure or figures, (if any,) that were to be carried to this denomination from the one lower. Proceed in this manner till you come to the highest denomination in the table employed, when you set down the whole number.

1. Multiply £82 8 s. 11 d. 3 qrs. by 8.

Ans. £32 14 s. 9 d.

Ans. £659 11 10

2. Multiply £3 12 s. 9 d. by 9.

3. Multiply 18 lb. 15 oz. 13 drs. by 9.

Ans. 1 cwt. 2 qrs. 20 lb. 14 oz. 5 dr. 4. A man bought 4 lots of wheat, each of which contained 8 bushels, 3 pecks, and 2 quarts; how much wheat did he buy? Ans. 35 bushels and 1 peck.

COMPOUND DIVISION.

Compound Division teaches to divide a compound number. RULE. Place the divisor at the right hand of the divi dend, and seek how many times it is contained in the highest

denomination of the dividend. Place the quotient figure under the divisor, and multiply as in simple numbers. Subtract, and reduce the remainder to the next lower denomination, and to the product add this lower denomination. Divide as before, and proceed in this manner to the close.

2. Bought 139 yards of cloth for £461 11 s. 11 d.; what was the cost per yard?

Ans. £3 6 s. 5 d.

3. Bought 84 pipes of brandy, containing 9468 gal. 1 qt. 1 pt.; how much in a pipe?

Ans. 112 gal. 2 qts. 1 pt. 3 gills.

X. Reduction of Currencies.

Previous to 1786, all calculations in money, throughout the United States, were made in pounds, shillings, pence and farthings. But these denominations, although the same in name as those of English money, had different values in different places. Thus, one dollar is reckoned

TO REDUCE POUNDS, SHILLINGS, PENCE, AND FARTHINGS, OF ANY GIVEN CURRENCY, TO FEDERAL MONEY.

Reduce the pounds and shillings in the given sum to pence, and the farthings to the decimal of a penny. Then divide by the number of pence ( in the currency to be reduced) that make a dollar, and the quotient will be the answer.

NOTE.-The process of reduction may be abbreviated in certain cases, by reducing the given sum to shillings and deci mal of a skilling, and dividing by the number of shillings (of the currency to be reduced) that make a dollar.