Hartford, Nov. 1, 1837.
Bought of W. Jones.

James Hughes 27 Bags of coffee at 14 dolls. per bag 18 Chests of tea at 25 dolls. per chest 75 Barrels of shad at 9 dolls. per barrel 87 Barrels of mackerel at 8 dolls. per barrel 67 Cheeses at 2 dolls. each

59 Hogsheads of molasses, at 29 dolls per hogshead.

Amount 4044 dollars.

per James Cross.

Received the amount in full, for W. Jones,

DIVISION OF SIMPLE NUMBERS.

28. Charles has 12 apples and wishes to divide them equally between his four brothers.

He gives one to each, which takes 4. Subtracting 4 from 12, 8 remains. He then gives another to each, which takes 4 more. Subtracting this 4 from 8 leaves 4. He then gives one more to each, which takes all his apples, and leaves nothing. He has then divided them equally, and found that 12 contains 4, three times, for he has three times subtracted 4 from 12.

OPERATION.

12

4

8 1st remain.

4

4 2d remain.

4

0 3d remain.

Suppose he had 28 apples and wished to divide them equally among 8 boys.

Giving each one, would take 8 and leave 20. Giving each one, a second time, would take 8 and leave 12. Giving each one, a third time, would take 8 and leave 4. Hence, 8 is contained three times in 28, and there are 4 over.

OPERATION.

28

8

20 1st remain. 8

12 2d remain.

8

By continued subtraction we can always find how many times one number is contained in another, and also, what is left when it is not contained an exact number of times.

4 3d remain.

We can arrive at the same result by a shorter method, called Division.

DIVISION teaches the manner of finding how many times a less number is contained in a greater. It is a short method of subtraction.

The less number is called the divisor.

The greater number is called the dividend.

The number expressing how many times the dividend contains the divisor, is called the quotient.

If there is a number left, it is called the remainder, which is always less then the divisor.

There are three signs used to denote division. They are the following.

18-4 expresses that 18 is to be divided by 4.
expresses that 18 is to be divided by 4.

18

4

4)18 expresses that 18 is to be divided by 4.

When the last sign is used, a curved line is also drawn on the right of the dividend to separate it from the quotient, which is generally set down on the right.

Q. When Charles divides 12 apples equally, among his four brothers, how many does he give to each? How many times does 12 contain 4? In dividing 28 apples equally among 8 boys, how many does each receive? How many remain? Which number is the dividend? Which the divisor? Which the quotient? Which the remainder ? What does division teach? What is the less number called? What is the greater called? What is the answer called? What is the number called which is left? Is this number greater or less than the divisor? How many signs are there in division? Make them.

§ 29. Let the following table be committed to memory. It is read 2 in 2, 1 time; 2 in 4, 2 times, &c.

Place the divisor on the left of the dividend, draw a curved line between them, and a straight line under the dividend.

Now, there are 8 tens and 6 units to be divided by 2. We say, 2 in 8, 4 times, which being 4 tens we write the 4 under the tens. We then say, 2 in 6, 3 times,

=

which are three units, and must be written under the 6. The quotient therefore, is 4 tens and 3 units, or 43.

Q. When you divide 8 tens by 2, is the quotient tens or units? When 6 units are divided by 2, what is the quotient?

2. Divide 729 by 3.

OPERATION.

3)729

243

In this example there are 7 hundreds 2 tens and 9 units, all to be divided by 3. Now, we say 3 in 7, 2 times and 1 over. Set down the 2, which is hundreds, under the 7. But of the 7 hundreds there is 1 hundred or 10 tens not yet divided. We put the 10 tens with the 2 tens, making 12 tens, and then say, 3 in 12, 4 times, and write the 4 in the quotient, in the ten's place; then say 3 in 9, 3 times. The quotient therefore, is 243.

Q. When the 7 hundreds are divided hy 3, of what denomination is the quotient? To how many tens is the undivided hundred equal? When the 12 tens are divided by 3, what is the quotient? When the 9 units are divided by 3, what is the quotient?

3. Divide 729 by 9.

In this example, we say, 9 in 7 we cannot, but 9 in 72, 8 times, which are 8 tens : then, 9 in 9, 1 time.

The quotient is therefore 81.

4. Divide 8040 by 8.

OPERATION.

9)729

81

OPERATION.

8)8040

1005

In this example, we say 8 in 8, 1 time, and set 1 in the quotient. We then say, 8 in 0, 0 times, and set the 0 in the quotient then say, 8 in 4, 0 times, and set the O in the quotient: then say, 8 in 40, 5 times, and set the 5 in the quotient. The true quotient is therefore 1005.

§ 30. It may be remarked that any number contains 1 as many times as there are units in the number, or that if any number be divided by 1, the quotient will be equal to the number itself.

Q. How many times will any number contain 1? If any number be divided by 1, what is the quotient?

CASE I.

§ 31. Short Division, or when the divisor does not ex

ceed 12.

RULE.

I. Set down the divisor on the left of the dividend, draw a curved line between them, and a straight line under the dividend.

II. Find how often the divisor is contained in the left hand figure or figures of the dividend, and place the figure so found under the straight line, for the first figure of the quotient.

III. If there is no remainder, divide the next figure of the dividend for the next figure of the quotient. But when there is a remainder consider it as tens, to which add the next figure of the dividend, regarded as units, and divide this sum for the next figure of the quotient, and do the same for each of the figures of the dividend.

IV. When any of the figures, or sums, that are to be divided, is less than the divisor, set down 0 in the quotient, and to such number regarded as tens, add the next figure of the dividend considered as units, and divide the sum for the next figure of the quotient.

EXAMPLES.

OPERATION.

5)36458

7291-3 remain.

1. Let it be required to divide 36458 by 5. In this example, we find the quotient to be 7291 and a remainder 3. This 3 ought in fact to be divided by the divisor 5; but the division cannot be effected, since 3 does not contain 5. The division must then be expressed by placing 5 under the 3, thus,. The true quotient, therefore, is 7291, which is read, seven thousand two hundred and ninety one, and three divided by five. Therefore,

When there is a remainder after the division, it may be written after the quotient, and the divisor placed under it.

Q. What is short division? How do you set down the numbers to be divided? How do you divide? Repeat the rule. If there is a remainder after division, how may it be written?