it under the column; if it be ten or any number of tens, write a cipher; if there be an excess over ten or tens, write down this excess, and carry as many units to the next column, as there are tens; and thus proceed with each remaining column, writing the whole sum under the last.

Or,

PROOF.-Draw a line below the upper number, and add the remaining numbers as shown in the rule; add the sum thus found and the upper number together, and if the sum be equal to the first addition, the work is right. begin at the top number, add downwards, and carry as before; if the two sums come alike, the work is probably right.

1. What is the sum of 37, 509, 7126, 17630, and 459273 yards?

2. Required, the sum of 3579, 41, 96120, 725, 11, 1820, 5, and 720139 bushels.

3. What is the sum of 2591, 720396, 14, 259, 6, 370214, 9740, 53, 1692, and 137 dollars?

4. How many days are in the 12 calendar months, in a leap year?

5. A person dying left to his widow 1500 dollars, to his eldest son 30500, to each of his other two 3406; also 2700 to each of his three daughters, besides 751 dollars in other small legacies; what did his estate amount to?

6. If the distance from Hallowell to Portland be fifty six miles, thence to Portsmouth fifty-four miles, thence to Boston sixty-four miles, thence to Hartford ninety-eight miles, thence to New-York one hundred and eleven miles, thence to Philadelphia ninety miles, thence to Baltimore ninety-nine miles, and thence to Washington thirty-eight miles; what is the whole distance between Hallowell and the city of Washington?

7. John, James, and Paul counting their prize-money, John had one thousand, three hundred and seventy-five dollars; James had just three times as much as John: and Paul had just as much as both the others; pray how many dollars had Paul?

SIMPLE SUBTRACTION.

SUBTRACTION is finding the difference of two numbers, by taking the less from the greater. It is simple subtraction if the numbers are of one denomination; as, 5 feet taken from 8 feet, will leave 3 feet.

The greater number is called the minuend, or substra tum; the less, the subtrahend; and the number found by the operation, the difference, or remainder.

RULE. Write the less number under the greater, placing units under units, tens under tens, &c. and draw a line under them. Begin at the right, and take each figure in the subtrahend from its corresponding one in the minuend, setting down the remainder straight under it below the line. If the lower figure be greater than the one above it, add ten to the upper figure, from which sum take the lower, and set down the remainder, carrying one to the next lower figure; and thus proceed until the whole is finished.

PROOF.-Add the remainder to the subtrahend, and if the sum be equal to the minuend, the work is right.

10.

100200300400

98087076065

11.

10000000
9999991

APPLICATION.

1. From 360418 tons, take 293752.

2. From 100046 acres, take 10009.

3. What is the difference between 1735, and 1897348 hours?

4. How much do 540312 days exceed 7953 ?

5. How much are 30491 gallons less than 57321469 ? 6. If the distance from Hallowell to Savannah, through Washington, be 1268 miles and that from Washington to Savannah, 658 miles; how far is Washington from

Hallowell?

7. From Hallowell to the city of New-York is 383 Now, if a man should travel 10 days from Hal

miles.

lowell towards New-York, at the rate of thirty-six miles each day; how far would he then be from that city? 8. If a farmer kills six hogs, which weigh two hundred one hundred and ninety-seven, two hunand fifty-four, dred and sixteen, two hundred and forty-nine, three hundred and twelve, and three hundred and sixty-three, and markets one thousand weight of pork; what quantity does he reserve for his own use?

SIMPLE MULTIPLICATION.

MULTIPLICATION is finding the amount of any given number, by repeating it any proposed number of times; as, 4 times 7 are 28. The number to be multiplied is called the multiplicand. The number which multiplies is called the multiplier. The number arising from the operation is called the product.

The multiplicand and multiplier are called factors; and if these are of one denomination it is called Simple Multiplication.

MULTIPLICATION AND DIVISION TABLE.

1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 810|12|14|16| 18| 20| 22| 24 31 6 9|12|15|18|21|24| 27| 30| 33 36 4| 8|12|16|20|24|28|32|36| 40| 44| 48 5/10/15 20 25 30 35 40 45 50 55 60 6|12|18|24|30|36|42|48| 54| 60 66 72 714 21 28 35 42 49 56 63 70 77 84 816 24 32 40 48 56 64 72 80 88 96 9|18|27|36|45|54|63|72 81 90 99108 10 20 30 40 50 60 70 80 90 100 110 120 |11|22|33|44|55|66|77|88 99|110|121|132 12 24 36 48 60 72 84 96 108|120|132|144

USE of the TABLE in MULTIPLICATION.

Find the multiplier in the left hand column, and the multiplicand in the uppermost line; and the product is in the common angle of meeting, or against the multiplier, and under the multiplicand.

To use the above Table in Division, seek your divisor in the left hand column; then run your eye along the line, to the right hand, till you come to your dividend; and the figure in the top line, of the same column, will be the quotient, or number of times the divisor is contained in the dividend.

CASE I.—When the multiplier is not more than twelve. RULE.-Multiply each figure in the multiplicand by the multiplier, beginning at the right hand side, and setting down the whole of such products as are less than ten ; but for such as are just equal to a certain number of tens, write down 0, and carry 1 for each ten to the next pro¬ duct; and for such as exceed a certain number of tens, set down the excess, and carry for the teus as before.

EXAMPLES.

1. What number is equal to 4 times 365?