11. Divide 6274 by 5 5) 6274

1254-4

EXAMPLES.

Here I say 5 in 6 once and one over; the one I call ten and 2 are 12, then 5 in 12 twice 2 over, I call this 20 and 7 are 27; 5 in 27, 5

times and two over; then 5 in 24, 4 times and 4 over,

is the remainder.

which

m 2. When the divisor is a composite number. Divide first by one of the component parts, and the quotient, arising from that division, by the other. Multiply the first divisor by the last remainder, and to the product add the first remainder, which will give the true remainder.

n 3. When there are cyphers at the right hand of the divisor. Cut them off, also cut off an equal number of figures from the right hand of the dividend, and when the operation is performed, bring the figures cut off, down to the right hand of the remainder.

{

EXAMPLES.

27, Divide 364006 by 6400 23. Divide 73464467 by 64300

64,00)3640,06(56

320

440

384

5606 remainder

29. Divide 76546037 by 250000

Quo. 306 Rem. 46037

30. Divide 43563754 by 63400

Quo. 687 Rem. 7954

643,00)734614,67(1142

o 4. When the divisor is 10, 100, 1000, or a unit with any number of cyphers. Cut off as many figures from the right hand of the dividend as there are cyphers in the divisor, and the work is done. The figures which remain of the dividend are the quotient, those cut off the remainder.

EXAMPLES.

31. Divide 64073 by 100, 32. Divide 6457643 by 1000 100)640,73( 1000)6457,643

APPLICATION.

1. Suppose an estate of $51800 to be divided among 8 sons: how much would each one receive? Ans. $6475 2. Suppose a man's income to be 1095 dollars a years there being 365 days in a year: how much is that per day? Ans. 3 dollars. 3. A field of 27 acres produces 675 bushels of wheat: how much is that per acre? Ans. 25 bushels. 4. Suppose 49875 days work to be performed by 1425 men: how many days did each man labour? Ans. 35 days. 5. Suppose the whole expense of a gentleman's family to be 2100 dollars a year, and the expense of each individual member 120 dollars: of how many persons does the family consist? Ans, 20,

QUESTIONS.

a What is Simple Division?

b What are the given numbers called?

c What is the answer or number sought called? d Is there any uncertain part in division?

e What is the first thing to be done to perform the operation? f What is the second?

g What is the third?

h What is the fourth?

i How should the given numbers stand for division? j How is division proved?

k How may division be proved by casting out the 9s? 7 When the divisor does not exceed 12, how are you to proceed?

m When the divisor is a composite number, how may the work be done?

n How are you to proceed when there are cyphers on the right hand of the divisor?

o When the divisor is 1 with cyphers, how may the operation be contracted?

FEDERAL MONEY.

a Federal Money is the coin of the United States, estab lished by Congress in 1786. As it is the nearest allied to whole numbers, and more useful in the common business of life than almost any part of Arithmetick, I have thought proper to introduce it in this place, as a kind of Supplement to the simple rules.

The denominations are exhibited in the following

By the foregoing table, it is plain that the denominations in Federal Money, have the same relative value as units, teas, hundreds, &c. and are arranged in a similar manner c] in numeration. The same rules, given for Simple Addition, Subtraction, Multiplication and Division will apply in Addition, Subtraction, Multiplication and Division of d] Federal Money; except in cases where the parts of a cent are expressed by two numbers, placed one above the other, thus, in which case the is to be called 2, the 11, and the, 3; and one to be carried to the place of cents for every 4 thus reckoned.

It is customary, in reckoning Federal Money, to omit the name of eagle, and dime, and sometimes mill, and reckon e] only dollars, cents, and parts of a cent. A comma or sep

aratrix should be placed between the dollars and cents, in order to prevent mistakes in placing them in the operation.

ADDITION OF FEDERAL MONEY.

RULE.

f Place the numbers according to their value; that is, dollars under dollars, cents under cents, &c. and proceed as in Simple Addition, for whole numbers, and according to the above observations for parts of a cent. Proof, as in g] Simple Addition. Point, directly under those in the examples.

h Place the numbers as in Addition, and proceed as in Simple Subtraction, except where parts of a cent are expressed as above, in which case, borrow 4, when necessary, i] and carry one to the place of cents. Proof, as in Simple Subtraction. Point, as in Addition.

j Place the numbers and proceed as in Multiplication of whole numbers; point off as many places for cents and mills k] as there are in either of the factors. To multiply by parts of a cent, multiply the upper number of the fraction and divide its product by the under one.

PROOF-As in Simple Multiplication.

3. Multiply $425, 40 cts. by 7 Products, $2,977,80

4.

$20, 44

9

5.

$141, 25

34

$183, 96 $4802, 50 $190316, 50 $58794, 061

m Place the numbers, d proceed as in Simple Divin] sion. Multiply the mainder by 4, and bring in the fraction, (if any,) to this product; divide as before, and the quotient will be fourths. Point off as many places for cents ] and mills in the quotient, as there are in the dividend.