CASE 3.

1. When the divisor has any number of cyphers placed to the right of the significant figures, reject them when you divide, as well as a like number of figures on the right of the dividend.

2. When the operation of division is finished, annex those figures of the dividend to the remainder, which was rejected, on account of the cyphers of the divisor not being used, and the amount will be the proper remainder which would have resulted had the whole divisor been used.

In the above operation, I only used the significant figures, 734, of the divisor, and for the eyphers omitted, I rejected 64, (as many figures to the right of the dividend;) when the operation was finished, 348 remained, to which I annexed the rejected 64, and the amount, 34864, was the whole remainder.

3509000)958362608(

10090000)32678568009(

69500000)7956385637(

55000000)3578572638(

In dividing by 10, 100, 1000, 10000, it is only necessary to strike from the right of the dividend as many figures, as the divisor contains cyphers, and the thing is done, the stricken off figures being the remainder.

1. When the divisor is a composite number, divide by the component parts of such number; first by the one, and the quotient by the other.

2. If a remainder be left at each division, multiply the last remainder by the first divisor, add to this the first remainder, and the sum will be the proper remainder in full.

EXAMPLES.

Divide 37464304 by 25.

Operation 5 x 5 being equal to 25
First 5)37464306

Second 5)7492861-1 first remainder.

Quotient 1498572-1 second remainder.

When the divisor and dividend are even numbers, it often happens that they may be diminished equally by some common divisor, in such a manner as to abridge the work very much.

EXAMPLE.

Divide 72480000 by 1200.

Operation 12,00)724800,00

60400 quotient required.

NOTE. We are not limited to any particular di

visors in the above operation.

CASE 5.

1. By case fifth, contracted Multiplication may be performed as follows, viz.

2. When the multiplier is any even part of 100, 1000, &c. increase the multiplicand by annexing as many cyphers to its right, as there are places in the multiplier.

3. Divide the multiplier thus augmented by the denominator of whatever part the multiplier is of 100, &c. &c. and the thing is done.

* It is plain that 334 is equal to 100, therefore any number which we would multiply by 334, is managed by annexing two cyphers first to the given multiplicand, and then dividing by 3. It is in fact nothing more than multiplying by 100. This doctrine seems, however, to be better calculated for a place in fractions, than here.

QUESTIONS

TO EXERCISE THE FOREGOING RULES.

1. Of Simple Addition.

1. It was 73 years from the discovery of America, by Christopher Columbus, to the time of introducing potatoes into Ireland, from New Spain; 18 years from thence to the introduction of tobacco into England, from Virginia; 100 years from thence to the founding of Philadelphia. How long after the discovery of America, did the latter circumstance occur? Ans. 191 years.

2. Bought 25 barrels of flour, at 13 dollars per barrel: Required, the price of the whole; also their weight; each being 196 pounds.

Ans. Price $325, weight 4900lb.

3. Thirty days are in September,
The same in April, June, November;
In February twenty-eight alone;
And all the rest just thirty-one.
Now sum them up and let us hear
How many days are in the year.

Ans. 365, except bissextile,* or leap

year, which has 366 days in it.

In every bissextile, or leap year, there is an additional day put to the month of February. This arises from the circumstance of our year containing 365 days and nearly six hours; these odd hours, in four years' time, amount to one day, and is accordingly placed to February. In a cycle of 130 years, the leap day may be thrown out of the reckoning; for allowing 365 days and 6 hours to each year, it is better than 11 minutes too much, which in 130 years amounts to a day too much.

D