billions; Trillions, tens of trillions, hundreds of trillions thousands of trillions, tens of thousands of trillions, hundreds of thousands of trillions; &c. without end. In what proportion do these numbers rise?

In a ten fold proportion; as 1; 10, ten ones; 100, one hundred ones; 1,000, one thousand ones; 10,000, ten thousand ones; 100,000, one hundred thousand ones; 1,000,000, one million of ones; 10,000,000, ten million of ones; &c. See Numeration Table No. 2, after No. 1.

A million has six ciphers on the right side of 1; as 1,000,000. A billion is equal to a million of millions, that is the product of a million when multiplied by itself; as, 1,000,000,000,000. A trillion is equal to a million multiplied by itself, and that product multilied again by a million, containing or requiring eighteen ciphers on the right hand of 1; thus, 1,000,000,000,000,000,000.

A Quatrillion is a million involved four times, and requires four times the number of ciphers on the right hand side of 1, that are in a million, viz. twenty-four; thus, 1,000,000,000,000,000,000,000,000.

Billions signify the involution or multiplication of millions twice; Trillions three times; Quatrillions four; Quintrillions five; Sextillions six; Septillions seven; Octillions eight; Nonillions nine; Decillions ten; Undecillions eleven; Duodecillions twelve; Triodecillions thirteen; &c. without end. The whole

of these sextuple numbers, or numbers by six, are formed by adding six ciphers or figures as before observed; for instance, a million contains six ciphers or places of figures; a billion twelve; a trillion eighteen ; a quatrillion twenty-four; and so for the residue.

But here let it be noted, that young students must not be puzzled with all these abstruse particulars, till they have advanced in the more profitable branches of arithmetic: the teacher must be the judge and su

perintend with discreetness in managing, and select from time to time, an appropriate part, suitable for the pupils. Nine or twelve figures at first, are abundantly sufficient.

SIMPLE MULTIPLICATION.

To the Teacher, but not for the learner till coming to Lesson 1st.

Now the Multiplication Table must be copied on the slates from Cards No. 8 and 9, and detached parts of it copied on pieces of paper for each one to look at occasionally-or the whole of the Tables may be hung round the room for daily inspection. After going over the lessons in simple Addition and Subtrac tion, and answering a few questions in Simple Multiplication, the learner may begin with Compound Addition of money.

The denominations of Federal Money however, are needless, except Dollars and Cents: These com prise the calculations of our business in the United States-they convey all our ideas respecting purchas es, sales, and amounts. When fractional parts of a cent are to be reckoned in the price of several articles, Addition or Multiplication will show the amount as in whole numbers.

EXAMPLE 1.

Bo't 255 finished penknives, at 75.4 cents* each; what is the amount? Answer, $192.27 cents.

* This number 75.4 must be read thus, "Seventy-five and fourtenths of a cent."

Operation as in whole numbers.

255 Penknives. 75.4 Cents.

1020

1275

1785

By the rule of Decimals, "point off as many fractional parts from the product, as are contained in the multiplicand and multiplier"-the remainder on the left hand will be whole numbers. Therefore, point off the 0, on the right hand, and the numbers 19227, will be whole numbers or cents; then cut off two figures of the residue, and those on the left will be dollars.

192 27.0

Rule to bring cents into dollars.

Cut off the two right hand figures of any number of cents, and those on the left will be dollars.

550 cents, or 5 dollars and 50 cents,

550

See Long Division, Lesson 13.

EXAMPLE 2.

Bo't 250 Copy-books, at 24.75* cents each, what did

they come to?

24.75 Cents.
250 Copy-books.

12375

4950

Operation.

Answer, $61.87

Here I point off two figures for decimal parts, because there are two decimals in the multiplicand; -then the figures 6187, are whole numbers or cents. Cut off the two right hand figures, 87, and those on the left are dollars. The fractional parts 50 first pointed off, may be called,, or 10, or 1, and when methodically inserted, they will stand thus, .50 or .5; and .5, equal of any thing.

61 87.50

* This number 24.75, must be read, "Twenty-four and seventyfive hundredths."

A little lecturing will soon show the learners how to value these fractional parts, and enable them to work United States currency, before they understand Decimals.*

.1 .2 .3 .4 .5 .6 .7 .8 .9 .25

.5 .75
15% or

75

These are of as small value as business will require ; and if the parties in commerce, know what part of a cent they agree to in the price of one or more articles, they may, by the above method of Multiplication, or by Addition, calculate the amount to a degree of minuteness. Consequently it is not requisite to trouble learners with a series of hard names; such as, "Ten mill make one cent; ten cents one dime; ten dimes one dollar; ten dollars one eagle," when one simple expression will answer every purpose intended,

viz :

One hundred Cents make One Dollar.

KEY TO CARD No. 10.

LESSON 1.

In 123456 pair of shoes, how many shoes? 2 Shoes in a pair.

246912

Twice 6 are 12; set down 2 and carry 1-twice 5 are 10, and one I carried makes 11; set down 1 and carry 1 twice 4 are 8, and one I carried makes 9; set down 9-twice 3 are 6; set down 6-twice 2 are 4; set down 4-twice 1 is 2; set down 2.

Write down the answer in letters, Two hundred and forty-six thousand, nine hundred and twelve.

*The modern mode of naming Fractions, is to call Vulgar Frac tions, fractions, and Decimal Fractions, decimals; but as books are printed differently we will not disagree about trifles: We will follow the usual method till the Teacher please to alter the phraseology.

Those who cannot read their answers in figures, may lose their place and number as in spelling.

Proof of Lesson first by Short Division.

2)246912

123456

NOTE.--When the divisor does not exceed 12, the work is called Short Division.

Say, 2 in 2, once; set down 1 under the 2. Tw in 4, twice; set down 2 under the 4. Two in 6. three times; set down 3 under the 6. Two in 9 four times and 1 over; set down 4 under the 9-carry the 1 over, to the left side of the 1, makes 11. Two in 11 five times and one over; set down 5 under the 1 and carry the 1 over to the left side of the 2, makes' 12. Two in 12, six times; set down 6 under the 2. Write down in letters, One hundred and twentythree thousand, four hundred and fifty-six.

LESSON 2.

In 654321 yards of three feet each, how many feet? Answer, 1962963,

Operation.

654321 Yards,

3 Feet in a yard,

1962963 Total, or Product in feet.

n

Three times 1 are 3-set down 3-3 times 2 are 6set down 6-three times 3 are 9-set down 9-thre e times 4 are 12-set down 2 and carry 1-three tim es 5 are 15, and 1 that I carried makes 16-set dow 6 and carry 1--three times 6 are 18, and 1 that I c rried makes 19-set down 19. Answer in words, One million, nine hundred and sixty-two thousand, nine hundred and sixty-three.

PROOF BY DIVISION.

3)1962963 Divisor and Dividend.
654321 Quotient or proof.

a