Note 1.--Cyphers on the right of the divisor may be omitted in the operation, observing to separate as many figures from the right of the dividend, which annex to the remainder.

EXAMPLES.

1. Divide 146340 by 5400. Facit 27, remainder 540. 5400)1463|40(27

1345680000 by 120000

manner.

Note 2.-When the divisor is the exact product of any two factors in the multiplication table, the division may be performed thus:--Divide first by one of the factors agreeably to Rule I.; then divide the quotient by the other factor in the same When a remainder occu in the first operation and none in the last, it is the true one: but a remainder in the last operation must be multiplied by the first divisor, and its product added to the first remainder (if any) for the true remainder.

EXAMPLES.

1. Divide 46508974 by 96. Facit 484468. Rem. 46. 8)46508974

12)5813621-6 first remainder.

484468-5 last remainder.

8

40

6

46 true remainder.

2. Divide

3.

4.

SUBTRACTION AND DIVISION.

19

34320 by 99 Facit 346 Rem. 66 20208 by 48

5704392 by 108

APPLICATION.

421

1. As division is a short method of discovering how often one number is contained in another, how often is 3 contained in 3699 ? Ans. 1233 times.

2. How many times is 25 contained in 132 ? Ans. 5 times with 7 over.

3. There are 12 pence in one shilling. How many shillings are there in 480 pence ?

Ans. 40.

4. The price of a pair of shoes is 2 dollars. How many pair may be had for 56 dollars?

Ans. 28.

5. Fifty-four apples are to be divided equally between

2 boys. How many must each boy have?

Ans. 27.

6. Suppose a man travel 40 miles a day: how many days will he be in travelling 240 miles?

Ans. 6.

ADDITION AND DIVISION.

1. If I add 167, 394, and 447; and divide their amount by 12: what number will result?

Ans. 84.

2. A person has in money 5000 dollars; in bankstock, 3500 dollars; and in merchandize 12500 dollars. He intends to divide this property equally among his 3 sons. What will be the share of each son?

Ans. 7000 dollars. 3. Suppose a farmer, who has a plantation of 520 acres, buys an adjoining one of 375 acres, and divides the whole into five equal portions: how many acres will there be in each portion?

SUBTRACTION AND DIVISION.

Ans. 179.

1. Subtract 2468 from 5796, and divide the remainder by 26. Result 128. 2. William hought 12 pears: he kept 6 of them, and divided the rest between his two sisters. How many did each sister receive?

Ans. 3.

3. A man, at his decease, left property amounting to 12426 pounds. He directed in his will that 1000 pounds should be given to his niece; and that the

remainder of the property should be divided equally between his two nephews. What is the share of each nephew? Ans. 5713 pounds.

MULTIPLICATION AND DIVISION.

1. Multiply 145 by 12, and divide the product by 6. Result 290.

2. To find how many dollars are contained in any number of pounds, we multiply the pounds by 8, and divide their product by 3. How many dollars are there in 456 pounds?

Ans. 1216. 3. To find how many pounds are contained in any number of dollars, we multiply the dollars by 3, and divide their product by 8. How many pounds are

there in 8576 dollars?

FEDERAL MONEY,

Ans. 3216.

OR MONEY OF THE UNITED STATES.

The denominations of Federal Money are; Eagle, Dollar, Dime, Cent, and Mill.

1 dollar, D. or $.
1 eagle.

10 dimes (or 100 cts. 10 dollars These denominations have precisely the same relative values as those of unit, ten, hundred, &c., and are also similarly ranged in Numeration. Federal money is therefore added, subtracted, multiplied, and divided by the same rules that are given for Simple Addition, Subtraction, Multiplication, and Division.

It must be remarked, however, that in writing sums of Federal Money, parts of a cent are generally used instead of mills; and that, in reading those sums, neither the eagles nor dimes are mentioned: the former being considered as tens of dollars; and the latter as tens of cents.

The parts or fractions of a cent, used instead of mills, are expressed by two numbers, placed one above the other, with a line drawn between them. The under number denotes the part; and the upper one informs how many of that part are designed to be expressed: as,

NUMERATION OF FEDERAL MONEY.

21

one fourth; three fourths; one third; two thirds; a half.

NUMERATION OF FEDERAL MONEY.

In writing sums of Federal Money, the cents are placed on the right of the dollars, and are separated from them by a point. If there are not more than nine cents in the sum, a cypher is put in the tens' place; and if there are no cents, two cyphers are used.

If the point which separates the dollars from the cents be removed or supposed to be removed, the sum may be considered as cents only: and when the sum is cents only, if two figures be separated from the right, all on the left of these will be dollars. See the following

To be read by the learner as dollars and cents, and also as cents only.

1.49 3.26 4.75 9.18 17.90 21.09 14.02 125.00 426.00 900.00 340.061 3911.101 4006.183 76420.01 19560.00 11904.10 4896.73 400.001 4500.061.

The following to be written in figures: Seventeen dollars and fifty-two cents. Forty-nine dollars and seventeen cents. Eighty-four dollars and ten cents. Sixty dollars and twelve and a half cents. Two hundred and fourteen dollars and six cents and a half. Three hundred dollars. One thousand dollars. Seven thousand dollars and four cents.

ADDITION OF FEDERAL MONEY.

RULE.

Place the sums one under another, with dollars under dollars and cents under cents; then, if there are no fractions, proceed in the same manner as in Simple Addition, observing to separate the cents of the amount from the dollars thereof, by placing a point between them. When fractions occur, find their amount in fourths;* consider how many cents these fourths will make e; add them with the cents in the right hand column, and proceed as before directed.

Proof; as in Simple Addition.

Note.-To find how many cents there are in any number of fourths of a cent, divide them by 4, and the quotient will be cents.

* In Addition, Subtraction, and Division of Federal Money, all fraotions less than a fourth are omitted, and every fraction greater than a fourth is reckoned a half, three fourths, or a whole cent, according to its value: so that in these three operations, no fractions are used excepting fourths-a half being counted two fourths. But in Multiplication it is often material that no fraction be omitted, and that all fractions should be estimated at their real value.