OPERATION. Divisor. Dividend. Quotient. 21) 4370 (208.

42

170

168

2 Remainder.

We may write the divisor and dividend as in short division, but, instead of writing the quotient under the dividend, it will be found more convenient to set it to the right hand.

Taking the dividend by parts, we seek how often we can have 21 in 43 (hundreds ;) tinding it to be 2 times, we set down 2 on the right hand of the dividend for the highest figure in the quotient. The 43 being hundreds, it follows, that the 2 must also be hundreds. This, however, we need not regard, for it is to be followed by tens and units, obtained from the tens and units of the dividend, and will therefore, at the end of the operation, be in the place of hundreds, as it should be.

It is plain that 2 (hundred) times 21 dollars ought now to be taken out of the dividend; therefore, we multiply the divisor (21) by the quotient figure 2 (hundred) now found, making 42, (hundred,) which, written under the 43 in the dividend, we subtract, and to the remainder, 1, (hundred,) · bring down the 7, (tens,) making 17 tens.

We then seek how often the divisor is contained in 17, (tens;) finding that it will not go, we write a cipher in the quotient, and bring down the next figure, making the whole 170. We then seek how often 21 can be contained in 170, and, finding it to be 8 times, we write 8 in the quotient, and, multiplying the divisor by this number, we set the product, 168, under the 170; then, subtracting, we find the remainder to be 2, which, written as a fraction on the right hand of the quotient, as already explained, gives 208 dollars, for the answer.

This manner of performing the operation is called Long Division. It consists in writing down the whole computation. From the above example, we derive the following

RULE.

I. Place the divisor on the left of the dividend, separate them by a line, and draw another line on the right of the dividend to separate it from the quotient,

II. Take as many figures, on the left of the dividend, as

contain the divisor once or more; seek how many times they contain it, and place the answer on the right hand of the dividend for the first figure in the quotient.

III. Multiply the divisor by this quotient figure, and write the product under that part of the dividend taken.

IV. Subtract the product from the figures above, and to the remainder bring down the next figure in the dividend, and divide the number it makes up, as before. So continue to do, till all the figures in the dividend shall have been brought down and divided.

Note 1. Having brought down a figure to the remainder, if the number it makes up be less than the divisor, write a cipher in the quotient, and bring down the next figure.

Note 2. If the product of the divisor, by any quotient figure, be greater than the part of the dividend taken, it is an evidence that the quotient figure is too large, and must be diminished. If the remainder at any time be greater than the divisor, or equal to it, the quotient figure is too small, and must be increased.

EXAMPLES FOR PRACTICE.

1. How many hogsheads of molasses, at 27 dollars a hogshead, may be bought for 6318 dollars?

Ans. 234 hogsheads. 2. If a man's income be 1248 dollars a year, how much is that per week, there being 52 weeks in a year?

Ans. 24 dollars per week. 3. What will be the quotient of 153598, divided by 29? Ans. 52961

4. How many times is 63 contained in 30131 ? Ans. 478 times; that is, 478 times, and 3 of another time.

5. What will be the several quotients of 7652, divided by 16, 23, 34, 86, and 92 ?

6. If a farm, containing 256 acres, be worth 7168 dollars, what is that per acre?

7. What will be the quotient of 974932, divided by 365? Ans. 2671

8. Divide 3228242 dollars equally among 563 men; how many dollars must each man receive? Ans. 5734 dollars. 9. If 57624 be divided into 216, 586, and 976 equal parts, what will be the magnitude of one of each of these equal parts'

Ans. The magnitude of one of the last of these equal parts will be 59,7%.

10. How many times does 1030603615 contain 3215? Ans. 320561 times.

11. The earth, in its annual revolution round the sun, is said to travel 596088000 miles; what is that per hour, there being 8766 hours in a year?

12. 1234567890 how many?

CONTRACTIONS IN DIVISION.

I. When the DIVISOR is a COMPOSITE NUMBER.

20. 1. Bought 15 yards of cloth for 60 dollars; how much was that per yard?

If there had been but 5 yards,

15 yards are 3× 5 yards. the cost of one yard would be 12 dollars; but, as there are 3 times 5 yards, the cost of one yard will evidently be but one third part of 12 dollars; that is, 12: 4 dollars. Ans.

Hence, when the divisor is a composite number, we may, if we please, divide the dividend by one of the component parts, and the quotient, arising from that division, by the. other; the last quotient will be the answer.

2. If a man can travel 24 miles a day, how many days will it take him to travel 264 miles?

It will evidently take him as many days as 264 contains 24.

II. To divide by 10, 100, 1000, &c.

21. 1. A prize of 2478 dollars is owned by 10 men,

what is each man's share?

Each man's share will be equal to the number of tens contained in the whole sum, and, if one of the figures be cut off at the right hand, all the figures to the left may be considered so many tens; therefore, each man's share will be 247 dollars.

It is evident, also, that if 2 figures had been cut off from the right, all the remaining figures would have been so many hundreds; if 3 figures, so many thousands, &c. Hence we derive this general RULE for dividing by 10, 100, 1000, &c. Cut off from the right of the dividend so many figures as there are ciphers in the divisor; the figures to the left of the point will express the quotient, and those to the right, the remainder.

2. In one dollar are 100 cents; how many dollars in 42400 cents? Ans. 424 dollars.

424/00

Here the divisor is 100; we therefore cut off 2 figures on the right hand, and all the figures to the left (424) express the dollars.

3. How many dollars in 34567 cents?

Ans. 345 dollars.

4. How many dollars in 4567840 cents? 5. How many dollars in 345600 cents? 6. How many dollars in 42604 cents?

Ans. 426.

7. 1000 mills make one dollar; how many dollars in 4000 mills?

in 25000 mills?

in 845000?

8. How many dollars in 6487 mills? Ans. 68 dollars. 9. How many dollars in 42863 mills?

in 368456

how many cents in 40 in 20 mills?

in 34640 mills?

in 468

III. When there are CIPHERS on the right hand of the divisor.

¶ 22. 1. Divide 480 dollars among 40 men?

OPERATION.

4|0)48|0

In this example, our divisor, (40,) is a composite number, (10 X 4 =40;) we may, therefore, divide by one component part, (10,) and that quotient by the other, (4;) but to divide by 10, we have seen, is but to cut off the right hand figure, leaving the figures to the left

12 dolls. Ans.

of the point for the quotient, which we divide by 4, and the work is done. It is evident, that, if our divisor had been 400, we should have cut off 2 figures, and have divided in the same manner; if 4000, 3 figures, &c. Hence this general RULE : When there are ciphers at the right hand of the di visor, cut them off, and also as many places in the dividend; divide the remaining figures in the dividend by the remaining figures in the divisor; then annex the figures, cut off from the dividend, to the remainder.

4. How many yards of cloth can be bought for 346500 dollars, at 20 dollars per yard?

5. Divide 76428400 by 900000.

6. Divide 345006000 by 84000.

7. Divide 4680000 by 20, 200, 2000, 20000, 300, 4000, 50, 600, 70000, and 80.

SUPPLEMENT TO DIVISION.

QUESTIONS.

1. What is division? 2. In what does the process of division consist? 3. Division is the reverse of what? 4. What is the number to be divided called, and to what does it answer in multiplication? 5. What is the number to divide by called, and to what does it answer, &c.? 6. What is the result or answer called, &c.? 7, What is the sign of divi sion, and what does it show? 8. What is the other way of expressing division? 9. What is short division, and how is

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