figures of the dividend under which it stands. The next figure of the dividend, or more than one figure if necessary, must then be brought down to the right hand of the remainder, and the divisor must be multiplied by the next quotient figure, and the product substracted as before.

Q. When you have brought down a figure to the remainder, if there be any, and the divisor is not contained in the number, how must you then proceed?

A. A cipher must be placed in the quotient, and another figure, or more than one if necessary, must be brought down until the number is larger than the divisor.

EXAMPLES

For Exercise on a Slate.

1. A gentleman had 65 men in his employment, to whom he paid for wages due 7735 dollars; how many dollars had each man for his portion? Ans. 119 dollars.

EXPLANATIONS.

Dividend.

In order to enter Divisor 65)7735 (119 quotient.

with advantage on

this branch of the

65

123

65

585

585

ment requires a little more of your attention than any of the examples heretofore treated of. You must observe, therefore, carefully, the mode of making the statements, and the manner of working the sums. Here, instead of drawing a line down, and then carrying it immediately underneath the dividend, as you did in Short Division, when the divisor did not exceed 12, you must write down the divisor at the left hand of the dividend and draw a curve) after it; then write the dividend as a continuation of the line; and then another curve (at the right of the dividend, and the quotient at the right of that curve. Then beginning at the left hand of the dividend, you must take two figures, 77, and seek how many times the divisor, 65, is contained in 77, that is, 77 hundreds; and finding it to be 1 time, you must set down 1 on the right hand of the dividend for the highest figure in the quotient. You must then multiply the divisor by the 1, the figure in the quotient, and set the product, which is 65, under the 77, and substract it from the 77, which will leave a remainder of 12. You must then bring down the next figure, the 3, at the right hand of the 12, the remainder, and then say, 65 in 123, 1 time. You must set down 1 at the right hand of the 1 already in the quotient, as the second figure of the quotient, and multiply as before, and substract the 65 from the 123, which will leave a remainder of 58. You must then bring down the next figure of the dividend, the 5, at the right of the 58, the remainder, and then seek how many times 65 is contained in 585. Instead of saying how many times are 65 contained in 585, you may take the first figure of the divisor, the 6, and the first two figures of the 585, the 58, and say, 6 in 58, 9 times;

because you have learned in the division table, that 6 in 54, 9 times; you must, therefore, set down 9 in the quotient, at the right of the 11, and multiply the 65, the divisor, by it, and place the product under the 585. Thus, 9 times 5 are 45; 9 times 6 are fifty-four, and four to be carried makes 58; and as you have brought down all the figures the work is done. You have thus ascertained, that 65 is contained in 7735, 119 times; that is, 65 is contained in 77 hundreds, the first number of figures taken, 100 times; in 123 tens, the second number of figures taken, 10 times; and in 585 units, the last number taken, it was contained 9 times. Therefore, each man has 119 dollars, which shows that 7735 dollars, divided into 65 equal parts, give 119 in each; and it also shows, that 65 can be substracted from 7735, 119 times.

2. A gentleman has a yearly income of 75920 dollars; how many dollars is that a day, there being 365 days in a year? Ans. 208 dollars.

EXPLANATIONS.

Dividend.

In this exam- Divisor 365) 75920 (208 quotient.

ple, proceeding

as before, you must say, 365 in 759,-for here you must take

730

2920

2920

three figures first,—or, rather, you may say 3 the first figure in the divisor, in 7, the first figure in the dividend, 2 times. You must set down 2 for the first figure of the quotient, and multiply the divisor by the quotient, the 2, as in the preceding example,

and place the product under the 759, and substract as before. You must then bring down the 2, the next figure of the dividend. Here, you will perceive, the number, when the 2 is brought down, 292, is not as large as the divisor, 365; and you must place a cipher in the quotient, and bring down the next figure of the dividend; and then say, as before, 3, the first figure of the divisor, in 29, the first two figures of the sum to be divided, 8 times; and you must set down 8 at the right of the cipher in the quotient, and the work is done. You must always bear in mind, that for each figure you bring down of the dividend, you must write a figure, or cipher, in the quotient.

You should observe great care in bringing down each figure of the dividend; for in this, as in every other operation, accuracy is of the utmost importance.

When you have substracted the first product from the dividend, you may make a dot under every subsequent figure as you bring it down. The number of dots will, of course, be one less than the number of figures in the quotient.

Every remainder, before another figure of the dividend is joined to it, must be less than the divisor. If the remainder should be equal to, or greater than the divisor, the quotient figure, which produced such a result, is too small, and the operation must be repeated with a larger figure. But if the product of the divisor, by the quotient figure, be greater than the number from which it is to be taken, the quotient figure is then too large, and you must take a smaller figure.

In this easy manner, by paying particular attention to the preceding EXPLANATIONS, you will be able to work any sum in Division.

I will work out two sums more for you, and then, after having given you some few examples for farther exercise, I shall pass to the next part of the subject.

13. There were 16 men who 'owned a quantity of land which was sold for 47232 dollars; how many dollars did each man receive? Ans. 2952 dollars.

14. A drover bought a number of cows, for which he paid 3168 dollars, at 16 dollars each; how many cows did he buy? Ans. 198 cows.