containing six yards and one nail; how many yards did both pieces contain?

18. William bought two quires and sixteen sheets of paper at one store, and one quire and eight sheets of paper at another store; how many quires of paper did he buy at both places?

Note.-To TEACHERS. The learner should be required to answer, mentally, the preceding questions, and various others of an equally simple nature, before he is required to use a slate.

RULE.

Q. How must the different numbers, or quantities to be added, be placed in Compound Addition ?

A. They must be placed so that the numbers of the same denomination will stand directly under each other.

Q. Where must you begin to add in Compound Addition?

A. At the right hand, or lowest denomination, as in Simple Addition.

Q. Why do you begin to add at the right hand denomination?

A. Because the different denominations increase in quantity from the right hand to the left, as in Simple Addition.

Q. How must the first column be added? A. The same as in Simple Addition.

Q. What sum must you set down, and what must you carry to the next column in Compound Addition?

A. The amount must be divided by the num ber that it takes of that denomination to make one in the next higher denomination, and the remainder, if there be any, must be set down, and the quotient must be carried to the next higher denomination.

Q. How must the left hand, or highest denomination be added?

A. It must be added up, and the whole amount set down, as in Simple Addition.

EXAMPLES

For Theoretical Exercise on a Slate.

FEDERAL MONEY.

1. William paid 1 dime, 2 cents, and 5 mills for a spelling-book, 3 dimes and 1 cent for an arithmetick, 2 dimes and 5 cents for a slate, 4 dimes and 5 cents for a geography, and 7 dimes and 5 cents for a dictionary; how much did he pay for all of them? Ans. 1 dollar, 8 dimês, 8 cents, and 5 mills.

EXPLANATIONS.

d. c. m.

1, 2, 5

3, 1, 0

2, 5, 0

Federal money increases in a tenfold proportion, and is, in its simplicity, nearly allied to whole numbers; and, consequently, the rule which you used in adding whole numbers, may be used. You will remember, that the first thing to be done is to place the different denominations directly under each other; $1,8, 8, 5 as, dollars under dollars dimes under

4, 5, 0 7, 5, 0

dimes, cents under cents, and mills under mills. You must place a comma between the dollars, dimes, cents, and mills, then add as in whole numbers. If your sum consists of dollars and mills only, or of dollars and cents only, you must place a cipher in the vacant place, as in the present example. Accounts are generally kept, however, in dollars, cents, and mills, without a comma being used between the dimes and cents. Beginning at the right hand column, you must say, 5 is five, that is, five mills; you must set down the 5 in the place of mills. As there is nothing to be carried to the next column, you must begin anew with the 5 in the place of cents, and say, 5 and 5 are ten, and 5 make fifteen, 1 makes sixteen, and 2 make eighteen cents, that is, one dime and eight cents; you must set down the 8 under the column of cents, and add, or carry, the one dime to the next column, the place of dimes. Thus, one dime added to the 7, in the column of dimes, make eight, 4 make twelve, 2make fourteen, 3 make seventeen, and 1 make eighteen dimes, that is, one dollar and eight dimes; you must set down the 8 under the column of dimes, and carry the one dollar to the next column, the place of dollars, which makes the whole amount 1 dollar, 8 dimes, 8 cents, and 5 mills.

PROOF.

The methods of proof are the same in Compound Addition as in Simple Addition.

2. James bought a suit of clothes for 25 dollars and 75 cents, a hat for 7 dollars and 25 cents, a pair of boots for 6 dollars, and a watch for 18 dollars, 37 cents, and 5 mills; how much did he pay for the whole? Ans. $57,37,5.

EXPLANATIONS.

c. m.

25, 75, 0

7, 25, 0 6, 00, 0 18, 37, 5

$57, 37, 5

You will perceive that, in this example, I have placed the comma between dollars, cents, and mills only, as accounts are thus generally kept, without reference to dimes. You must begin, as before, with the column at the right hand, and say, 5 is five, that is, five mills; you must set down the 5 in the place of mills. As there is nothing to be carried to the next column, you must begin anew with the 7, in the place of cents, and say, 7 and 5 are twelve, and 5 make seventeen cents; you must set down the 7 under the right hand column of cents, and add, or carry, one to the next column, the tens of cents. Thus, one ten added to the 3, in the next column, make four, 2 make six, and 7 make thirteen dimes, or tens of cents, that is, one dollar and thirty cents; you must set down the 3 under the second column of cents, or place of dimes, and add, or carry, the one to the next column, the place of dollars. Thus, one dollar added to the 8, in the next column, make nine, 6 make fifteen, 7 make twenty-two, and 5 make twenty-seven dollars, that is, seven units of dollars, and two tens of dollars; you must set down the 7 in the first column of dollars, and add, or carry, two to the next column, the place of tens of dollars. Thus, two tens of dollars added to the 1, in the second column of dollars, make three, and 2 make five, that is, five tens of dollars; you must set down the 5 in the second column of dollars. Thus you have fifty-seven dollars, thirty-seven cents, and five mills, and your work is done."

By paying particular attention to the use of the

comma, in separating the dollars, cents, and mills, you will be able to work any sum in Addition of federal money; for, indeed, the proper placing of the comma is the only operation which distinguishes this from Simple Addition. I shall, therefore, give you a few examples for farther exercise, and pass to the next part of this subject.

1. A man bought a firkin of butter for £6 9s. 7d. 2qr., a barrel of pork for £8 7s. 8d., a cag of molasses for £2 5s. 6d. 3qr., and a barrel of flour for £3 10s.; how much did he pay for the whole? Ans. £20 12s. 10d. 1gr.