To express in figures, Numbers which exceed Nine. RULE. Write down ciphers to so many places as are named in the given number; then, beginning at the left, observe at each place what significant figure is named, and, taking away the cipher, write the significant figure in its place; and thus proceed with each place till you come to the place of units.

Twenty-five,

One hundred,

EXAMPLES.

Three thousand and fifteen,

Eight hundred and twelve thousand,
Thirty-one thousand, two hundred and six,
Six millions, seven thousand and eight,

One hundred and one millions, fourteen thousand and fourteen.

To read NUMBERS.

RULE.-First numerate, from the right to the left hand, each figure, in its proper place, by saying, units, tens, hundreds, &c., as in the Numeration Table. Then, te the simple value of each figure, join the name of its place, beginning at the left hand, an reading to the right.

EXAMPLES.

64,

396,

4015,

76920,

104080,

5300648,

NOTE. The pupil should be accustomed, in each Example, in the following Rules, to read correctly not only every answer, but every line of numbers in his sum.

ADDITION.

ADDITION in Arithmetic is the uniting or joining together of two or more numbers.

SIMPLE ADDITION is the collecting of several numbers, of the same denomination into one sum; as, 4 yards and 6 yards, expressed in one sum, are 10 yards.

ADDITION AND SUBTRACTION TABLE.

When you would add two numbers, seek one of them in the left hand column, and the other in the top line; and in the common angle of meeting, or at the right hand of the first, and under the second, you will find the sum ; as, 6 and 9 are 15; and so of any others.

When you would subtract, seek, in the left hand column, the number to be subtracted from the greater; then run your eye along, in the same line, towards the right hand, till you find the number from which the other is to be taken; and exactly over this last, in the top line, you will find the difference; as, 6 from 15, and there remain 9; and so of any others.

SIMPLE ADDITION.

RULE. Write the numbers, units under units, tens under tens, &c. and draw a line under the whole. Add up the unit column, and if the sum be less than ten, write

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.

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. Or, 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 fiftysix 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 substratum; 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.