1. Seven boys have 161 apples, which they divide equally among them. How many does each have? Answer, 23.

2. What is the quotient, if 8736 be divided by 8, and that quotient by 4?

Ans. 273. 3. If 350 dollars be equally divided among 7 men, what will be the share of each?

Ans. 50.

4. How many times are 27 contained in 952?· Ans. 35 times and 7 over.

5. Suppose 2072 trees planted in 14 rows. How many trees will there be in each row?

Ans. 148.

6. Several boys who went to gather nuts, collected 4741, of which each boy received 431. How many boys were there? Ans. 11.

7. If the expense of erecting a bridge, which is 15036 dollars, be equally defrayed by 179 persons, what must each pay? Ans. 84 dollars.

8. Suppose a man receive in one year 2920 dollars; how much a day is his income at that rate; and suppose that his expenses for the year amount to 1769 dollars. How much will he save in a year?

Ans. His income will be 8 dollars a day; he will save 1151 dollars in a year.

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What is division?

Questions.

What do you call the number that is to be divided? What do you call the number you divide by?

What do you call the number obtained by division? What do you call that which is left when the work is done?

When the divisor does not exceed 12, how do you perform the operation?

When the divisor exceed 12, how do you proceed? How do you prove division?

How may the operation be performed when there are cyphers at the right hand of the divisor?

How may it be performed when the divisor is the exact product of two numbers in the multiplication table?

How do you obtain the true remainder in the last case?

PROMISCUOUS EXERCISES IN THE PRECEDING RULES.

1. If the contents of five bags of dollars, containing $295, $410, $371, $355, and $520, be divided equally among 25 persons, how much is the share of each? Ans. $78.04

2. A man possessed of an estate of $30,000, disposed of it in the following manner: to his brother he gave $1500, and the balance to his 5 sons, to be equally divided among them. What was each one's share?

Ans. $5700. 3. What number is it, which being added to 9709, will make 110901? Ans. 101192. 4. Add up twice 397, three times 794, four times 31196, five times 15980, six times 95280, and once 33304. Ans. 812,344.

5. Three merchants have a stock of 14876 dollars, of which A owns 4963 dollars, B 5188, and C the remainder. How much does C own? Ans. 4725 dolls.

These denominations bear the same relation to each other as those of units, tens, hundreds, &c. Federal money is therefore added, subtracted, multiplied, and divided by the same rules as Simple Addition, Subtraction, Multiplication, and Division.

ADDITION OF FEDERAL MONEY.

Rule.

Place the numbers one under another, with mills on the right, cents, dimes, &c., in succession; observing to keep mills under mills, cents under cents, &c. Then proceed as in simple addition.

When halves or fourths of a cent occur, find their amount in fourths, and consider how many cents these fourths will make, and carry them to the column of cents.

EXAMPLES.

Eagles. Dolls. Dimes. Cents Mills. Dolls. Ds. Cts.

NOTE.-In common business transactions, eagles, dimes, and mills are not used: dollars, cents, and fractions of a cent, are the only denominations kept in

accounts.

One half is two-fourths; and one half more make four fourths, and three fourths more make seven fourths, and one fourth more make eight fourths, and one half (or two fourths) more make ten fourths. Four fourths make one cent, then ten fourths make two cents, and leave two fourths, or one half cent. Set down the cent, and carry the two cents to the next column.

APPLICATION.

1. Add 48 dollars 20 cents; 14 dollars 58 cents; 100 dollars 25 cents; and 84 dollars 36 cents.

Ans. 247 dollars 39 cents.

2. Add $7,624, $34,314, $72,061, $41,314, $25, 684, and $87,434 together, and tell the amount.

Ans. $268,434.

3. Bought a hat for $4,25 cents; a pair of shoes for $2,25; a pair of stockings for $1,25, and a pair of gloves for 75 cents. What is the cost of the whole?

Ans. $8 50 cents. 4. If I buy coffee for $1,184, tea for $2,50, cloves for 874, mace for 934, cinnamon for $1,871, raisins for $2,684, nutmegs for 371, candles for 871, and wine for $1,931, what must I pay for them? Áns. $13,25.

Questions.

What relation do mills, cents, dimes, &c., bear to each other?

How are the addition, subtraction, multiplication, and division of Federal money performed?

How do you place the numbers to be added?

How do you proceed when halves, fourths, &c., occur?

SUBTRACTION OF FEDERAL MONEY.

RULE. Place the less under the greater, with dollars under dollars, and cents under cents; then, if there are no fractions, proceed as in simple subtraction.

If there is a fraction in the upper sum and none in the lower, set it down as a part of the remainder, and proceed as before.

If there is a fraction in each sum, and the lower be less than the upper, subtract the lower from the upper, and set down the difference.

If the lower fraction be greater than the upper one, borrow one cent, and call it four fourths, and add them to the upper fraction, and subtract the lower one from the sum.

Proof-As in simple subtraction.